> ## Documentation Index
> Fetch the complete documentation index at: https://docs.iotools.cloud/llms.txt
> Use this file to discover all available pages before exploring further.

# Loot Drop Probability Calculator

> Calculate the odds of landing at least K loot drops across N independent attempts, plus expected drops, the number of attempts needed for 50%/90%/99% confidence, and a full attempt-by-attempt probability curve.

[Try Loot Drop Probability Calculator in your browser →](https://iotools.cloud/tool/loot-drop-probability-calculator/)



## OpenAPI

````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/loot-drop-probability-calculator
openapi: 3.1.0
info:
  title: iotools.cloud API
  version: 1.0.0
  description: >-
    Run any iotools.cloud tool over HTTP.


    Authenticate with `Authorization: Bearer iot_live_…`.


    **Only `POST /v1/tool/{slug}` costs credits.** Every GET here — the catalog,
    a tool's schema, your balance — is free. A tool call is charged its own
    weight or your plan's per-call minimum, whichever is larger;
    `x-iotools-credit-cost` on each operation is quoted at the free-tier
    minimum, and `GET /v1/tools/list` returns the exact figure for your key.
    `GET /v1/me/credits` reports what you have left, and `GET /v1/me/usage`
    reports what it went on.


    Failures are RFC 9457 problem documents — branch on `code`.
servers:
  - url: https://api.iotools.cloud
    description: Production
security:
  - bearerAuth: []
tags:
  - name: Catalog
    description: Find a tool and read its contract. Free.
  - name: Converters
    description: >-
      Convert between formats, encodings, and units — Base64, CSV and JSON,
      timestamps, and more. Fast, free, and processed right in your browser.
  - name: Formatters
    description: >-
      Format, beautify, minify, and validate code and data — JSON, HTML, CSS,
      SQL, and regex. Clean up messy input in one click, with nothing to upload.
  - name: Generators
    description: >-
      Generate exactly what you need and on demand — passwords, UUIDs, QR codes,
      hashes, random numbers, and more. Secure, instant, and free.
  - name: Calculators
    description: >-
      Crunch the numbers fast — from everyday math to specialized conversions
      and unit work. Free online calculators that run entirely in your browser.
  - name: Editors
    description: >-
      Edit and transform text, code, and images with quick, focused editors that
      run entirely in your browser — nothing to install, and no sign-up needed.
  - name: Utilities
    description: >-
      Everyday developer and web utilities — DNS and IP lookups, redirect and
      certificate checkers, and other quick diagnostics. Free and
      privacy-friendly.
  - name: Account
    description: Your key's allowance, limits and usage history.
paths:
  /v1/tool/loot-drop-probability-calculator:
    post:
      tags:
        - Calculators
      summary: Loot Drop Probability Calculator
      description: >-
        Calculate the odds of landing at least K loot drops across N independent
        attempts, plus expected drops, the number of attempts needed for
        50%/90%/99% confidence, and a full attempt-by-attempt probability curve.


        [Try Loot Drop Probability Calculator in your browser
        →](https://iotools.cloud/tool/loot-drop-probability-calculator/)
      operationId: run_loot_drop_probability_calculator
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              properties:
                dropRate:
                  type: number
                  description: Drop Rate (%)
                  minimum: 0.0001
                  maximum: 100
                attempts:
                  type: number
                  description: Number of Attempts
                  minimum: 1
                  maximum: 200
                targetDrops:
                  type: number
                  description: Target Number of Drops
                  minimum: 1
                  maximum: 50
              required:
                - dropRate
            examples:
              10_drop_rate_20_attempts_at_least_1:
                summary: 10% drop rate, 20 attempts, at least 1
                value:
                  dropRate: '10'
                  attempts: '20'
                  targetDrops: '1'
              5_drop_rate_50_attempts_at_least_3:
                summary: 5% drop rate, 50 attempts, at least 3
                value:
                  dropRate: '5'
                  attempts: '50'
                  targetDrops: '3'
              99_drop_rate_200_attempts_at_least_1_numerical_stability_edge_case:
                summary: >-
                  99% drop rate, 200 attempts, at least 1 (numerical-stability
                  edge case)
                value:
                  dropRate: '99'
                  attempts: '200'
                  targetDrops: '1'
      responses:
        '200':
          description: Tool output
          content:
            application/json:
              examples:
                10_drop_rate_20_attempts_at_least_1:
                  summary: 10% drop rate, 20 attempts, at least 1
                  value:
                    tool: loot-drop-probability-calculator
                    tool_version: 1.0.2
                    outputs:
                      summary:
                        - metric: Drop Rate
                          value: 10%
                        - metric: Number of Attempts
                          value: '20'
                        - metric: Target Number of Drops
                          value: '1'
                        - metric: Probability of At Least 1 Drop(s)
                          value: 87.8423%
                        - metric: Probability of Fewer Than 1 Drop(s)
                          value: 12.1577%
                        - metric: Expected Number of Drops
                          value: '2'
                        - metric: Attempts for 50% Confidence (at least one drop)
                          value: '7'
                        - metric: Attempts for 90% Confidence (at least one drop)
                          value: '22'
                        - metric: Attempts for 99% Confidence (at least one drop)
                          value: '44'
                      curve:
