> ## 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.

# Nernst Equation Calculator

> Calculate cell potential with the Nernst equation from the standard potential E°, electrons transferred, temperature, and the reaction quotient Q (or product and reactant concentrations) — or solve backward for Q from a measured potential. Also returns ΔG, ΔG°, the equilibrium constant K, and the voltage change per tenfold change in Q (59.16/n mV at 25°C).

[Try Nernst Equation Calculator in your browser →](https://iotools.cloud/tool/nernst-equation-calculator/)



## OpenAPI

````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/nernst-equation-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/nernst-equation-calculator:
    post:
      tags:
        - Calculators
      summary: Nernst Equation Calculator
      description: >-
        Calculate cell potential with the Nernst equation from the standard
        potential E°, electrons transferred, temperature, and the reaction
        quotient Q (or product and reactant concentrations) — or solve backward
        for Q from a measured potential. Also returns ΔG, ΔG°, the equilibrium
        constant K, and the voltage change per tenfold change in Q (59.16/n mV
        at 25°C).


        [Try Nernst Equation Calculator in your browser
        →](https://iotools.cloud/tool/nernst-equation-calculator/)
      operationId: run_nernst_equation_calculator
      requestBody:
        required: false
        content:
          application/json:
            schema:
              type: object
              properties:
                solveFor:
                  enum:
                    - e
                    - q
                  description: Solve For
                standardPotential:
                  type: number
                  description: Standard Potential E° (V)
                electrons:
                  type: number
                  description: Electrons Transferred (n)
                  minimum: 1
                temperature:
                  type: number
                  description: Temperature
                temperatureUnit:
                  enum:
                    - c
                    - k
                    - f
                  description: Temperature Unit
                quotientInput:
                  enum:
                    - q
                    - conc
                  description: Reaction Quotient From
                qValue:
                  type: number
                  description: Reaction Quotient Q
                productTerm:
                  type: number
                  description: Product Term
                reactantTerm:
                  type: number
                  description: Reactant Term
                cellPotential:
                  type: number
                  description: Measured Cell Potential E (V)
              required: []
            examples:
              daniell_cell_zn_cu_at_25_c_q_1000:
                summary: Daniell cell (Zn/Cu) at 25°C, Q = 1000
                value:
                  solveFor: e
                  standardPotential: '1.10'
                  electrons: '2'
                  temperature: '25'
                  temperatureUnit: c
                  quotientInput: q
                  qValue: '1000'
                  productTerm: '1'
                  reactantTerm: '0.001'
                  cellPotential: '1.0112'
              cu_cu_half_cell_at_body_temperature_from_concentrations:
                summary: Cu²⁺/Cu half-cell at body temperature, from concentrations
                value:
                  solveFor: e
                  standardPotential: '0.34'
                  electrons: '2'
                  temperature: '310.15'
                  temperatureUnit: k
                  quotientInput: conc
                  qValue: '1000'
                  productTerm: '1'
                  reactantTerm: '0.001'
                  cellPotential: '1.0112'
              solve_for_q_from_a_measured_1_0112_v:
                summary: Solve for Q from a measured 1.0112 V
                value:
                  solveFor: q
                  standardPotential: '1.10'
                  electrons: '2'
                  temperature: '25'
                  temperatureUnit: c
                  quotientInput: q
                  qValue: '1000'
                  productTerm: '1'
                  reactantTerm: '0.001'
                  cellPotential: '1.0112'
      responses:
        '200':
          description: Tool output
          content:
            application/json:
              examples:
                daniell_cell_zn_cu_at_25_c_q_1000:
                  summary: Daniell cell (Zn/Cu) at 25°C, Q = 1000
                  value:
                    tool: nernst-equation-calculator
                    tool_version: 1.0.2
                    outputs:
                      result:
                        - metric: Cell potential E (V)
                          value: '1.01126'
                        - metric: Shift from E° (V)
                          value: '-0.088739'
                        - metric: Reaction quotient Q
                          value: '1000'
                        - metric: log10 Q
                          value: '3'
                        - metric: Temperature (K)
                          value: '298.15'
                        - metric: RT/nF (V)
                          value: '0.0128463'
                        - metric: Slope per decade of Q (V)
                          value: '0.0295797'
                        - metric: ΔG (kJ/mol)
                          value: '-195.144'
                        - metric: ΔG° (kJ/mol)
                          value: '-212.268'
                        - metric: Equilibrium constant K
