Documentation sections

Gear Ratio Calculator

POSThttps://rftools.io/api/py/v1/calculate

Slug gear-ratio. Calculate gear ratio, output speed, torque multiplication, and power transmission efficiency for gear trains.

Inputs

Send every one of these in inputs, in the units shown. Most are required: a call without one is refused (400) and costs nothing; one the calculator can do without takes the default shown. An input outside its range is still computed and flagged in the provenance.

Inputs of gear-ratio
Name	Unit	Range	Default	Description
driverTeethnumber	teeth	at least 1	10	Driver (Input) Teeth
drivenTeethnumber	teeth	at least 1	40	Driven (Output) Teeth
inputSpeednumber	RPM	at least 0	1000	Input Speed
inputTorquenumber	N·m	at least 0	0.5	Input Torque
efficiencynumber	%	10 … 100	95	Gear Efficiency
extraStagesnumber	none	0 … 5	0	Gear stages between the input shaft and the output pair, in order from the input (0–5)
stage1Drivernumber	teeth	1 … 1000	12	Teeth (or worm starts) on stage 1’s driving gear
stage1Drivennumber	teeth	1 … 1000	36	Teeth on stage 1’s driven gear
stage1Efficiencynumber	%	10 … 100	98	Mesh efficiency of stage 1
stage2Drivernumber	teeth	1 … 1000	12	Teeth (or worm starts) on stage 2’s driving gear
stage2Drivennumber	teeth	1 … 1000	36	Teeth on stage 2’s driven gear
stage2Efficiencynumber	%	10 … 100	98	Mesh efficiency of stage 2
stage3Drivernumber	teeth	1 … 1000	12	Teeth (or worm starts) on stage 3’s driving gear
stage3Drivennumber	teeth	1 … 1000	36	Teeth on stage 3’s driven gear
stage3Efficiencynumber	%	10 … 100	98	Mesh efficiency of stage 3
stage4Drivernumber	teeth	1 … 1000	12	Teeth (or worm starts) on stage 4’s driving gear
stage4Drivennumber	teeth	1 … 1000	36	Teeth on stage 4’s driven gear
stage4Efficiencynumber	%	10 … 100	98	Mesh efficiency of stage 4
stage5Drivernumber	teeth	1 … 1000	12	Teeth (or worm starts) on stage 5’s driving gear
stage5Drivennumber	teeth	1 … 1000	36	Teeth on stage 5’s driven gear
stage5Efficiencynumber	%	10 … 100	98	Mesh efficiency of stage 5

Outputs

Returned in values, by key. A value that is unbounded or undefined is null.

Outputs of gear-ratio
Field	Unit	Description
gearRatioheadline	:1	Gear Ratio
outputSpeed	RPM	Output Speed
outputTorque	N·m	Output Torque
inputPower	W	Input Power
outputPower	W	Output Power
totalEfficiency	%	The product of every stage’s efficiency, the output pair’s included

Calling it

Calculate: one call, the request and response in full, and its errors.
Batch: this calculator with others, or a sweep, in one request.
Solve for a target: the value of one input that brings an output to a target.

curl -X POST https://rftools.io/api/py/v1/calculate \
  -H "X-API-Key: $RFTOOLS_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "slug": "gear-ratio",
    "inputs": {
      "driverTeeth": 10,
      "drivenTeeth": 40,
      "inputSpeed": 1000,
      "inputTorque": 0.5,
      "efficiency": 95,
      "extraStages": 0,
      "stage1Driver": 12,
      "stage1Driven": 36,
      "stage1Efficiency": 98,
      "stage2Driver": 12,
      "stage2Driven": 36,
      "stage2Efficiency": 98,
      "stage3Driver": 12,
      "stage3Driven": 36,
      "stage3Efficiency": 98,
      "stage4Driver": 12,
      "stage4Driven": 36,
      "stage4Efficiency": 98,
      "stage5Driver": 12,
      "stage5Driven": 36,
      "stage5Efficiency": 98
    }
  }'

import rftools

client = rftools.Client()  # reads RFTOOLS_API_KEY, or the key `rftools login` saved

result = client.calculate("gear-ratio", {
    "driverTeeth": 10,
    "drivenTeeth": 40,
    "inputSpeed": 1000,
    "inputTorque": 0.5,
    "efficiency": 95,
    "extraStages": 0,
    "stage1Driver": 12,
    "stage1Driven": 36,
    "stage1Efficiency": 98,
    "stage2Driver": 12,
    "stage2Driven": 36,
    "stage2Efficiency": 98,
    "stage3Driver": 12,
    "stage3Driven": 36,
    "stage3Efficiency": 98,
    "stage4Driver": 12,
    "stage4Driven": 36,
    "stage4Efficiency": 98,
    "stage5Driver": 12,
    "stage5Driven": 36,
    "stage5Efficiency": 98,
})
print(result.values)
print(result.warnings, result.provenance.formula_ref)