                        - attempt: '1'
                          cumulative-probability: 10%
                        - attempt: '2'
                          cumulative-probability: 19%
                        - attempt: '3'
                          cumulative-probability: 27.1%
                        - attempt: '4'
                          cumulative-probability: 34.39%
                        - attempt: '5'
                          cumulative-probability: 40.951%
                        - attempt: '6'
                          cumulative-probability: 46.8559%
                        - attempt: '7'
                          cumulative-probability: 52.1703%
                        - attempt: '8'
                          cumulative-probability: 56.9533%
                        - attempt: '9'
                          cumulative-probability: 61.258%
                        - attempt: '10'
                          cumulative-probability: 65.1322%
                        - attempt: '11'
                          cumulative-probability: 68.6189%
                        - attempt: '12'
                          cumulative-probability: 71.757%
                        - attempt: '13'
                          cumulative-probability: 74.5813%
                        - attempt: '14'
                          cumulative-probability: 77.1232%
                        - attempt: '15'
                          cumulative-probability: 79.4109%
                        - attempt: '16'
                          cumulative-probability: 81.4698%
                        - attempt: '17'
                          cumulative-probability: 83.3228%
                        - attempt: '18'
                          cumulative-probability: 84.9905%
                        - attempt: '19'
                          cumulative-probability: 86.4915%
                        - attempt: '20'
                          cumulative-probability: 87.8423%
                    credits_used: 5
                    credits_remaining: null
                5_drop_rate_50_attempts_at_least_3:
                  summary: 5% drop rate, 50 attempts, at least 3
                  value:
                    tool: loot-drop-probability-calculator
                    tool_version: 1.0.2
                    outputs:
                      summary:
                        - metric: Drop Rate
                          value: 5%
                        - metric: Number of Attempts
                          value: '50'
                        - metric: Target Number of Drops
                          value: '3'
                        - metric: Probability of At Least 3 Drop(s)
                          value: 45.9467%
                        - metric: Probability of Fewer Than 3 Drop(s)
                          value: 54.0533%
                        - metric: Expected Number of Drops
                          value: '2.5'
                        - metric: Attempts for 50% Confidence (at least one drop)
                          value: '14'
                        - metric: Attempts for 90% Confidence (at least one drop)
                          value: '45'
                        - metric: Attempts for 99% Confidence (at least one drop)
                          value: '90'
                      curve:
                        - attempt: '1'
                          cumulative-probability: 5%
                        - attempt: '2'
                          cumulative-probability: 9.75%
                        - attempt: '3'
                          cumulative-probability: 14.2625%
                        - attempt: '4'
                          cumulative-probability: 18.5494%
                        - attempt: '5'
                          cumulative-probability: 22.6219%
                        - attempt: '6'
                          cumulative-probability: 26.4908%
                        - attempt: '7'
                          cumulative-probability: 30.1663%
                        - attempt: '8'
                          cumulative-probability: 33.658%
                        - attempt: '9'
                          cumulative-probability: 36.9751%
                        - attempt: '10'
                          cumulative-probability: 40.1263%
                        - attempt: '11'
                          cumulative-probability: 43.12%
                        - attempt: '12'
                          cumulative-probability: 45.964%
                        - attempt: '13'
                          cumulative-probability: 48.6658%
                        - attempt: '14'
                          cumulative-probability: 51.2325%
                        - attempt: '15'
                          cumulative-probability: 53.6709%
                        - attempt: '16'
                          cumulative-probability: 55.9873%
                        - attempt: '17'
                          cumulative-probability: 58.188%
                        - attempt: '18'
                          cumulative-probability: 60.2786%
                        - attempt: '19'
                          cumulative-probability: 62.2646%
                        - attempt: '20'
                          cumulative-probability: 64.1514%
                        - attempt: '21'
                          cumulative-probability: 65.9438%
                        - attempt: '22'
                          cumulative-probability: 67.6466%
                        - attempt: '23'
                          cumulative-probability: 69.2643%
                        - attempt: '24'
                          cumulative-probability: 70.8011%
                        - attempt: '25'
                          cumulative-probability: 72.261%
                        - attempt: '26'
                          cumulative-probability: 73.648%
                        - attempt: '27'
                          cumulative-probability: 74.9656%
                        - attempt: '28'
                          cumulative-probability: 76.2173%
                        - attempt: '29'
                          cumulative-probability: 77.4064%
                        - attempt: '30'
                          cumulative-probability: 78.5361%
                        - attempt: '31'
                          cumulative-probability: 79.6093%