                          value: '1.5406e+37'
                        - metric: log10 K
                          value: '37.1877'
                        - metric: Verdict
                          value: Spontaneous as written (galvanic, ΔG < 0)
                      steps: >-
                        T = 298.15 K; RT/nF = (8.314462618 × 298.15) ÷ (2 ×
                        96485.33212) = 0.0128463 V

                        Slope = 2.302585 × RT/nF = 0.0295797 V per decade of Q
                        (29.5797 mV)

                        E = E° − slope × log10 Q = 1.1 − 0.0295797 × 3 = 1.01126
                        V
                    credits_used: 5
                    credits_remaining: null
                cu_cu_half_cell_at_body_temperature_from_concentrations:
                  summary: Cu²⁺/Cu half-cell at body temperature, from concentrations
                  value:
                    tool: nernst-equation-calculator
                    tool_version: 1.0.2
                    outputs:
                      result:
                        - metric: Cell potential E (V)
                          value: '0.247689'
                        - metric: Shift from E° (V)
                          value: '-0.0923106'
                        - metric: Reaction quotient Q
                          value: '1000'
                        - metric: log10 Q
                          value: '3'
                        - metric: Temperature (K)
                          value: '310.15'
                        - metric: RT/nF (V)
                          value: '0.0133633'
                        - metric: Slope per decade of Q (V)
                          value: '0.0307702'
                        - metric: ΔG (kJ/mol)
                          value: '-47.7968'
                        - metric: ΔG° (kJ/mol)
                          value: '-65.61'
                        - metric: Equilibrium constant K
                          value: '1.1211e+11'
                        - metric: log10 K
                          value: '11.0497'
                        - metric: Verdict
                          value: Spontaneous as written (galvanic, ΔG < 0)
                      steps: >-
                        T = 310.15 K; RT/nF = (8.314462618 × 310.15) ÷ (2 ×
                        96485.33212) = 0.0133633 V

                        Slope = 2.302585 × RT/nF = 0.0307702 V per decade of Q
                        (30.7702 mV)

                        Q = products ÷ reactants = 1 ÷ 0.001 = 1000

                        E = E° − slope × log10 Q = 0.34 − 0.0307702 × 3 =
                        0.247689 V
                    credits_used: 5
                    credits_remaining: null
                solve_for_q_from_a_measured_1_0112_v:
                  summary: Solve for Q from a measured 1.0112 V
                  value:
                    tool: nernst-equation-calculator
                    tool_version: 1.0.2
                    outputs:
                      result:
                        - metric: Cell potential E (V)
                          value: '1.0112'
                        - metric: Shift from E° (V)
                          value: '-0.0888'
                        - metric: Reaction quotient Q
                          value: '1004.76'
                        - metric: log10 Q
                          value: '3.00206'
                        - metric: Temperature (K)
                          value: '298.15'
                        - metric: RT/nF (V)
                          value: '0.0128463'
                        - metric: Slope per decade of Q (V)
                          value: '0.0295797'
                        - metric: ΔG (kJ/mol)
                          value: '-195.132'
                        - metric: ΔG° (kJ/mol)
                          value: '-212.268'
                        - metric: Equilibrium constant K
                          value: '1.5406e+37'
                        - metric: log10 K
                          value: '37.1877'
                        - metric: Verdict
                          value: Spontaneous as written (galvanic, ΔG < 0)
                      steps: >-
                        T = 298.15 K; RT/nF = (8.314462618 × 298.15) ÷ (2 ×
                        96485.33212) = 0.0128463 V

                        Slope = 2.302585 × RT/nF = 0.0295797 V per decade of Q
                        (29.5797 mV)

                        log10 Q = (E° − E) ÷ slope = (1.1 − 1.0112) ÷ 0.0295797
                        = 3.00206

                        Q = 10^3.00206 = 1004.76
                    credits_used: 5
                    credits_remaining: null
              schema:
                type: object
                required:
                  - tool
                  - tool_version
                  - outputs
                  - credits_used
                  - credits_remaining
                properties:
                  outputs:
                    type: object
                    properties:
                      result:
                        type: array
                        description: Result
                        items:
                          type: object
                          properties:
                            metric:
                              type: string
                              description: Metric
                            value:
                              type: string
                              description: Value
                        x-iotools-columns:
                          - metric
                          - value
                      steps:
                        type: string
                        description: Steps
                  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_…

````