> ## 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. # Survey Sample Size Calculator > Calculate the minimum survey sample size for a target margin of error and confidence level using Cochran's formula, with an optional finite population correction for known population sizes. [Try Survey Sample Size Calculator in your browser →](https://iotools.cloud/tool/survey-sample-size-calculator/) ## OpenAPI ````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/survey-sample-size-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/survey-sample-size-calculator: post: tags: - Calculators summary: Survey Sample Size Calculator description: >- Calculate the minimum survey sample size for a target margin of error and confidence level using Cochran's formula, with an optional finite population correction for known population sizes. [Try Survey Sample Size Calculator in your browser →](https://iotools.cloud/tool/survey-sample-size-calculator/) operationId: run_survey_sample_size_calculator requestBody: required: false content: application/json: schema: type: object properties: population: type: number description: Population size minimum: 0 marginError: type: number description: Margin of error (%) minimum: 0.1 maximum: 50 confidenceLevel: enum: - '80' - '85' - '90' - '95' - '99' - '99.9' description: Confidence level proportion: type: number description: Expected proportion (%) minimum: 1 maximum: 99 required: [] examples: unknown_population_95_confidence_5: summary: Unknown population (95% confidence, ±5%) value: population: '' marginError: '5' confidenceLevel: '95' proportion: '50' population_of_5_000_95_confidence_5: summary: Population of 5,000 (95% confidence, ±5%) value: population: '5000' marginError: '5' confidenceLevel: '95' proportion: '50' employee_survey_250_staff_99_confidence_5: summary: Employee survey — 250 staff (99% confidence, ±5%) value: population: '250' marginError: '5' confidenceLevel: '99' proportion: '50' responses: '200': description: Tool output content: application/json: examples: unknown_population_95_confidence_5: summary: Unknown population (95% confidence, ±5%) value: tool: survey-sample-size-calculator tool_version: 1.0.1 outputs: sampleSize: '385' breakdown: - metric: Confidence level value: 95% - metric: Critical z-score value: '1.9600' - metric: Margin of error (e) value: ±5% - metric: Expected proportion (p) value: 50% - metric: Required sample (Cochran) value: '384' - metric: Population (N) value: Unknown / very large - metric: Recommended minimum sample value: '385' sensitivity: - margin-of-error: ±1% sample-cochran: 9,604 sample-with-fpc: — - margin-of-error: ±2% sample-cochran: 2,401 sample-with-fpc: — - margin-of-error: ±3% sample-cochran: 1,067 sample-with-fpc: — - margin-of-error: ±4% sample-cochran: '600' sample-with-fpc: — - margin-of-error: ±5% sample-cochran: '384' sample-with-fpc: — - margin-of-error: ±7% sample-cochran: '196' sample-with-fpc: — - margin-of-error: ±10% sample-cochran: '96' sample-with-fpc: — credits_used: 3 credits_remaining: null population_of_5_000_95_confidence_5: summary: Population of 5,000 (95% confidence, ±5%) value: tool: survey-sample-size-calculator tool_version: 1.0.1 outputs: sampleSize: '357' breakdown: - metric: Confidence level value: 95% - metric: Critical z-score value: '1.9600' - metric: Margin of error (e) value: ±5% - metric: Expected proportion (p) value: 50% - metric: Required sample (Cochran) value: '384' - metric: Population (N) value: 5,000 - metric: Required sample (with FPC) value: '357' - metric: Sample fraction (n / N) value: 7.14% - metric: Recommended minimum sample value: '357' sensitivity: - margin-of-error: ±1% sample-cochran: 9,604 sample-with-fpc: 3,288 - margin-of-error: ±2% sample-cochran: 2,401 sample-with-fpc: 1,622 - margin-of-error: ±3% sample-cochran: 1,067 sample-with-fpc: '880' - margin-of-error: ±4% sample-cochran: '600' sample-with-fpc: '536' - margin-of-error: ±5% sample-cochran: '384' sample-with-fpc: '357' - margin-of-error: ±7% sample-cochran: '196' sample-with-fpc: '189' - margin-of-error: ±10% sample-cochran: '96' sample-with-fpc: '94' credits_used: 3 credits_remaining: null employee_survey_250_staff_99_confidence_5: summary: Employee survey — 250 staff (99% confidence, ±5%) value: tool: survey-sample-size-calculator tool_version: 1.0.1 outputs: sampleSize: '182' breakdown: - metric: Confidence level value: 99% - metric: Critical z-score value: '2.5758' - metric: Margin of error (e) value: ±5% - metric: Expected proportion (p) value: 50% - metric: Required sample (Cochran) value: '663' - metric: Population (N) value: '250' - metric: Required sample (with FPC) value: '182' - metric: Sample fraction (n / N) value: 72.80% - metric: Recommended minimum sample value: '182' sensitivity: - margin-of-error: ±1% sample-cochran: 16,587 sample-with-fpc: '246' - margin-of-error: ±2% sample-cochran: 4,147 sample-with-fpc: '236' - margin-of-error: ±3% sample-cochran: 1,843 sample-with-fpc: '220' - margin-of-error: ±4% sample-cochran: 1,037 sample-with-fpc: '202' - margin-of-error: ±5% sample-cochran: '663' sample-with-fpc: '182' - margin-of-error: ±7% sample-cochran: '339' sample-with-fpc: '144' - margin-of-error: ±10% sample-cochran: '166' sample-with-fpc: '100' credits_used: 3 credits_remaining: null schema: type: object required: - tool - tool_version - outputs - credits_used - credits_remaining properties: outputs: type: object properties: sampleSize: type: string description: Recommended sample size breakdown: type: array description: Statistical breakdown items: type: object properties: metric: type: string description: Metric value: type: string description: Value x-iotools-columns: - metric - value sensitivity: type: array description: Sample size by margin of error items: type: object properties: margin-of-error: type: string description: Margin of error sample-cochran: type: string description: Sample (Cochran) sample-with-fpc: type: string description: Sample (with FPC) x-iotools-columns: - margin-of-error - sample-cochran - sample-with-fpc 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' '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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/errors/invalid_api_key title: Invalid API key status: 401 code: invalid_api_key detail: 'Provide ''Authorization: Bearer ''.' 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://iotools.cloud/docs/errors/insufficient_credits title: type: string description: Short human-readable summary of the failure. examples: - Insufficient credits 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 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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/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 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://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/errors/processing_error - https://iotools.cloud/docs/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://iotools.cloud/docs/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://iotools.cloud/docs/errors/tool_disabled - https://iotools.cloud/docs/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://iotools.cloud/docs/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_… ````