                        - attempt: '32'
                          cumulative-probability: 80.6289%
                        - attempt: '33'
                          cumulative-probability: 81.5974%
                        - attempt: '34'
                          cumulative-probability: 82.5175%
                        - attempt: '35'
                          cumulative-probability: 83.3917%
                        - attempt: '36'
                          cumulative-probability: 84.2221%
                        - attempt: '37'
                          cumulative-probability: 85.011%
                        - attempt: '38'
                          cumulative-probability: 85.7604%
                        - attempt: '39'
                          cumulative-probability: 86.4724%
                        - attempt: '40'
                          cumulative-probability: 87.1488%
                        - attempt: '41'
                          cumulative-probability: 87.7913%
                        - attempt: '42'
                          cumulative-probability: 88.4018%
                        - attempt: '43'
                          cumulative-probability: 88.9817%
                        - attempt: '44'
                          cumulative-probability: 89.5326%
                        - attempt: '45'
                          cumulative-probability: 90.056%
                        - attempt: '46'
                          cumulative-probability: 90.5532%
                        - attempt: '47'
                          cumulative-probability: 91.0255%
                        - attempt: '48'
                          cumulative-probability: 91.4742%
                        - attempt: '49'
                          cumulative-probability: 91.9005%
                        - attempt: '50'
                          cumulative-probability: 92.3055%
                    credits_used: 5
                    credits_remaining: null
                99_drop_rate_200_attempts_at_least_1_numerical_stability_edge_case:
                  summary: >-
                    99% drop rate, 200 attempts, at least 1 (numerical-stability
                    edge case)
                  value:
                    tool: loot-drop-probability-calculator
                    tool_version: 1.0.2
                    outputs:
                      summary:
                        - metric: Drop Rate
                          value: 99%
                        - metric: Number of Attempts
                          value: '200'
                        - metric: Target Number of Drops
                          value: '1'
                        - metric: Probability of At Least 1 Drop(s)
                          value: 100%
                        - metric: Probability of Fewer Than 1 Drop(s)
                          value: 3.9e-10%
                        - metric: Expected Number of Drops
                          value: '198'
                        - metric: Attempts for 50% Confidence (at least one drop)
                          value: '1'
                        - metric: Attempts for 90% Confidence (at least one drop)
                          value: '1'
                        - metric: Attempts for 99% Confidence (at least one drop)
                          value: '1'
                      curve:
                        - attempt: '1'
                          cumulative-probability: 99%
                        - attempt: '2'
                          cumulative-probability: 99.99%
                        - attempt: '3'
                          cumulative-probability: 99.9999%
                        - attempt: '4'
                          cumulative-probability: 100%
                        - attempt: '5'
                          cumulative-probability: 100%
                        - attempt: '6'
                          cumulative-probability: 100%
                        - attempt: '7'
                          cumulative-probability: 100%
                        - attempt: '8'
                          cumulative-probability: 100%
                        - attempt: '9'
                          cumulative-probability: 100%
                        - attempt: '10'
                          cumulative-probability: 100%
                        - attempt: '11'
                          cumulative-probability: 100%
                        - attempt: '12'
                          cumulative-probability: 100%
                        - attempt: '13'
                          cumulative-probability: 100%
                        - attempt: '14'
                          cumulative-probability: 100%
                        - attempt: '15'
                          cumulative-probability: 100%
                        - attempt: '16'
                          cumulative-probability: 100%
                        - attempt: '17'
                          cumulative-probability: 100%
                        - attempt: '18'
                          cumulative-probability: 100%
                        - attempt: '19'
                          cumulative-probability: 100%
                        - attempt: '20'
                          cumulative-probability: 100%
                        - attempt: '21'
                          cumulative-probability: 100%
                        - attempt: '22'
                          cumulative-probability: 100%
                        - attempt: '23'
                          cumulative-probability: 100%
                        - attempt: '24'
                          cumulative-probability: 100%
                        - attempt: '25'
                          cumulative-probability: 100%
                        - attempt: '26'
                          cumulative-probability: 100%
                        - attempt: '27'
                          cumulative-probability: 100%
                        - attempt: '28'
                          cumulative-probability: 100%
                        - attempt: '29'
                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                          cumulative-probability: 100%
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                        - attempt: '196'
                          cumulative-probability: 100%
                        - attempt: '197'
