> ## 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. # Gear Ratio Calculator > Calculate gear ratio, output speed and output torque from driver and driven tooth counts. Handles compound multi-stage gear trains with a per-stage breakdown, applies a per-mesh efficiency to the torque, and reports the ratio as a decimal, as N:1 and as a speed change. [Try Gear Ratio Calculator in your browser →](https://iotools.cloud/tool/gear-ratio-calculator/) ## OpenAPI ````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/gear-ratio-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/gear-ratio-calculator: post: tags: - Calculators summary: Gear Ratio Calculator description: >- Calculate gear ratio, output speed and output torque from driver and driven tooth counts. Handles compound multi-stage gear trains with a per-stage breakdown, applies a per-mesh efficiency to the torque, and reports the ratio as a decimal, as N:1 and as a speed change. [Try Gear Ratio Calculator in your browser →](https://iotools.cloud/tool/gear-ratio-calculator/) operationId: run_gear_ratio_calculator requestBody: required: false content: application/json: schema: type: object properties: mode: enum: - single - compound description: Gear Train driverTeeth: type: number description: Driver Teeth minimum: 1 drivenTeeth: type: number description: Driven Teeth minimum: 1 train: type: string description: Stages inputSpeed: type: number description: Input Speed (rpm) minimum: 0 inputTorque: type: number description: Input Torque (N·m) minimum: 0 efficiency: type: number description: Efficiency per Mesh (%) minimum: 50 maximum: 100 required: [] examples: 20_60_teeth_3_1_reduction_at_1750_rpm: summary: 20 → 60 teeth, 3:1 reduction at 1750 rpm value: mode: single driverTeeth: '20' drivenTeeth: '60' train: |- 20, 60 15, 45 inputSpeed: '1750' inputTorque: '50' efficiency: '100' two_stage_compound_train_at_97_per_mesh: summary: Two-stage compound train at 97% per mesh value: mode: compound driverTeeth: '20' drivenTeeth: '60' train: |- 20, 60 15, 45 inputSpeed: '1750' inputTorque: '50' efficiency: '97' overdrive_40_driver_20_driven: summary: Overdrive — 40 driver, 20 driven value: mode: single driverTeeth: '40' drivenTeeth: '20' train: |- 20, 60 15, 45 inputSpeed: '1000' inputTorque: '' efficiency: '100' responses: '200': description: Tool output content: application/json: examples: 20_60_teeth_3_1_reduction_at_1750_rpm: summary: 20 → 60 teeth, 3:1 reduction at 1750 rpm value: tool: gear-ratio-calculator tool_version: 1.0.1 outputs: results: - quantity: Total gear ratio value: '3' - quantity: Ratio notation value: '3 : 1' - quantity: Drive type value: Reduction — output turns slower with more torque - quantity: Stages value: '1' - quantity: Mechanical advantage value: 3× - quantity: Output speed value: 583.333 rpm - quantity: Speed change value: '-66.6667 %' - quantity: Output torque (ideal) value: 150 N·m stageTable: - stage: '1' driver-driven: 20 → 60 stage-ratio: '3 : 1' speed-out-rpm: '583.333' torque-out-n-m: '150' breakdown: >- Stage ratio = driven teeth ÷ driver teeth Total ratio = 60/20 = 3 Output speed = 1750 rpm ÷ 3 = 583.333 rpm Output torque = 50 N·m × 3 = 150 N·m Ideal calculation — drop the efficiency below 100% to account for mesh losses. credits_used: 3 credits_remaining: null two_stage_compound_train_at_97_per_mesh: summary: Two-stage compound train at 97% per mesh value: tool: gear-ratio-calculator tool_version: 1.0.1 outputs: results: - quantity: Total gear ratio value: '9' - quantity: Ratio notation value: '9 : 1' - quantity: Drive type value: Reduction — output turns slower with more torque - quantity: Stages value: '2' - quantity: Mechanical advantage value: 9× - quantity: Output speed value: 194.444 rpm - quantity: Speed change value: '-88.8889 %' - quantity: Output torque (ideal) value: 450 N·m - quantity: Output torque at 97% per mesh value: 423.405 N·m - quantity: Train efficiency value: 94.09 % stageTable: - stage: '1' driver-driven: 20 → 60 stage-ratio: '3 : 1' speed-out-rpm: '583.333' torque-out-n-m: '145.5' - stage: '2' driver-driven: 15 → 45 stage-ratio: '3 : 1' speed-out-rpm: '194.444' torque-out-n-m: '423.405' breakdown: |- Stage ratio = driven teeth ÷ driver teeth Total ratio = 60/20 × 45/15 = 9 Output speed = 1750 rpm ÷ 9 = 194.444 rpm Output torque = 50 N·m × 9 × 97%^2 = 423.405 N·m Train efficiency = 97%^2 = 94.09% credits_used: 3 credits_remaining: null overdrive_40_driver_20_driven: summary: Overdrive — 40 driver, 20 driven value: tool: gear-ratio-calculator tool_version: 1.0.1 outputs: results: - quantity: Total gear ratio value: '0.5' - quantity: Ratio notation value: '1 : 2' - quantity: Drive type value: Overdrive — output turns faster with less torque - quantity: Stages value: '1' - quantity: Mechanical advantage value: 0.5× - quantity: Output speed value: 2000 rpm - quantity: Speed change value: 100 % stageTable: - stage: '1' driver-driven: 40 → 20 stage-ratio: '1 : 2' speed-out-rpm: '2000' torque-out-n-m: — breakdown: >- Stage ratio = driven teeth ÷ driver teeth Total ratio = 20/40 = 0.5 Output speed = 1000 rpm ÷ 0.5 = 2000 rpm Enter an input torque to get the output torque. Ideal calculation — drop the efficiency below 100% to account for mesh losses. 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: Gear Ratio & Output items: type: object properties: quantity: type: string description: Quantity value: type: string description: Value x-iotools-columns: - quantity - value stageTable: type: array description: Stage by Stage items: type: object properties: stage: type: string description: Stage driver-driven: type: string description: Driver → Driven stage-ratio: type: string description: Stage ratio speed-out-rpm: type: string description: Speed out (rpm) torque-out-n-m: type: string description: Torque out (N·m) x-iotools-columns: - stage - driver-driven - stage-ratio - speed-out-rpm - torque-out-n-m 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_… ````