> ## 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. # Belt Length Calculator > Calculate the belt length for a two-pulley drive from the pulley diameters and centre distance, for open or crossed belts. Also reports the wrap (contact) angle on each pulley, the speed ratio, and — from a driver speed — the driven pulley speed and belt linear speed. Works in mm, cm or inches. [Try Belt Length Calculator in your browser →](https://iotools.cloud/tool/belt-length-calculator/) ## OpenAPI ````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/belt-length-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/belt-length-calculator: post: tags: - Calculators summary: Belt Length Calculator description: >- Calculate the belt length for a two-pulley drive from the pulley diameters and centre distance, for open or crossed belts. Also reports the wrap (contact) angle on each pulley, the speed ratio, and — from a driver speed — the driven pulley speed and belt linear speed. Works in mm, cm or inches. [Try Belt Length Calculator in your browser →](https://iotools.cloud/tool/belt-length-calculator/) operationId: run_belt_length_calculator requestBody: required: false content: application/json: schema: type: object properties: unit: enum: - mm - cm - in description: Units smallDiameter: type: number description: Small Pulley Diameter (D₁) minimum: 0 largeDiameter: type: number description: Large Pulley Diameter (D₂) minimum: 0 centerDistance: type: number description: Centre Distance (C) minimum: 0 beltType: enum: - open - crossed description: Belt Arrangement driverRpm: type: number description: Small Pulley Speed (rpm, optional) minimum: 0 required: [] examples: open_belt_100_mm_and_250_mm_pulleys_500_mm_centres: summary: Open belt — 100 mm and 250 mm pulleys, 500 mm centres value: unit: mm smallDiameter: '100' largeDiameter: '250' centerDistance: '500' beltType: open driverRpm: '' open_belt_with_a_1450_rpm_driver_belt_and_driven_speeds: summary: Open belt with a 1450 rpm driver — belt and driven speeds value: unit: mm smallDiameter: '100' largeDiameter: '250' centerDistance: '500' beltType: open driverRpm: '1450' crossed_belt_4_in_and_10_in_pulleys_20_in_centres: summary: Crossed belt — 4 in and 10 in pulleys, 20 in centres value: unit: in smallDiameter: '4' largeDiameter: '10' centerDistance: '20' beltType: crossed driverRpm: '' responses: '200': description: Tool output content: application/json: examples: open_belt_100_mm_and_250_mm_pulleys_500_mm_centres: summary: Open belt — 100 mm and 250 mm pulleys, 500 mm centres value: tool: belt-length-calculator tool_version: 1.0.1 outputs: results: - quantity: Belt length (L) value: 1561.03 mm other-units: 156.103 cm · 61.4578 in - quantity: Wrap angle — small pulley value: 162.746° other-units: 2.84046 rad - quantity: Wrap angle — large pulley value: 197.254° other-units: 3.44273 rad - quantity: 'Speed ratio (D₂ : D₁)' value: '2.5 : 1' other-units: driven speed = 0.4 × driver speed - quantity: Belt span between pulleys value: 494.343 mm other-units: 49.4343 cm · 19.4623 in breakdown: >- Open belt drive L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)² ÷ 4C D₁ = 100 mm D₂ = 250 mm C = 500 mm L = 1561.03 mm (156.103 cm · 61.4578 in) Wrap angles: 162.746° on the small pulley, 197.254° on the large one. This is a theoretical length — round up to the nearest stock belt size and check the manufacturer's pitch-length table before ordering. credits_used: 3 credits_remaining: null open_belt_with_a_1450_rpm_driver_belt_and_driven_speeds: summary: Open belt with a 1450 rpm driver — belt and driven speeds value: tool: belt-length-calculator tool_version: 1.0.1 outputs: results: - quantity: Belt length (L) value: 1561.03 mm other-units: 156.103 cm · 61.4578 in - quantity: Wrap angle — small pulley value: 162.746° other-units: 2.84046 rad - quantity: Wrap angle — large pulley value: 197.254° other-units: 3.44273 rad - quantity: 'Speed ratio (D₂ : D₁)' value: '2.5 : 1' other-units: driven speed = 0.4 × driver speed - quantity: Belt span between pulleys value: 494.343 mm other-units: 49.4343 cm · 19.4623 in - quantity: Driven (large) pulley speed value: 580 rpm other-units: 9.66667 rev/s - quantity: Belt linear speed value: 7.59218 m/s other-units: 1494.52 ft/min breakdown: >- Open belt drive L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)² ÷ 4C D₁ = 100 mm D₂ = 250 mm C = 500 mm L = 1561.03 mm (156.103 cm · 61.4578 in) Wrap angles: 162.746° on the small pulley, 197.254° on the large one. This is a theoretical length — round up to the nearest stock belt size and check the manufacturer's pitch-length table before ordering. credits_used: 3 credits_remaining: null crossed_belt_4_in_and_10_in_pulleys_20_in_centres: summary: Crossed belt — 4 in and 10 in pulleys, 20 in centres value: tool: belt-length-calculator tool_version: 1.0.1 outputs: results: - quantity: Belt length (L) value: 64.4411 in other-units: 1636.81 mm · 163.681 cm - quantity: Wrap angle — small pulley value: 220.975° other-units: 3.85673 rad - quantity: Wrap angle — large pulley value: 220.975° other-units: 3.85673 rad - quantity: 'Speed ratio (D₂ : D₁)' value: '2.5 : 1' other-units: driven speed = 0.4 × driver speed - quantity: Belt span between pulleys value: 18.735 in other-units: 475.869 mm · 47.5869 cm breakdown: >- Crossed belt drive L = 2C + (π/2)(D₁ + D₂) + (D₁ + D₂)² ÷ 4C D₁ = 4 in D₂ = 10 in C = 20 in L = 64.4411 in (1636.81 mm · 163.681 cm) Wrap angles: 220.975° on the small pulley, 220.975° on the large one. This is a theoretical length — round up to the nearest stock belt size and check the manufacturer's pitch-length table before ordering. credits_used: 3 credits_remaining: null schema: type: object required: - tool - tool_version - outputs - credits_used - credits_remaining properties: outputs: type: object properties: results: type: array description: Belt & Drive Geometry items: type: object properties: quantity: type: string description: Quantity value: type: string description: Value other-units: type: string description: Other units x-iotools-columns: - quantity - value - other-units breakdown: type: string description: Formula & Breakdown 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_… ````