                          cumulative-probability: 100%
                        - attempt: '198'
                          cumulative-probability: 100%
                        - attempt: '199'
                          cumulative-probability: 100%
                        - attempt: '200'
                          cumulative-probability: 100%
                    credits_used: 5
                    credits_remaining: null
              schema:
                type: object
                required:
                  - tool
                  - tool_version
                  - outputs
                  - credits_used
                  - credits_remaining
                properties:
                  outputs:
                    type: object
                    properties:
                      summary:
                        type: array
                        description: Summary
                        items:
                          type: object
                          properties:
                            metric:
                              type: string
                              description: Metric
                            value:
                              type: string
                              description: Value
                        x-iotools-columns:
                          - metric
                          - value
                      curve:
                        type: array
                        description: Attempt-by-Attempt Odds (At Least One Drop)
                        items:
                          type: object
                          properties:
                            attempt:
                              type: string
                              description: 'Attempt #'
                            cumulative-probability:
                              type: string
                              description: Cumulative Probability
                        x-iotools-columns:
                          - attempt
                          - cumulative-probability
                  tool:
                    type: string
                    description: The tool's slug, echoing the {slug} in the request path.
                  tool_version:
                    type: string
                    description: Output-contract version for this tool.
                  credits_used:
                    type: integer
                    description: >-
                      Credits this call consumed, after any settlement refund. 0
                      when metering is disabled.
                  credits_remaining:
                    type:
                      - integer
                      - 'null'
                    description: >-
                      Credits left in the current monthly allowance, or null
                      when metering is disabled.
                  request_id:
                    type: string
                    description: Correlation id, also sent as x-request-id.
        '400':
          $ref: '#/components/responses/ValidationError'
        '401':
          $ref: '#/components/responses/Unauthorized'
        '402':
          $ref: '#/components/responses/InsufficientCredits'
        '403':
          $ref: '#/components/responses/ToolNotAllowed'
        '404':
          $ref: '#/components/responses/ToolNotFound'
        '413':
          $ref: '#/components/responses/PayloadTooLarge'
        '422':
          $ref: '#/components/responses/UnprocessableInput'
        '429':
          $ref: '#/components/responses/RateLimited'
        '500':
          $ref: '#/components/responses/ToolFailed'
        '503':
          $ref: '#/components/responses/ToolDisabled'
      security:
        - bearerAuth: []
components:
  responses:
    ValidationError:
      description: Invalid request.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/validation_error
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Invalid request
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - validation_error
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
              fields:
                type:
                  - object
                  - string
                additionalProperties:
                  type: string
                description: >-
                  What failed: a map of field name → message. Absent when the
                  body itself is malformed; a single string when the failure
                  isn't tied to one field.
          example:
            type: https://docs.iotools.cloud/errors/validation_error
            title: Invalid request
            status: 400
            code: validation_error
            detail: One or more inputs are invalid — see `fields`.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
            fields:
              inputString: Required
    Unauthorized:
      description: Missing or invalid API key.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/invalid_api_key
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Invalid API key
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - invalid_api_key
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
          example:
            type: https://docs.iotools.cloud/errors/invalid_api_key
            title: Invalid API key
            status: 401
            code: invalid_api_key
            detail: 'Provide ''Authorization: Bearer <key>''.'
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
    InsufficientCredits:
      description: Monthly credit allowance exhausted.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/insufficient_credits
                  - >-
                    https://docs.iotools.cloud/errors/vendor_api_tier_limit_exceeded
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Insufficient credits
                  - Free-tier API limit reached for this tool
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - insufficient_credits
                  - vendor_api_tier_limit_exceeded
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
              credits_used:
                type: integer
                description: Always 0 — a refused call charges nothing.
              credits_remaining:
                type: integer
                description: Credits left in the allowance — fewer than this call costs.
          example:
            type: https://docs.iotools.cloud/errors/insufficient_credits
            title: Insufficient credits
            status: 402
            code: insufficient_credits
            detail: This call costs 1 credit and 0 remain in this month's allowance.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
            credits_used: 0
            credits_remaining: 0
    ToolNotAllowed:
      description: Tool exists but has no API surface.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/tool_not_allowed
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Tool not available over the API
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - tool_not_allowed
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
          example:
            type: https://docs.iotools.cloud/errors/tool_not_allowed
            title: Tool not available over the API
            status: 403
            code: tool_not_allowed
            detail: >-
              "Background Remover" is available on iotools.cloud but has no API
              endpoint.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
    ToolNotFound:
      description: No such tool.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/tool_not_found
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Tool not found
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - tool_not_found
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
          example:
            type: https://docs.iotools.cloud/errors/tool_not_found
            title: Tool not found
            status: 404
            code: tool_not_found
            detail: No tool with that slug. See GET /v1/tools/list.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
    PayloadTooLarge:
      description: Body too large.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/payload_too_large
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Payload too large
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - payload_too_large
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
          example:
            type: https://docs.iotools.cloud/errors/payload_too_large
            title: Payload too large
            status: 413
            code: payload_too_large
            detail: Request body exceeds this tool's size limit.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
    UnprocessableInput:
      description: Well-formed request, but there is no result to return.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/unprocessable_input
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Input cannot be processed
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - unprocessable_input
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
              credits_used:
                type: integer
                description: >-
                  Always 0 on `unprocessable_input` — a failed run is refunded,
                  floor included.
              credits_remaining:
                type: integer
                description: >-
                  Credits left after the refund. Absent when metering is
                  disabled.
          example:
            type: https://docs.iotools.cloud/errors/unprocessable_input
            title: Input cannot be processed
            status: 422
            code: unprocessable_input
            detail: >-
              This video has no captions or subtitles, so there is no transcript
              to extract.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
            credits_used: 0
    RateLimited:
      description: Per-minute rate limit exceeded.
      headers:
        Retry-After:
          description: Seconds to wait before retrying (RFC 9110 delta-seconds).
          schema:
            type: integer
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/rate_limited
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Rate limit exceeded
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - rate_limited
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
              retry_after:
                type: integer
                description: >-
                  Seconds until the window resets — the same value as the
                  `Retry-After` header.
          example:
            type: https://docs.iotools.cloud/errors/rate_limited
            title: Rate limit exceeded
            status: 429
            code: rate_limited
            detail: Too many requests. Retry in 30s.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
            retry_after: 30
    ToolFailed:
      description: Tool failed to run.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/processing_error
                  - https://docs.iotools.cloud/errors/internal_error
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Tool failed to run
                  - Internal error
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - processing_error
                  - internal_error
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
              credits_used:
                type: integer
                description: >-
                  Always 0 on `processing_error` — a failed run is refunded,
                  floor included.
              credits_remaining:
                type: integer
                description: >-
                  Credits left after the refund. Absent when metering is
                  disabled.
          example:
            type: https://docs.iotools.cloud/errors/processing_error
            title: Tool failed to run
            status: 500
            code: processing_error
            detail: The tool failed to run. Please try again.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
            credits_used: 0
    ToolDisabled:
      description: Tool temporarily disabled.
      content:
        application/problem+json:
          schema:
            type: object
            description: >-
              RFC 9457 problem document, served as application/problem+json.
              Branch on `code`; `title` is human prose and may be reworded
              without notice. Some failures add extension members — `fields` on
              validation errors, `retry_after` on 429s,
              `credits_used`/`credits_remaining` on billing-adjacent failures —
              documented on the responses that carry them.
            required:
              - type
              - title
              - status
              - code
            properties:
              type:
                type: string
                format: uri
                description: Stable documentation URI for this failure.
                examples:
                  - https://docs.iotools.cloud/errors/tool_disabled
                  - https://docs.iotools.cloud/errors/api_unconfigured
              title:
                type: string
                description: Short human-readable summary of the failure.
                examples:
                  - Tool temporarily disabled
                  - API not configured
              status:
                type: integer
                description: HTTP status code, matching the response's own status.
              code:
                type: string
                description: >-
                  Stable machine-readable error code — branch on this, not
                  `title`.
                enum:
                  - tool_disabled
                  - api_unconfigured
              detail:
                type: string
                description: Human explanation of this occurrence.
              request_id:
                type: string
                description: Correlation id, also sent as x-request-id.
          example:
            type: https://docs.iotools.cloud/errors/tool_disabled
            title: Tool temporarily disabled
            status: 503
            code: tool_disabled
            detail: This tool is temporarily unavailable. Try again shortly.
            request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11
  securitySchemes:
    bearerAuth:
      type: http
      scheme: bearer
      bearerFormat: iot_live_…

````