const response = await fetch("https://rftools.io/api/py/v1/calculate", {
  method: "POST",
  headers: {
    "X-API-Key": process.env.RFTOOLS_API_KEY,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    "slug": "gear-ratio",
    "inputs": {
      "driverTeeth": 10,
      "drivenTeeth": 40,
      "inputSpeed": 1000,
      "inputTorque": 0.5,
      "efficiency": 95,
      "extraStages": 0,
      "stage1Driver": 12,
      "stage1Driven": 36,
      "stage1Efficiency": 98,
      "stage2Driver": 12,
      "stage2Driven": 36,
      "stage2Efficiency": 98,
      "stage3Driver": 12,
      "stage3Driven": 36,
      "stage3Efficiency": 98,
      "stage4Driver": 12,
      "stage4Driven": 36,
      "stage4Efficiency": 98,
      "stage5Driver": 12,
      "stage5Driven": 36,
      "stage5Efficiency": 98
    }
  }),
});
console.log(response.status, await response.json());

package main

import (
	"bytes"
	"fmt"
	"io"
	"net/http"
	"os"
)

func main() {
	body := []byte(`{
	  "slug": "gear-ratio",
	  "inputs": {
	    "driverTeeth": 10,
	    "drivenTeeth": 40,
	    "inputSpeed": 1000,
	    "inputTorque": 0.5,
	    "efficiency": 95,
	    "extraStages": 0,
	    "stage1Driver": 12,
	    "stage1Driven": 36,
	    "stage1Efficiency": 98,
	    "stage2Driver": 12,
	    "stage2Driven": 36,
	    "stage2Efficiency": 98,
	    "stage3Driver": 12,
	    "stage3Driven": 36,
	    "stage3Efficiency": 98,
	    "stage4Driver": 12,
	    "stage4Driven": 36,
	    "stage4Efficiency": 98,
	    "stage5Driver": 12,
	    "stage5Driven": 36,
	    "stage5Efficiency": 98
	  }
	}`)
	req, err := http.NewRequest("POST", "https://rftools.io/api/py/v1/calculate", bytes.NewReader(body))
	if err != nil {
		panic(err)
	}
	req.Header.Set("X-API-Key", os.Getenv("RFTOOLS_API_KEY"))
	req.Header.Set("Content-Type", "application/json")
	res, err := http.DefaultClient.Do(req)
	if err != nil {
		panic(err)
	}
	defer res.Body.Close()
	out, _ := io.ReadAll(res.Body)
	fmt.Println(res.Status, string(out))
}

application/json

{
  "slug": "gear-ratio",
  "values": {
    "gearRatio": 4,
    "outputSpeed": 250,
    "outputTorque": 1.9,
    "inputPower": 52.35987755982988,
    "outputPower": 49.74188368183839,
    "totalEfficiency": 95
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:gear-ratio",
    "version": "api@3f2c1a9b04de",
    "formulaRef": null,
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "driverTeeth": {
          "min": 1,
          "max": null,
          "unit": "teeth"
        },
        "drivenTeeth": {
          "min": 1,
          "max": null,
          "unit": "teeth"
        },
        "inputSpeed": {
          "min": 0,
          "max": null,
          "unit": "RPM"
        },
        "inputTorque": {
          "min": 0,
          "max": null,
          "unit": "N·m"
        },
        "efficiency": {
          "min": 10,
          "max": 100,
          "unit": "%"
        },
        "extraStages": {
          "min": 0,
          "max": 5,
          "unit": ""
        },
        "stage1Driver": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage1Driven": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage1Efficiency": {
          "min": 10,
          "max": 100,
          "unit": "%"
        },
        "stage2Driver": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage2Driven": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage2Efficiency": {
          "min": 10,
          "max": 100,
          "unit": "%"
        },
        "stage3Driver": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage3Driven": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage3Efficiency": {
          "min": 10,
          "max": 100,
          "unit": "%"
        },
        "stage4Driver": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage4Driven": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage4Efficiency": {
          "min": 10,
          "max": 100,
          "unit": "%"
        },
        "stage5Driver": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage5Driven": {
          "min": 1,
          "max": 1000,
          "unit": "teeth"
        },
        "stage5Efficiency": {
          "min": 10,
          "max": 100,
          "unit": "%"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "driverTeeth": 10,
      "drivenTeeth": 40,
      "inputSpeed": 1000,
      "inputTorque": 0.5,
      "efficiency": 95,
      "extraStages": 0,
      "stage1Driver": 12,
      "stage1Driven": 36,
      "stage1Efficiency": 98,
      "stage2Driver": 12,
      "stage2Driven": 36,
      "stage2Efficiency": 98,
      "stage3Driver": 12,
      "stage3Driven": 36,
      "stage3Efficiency": 98,
      "stage4Driver": 12,
      "stage4Driven": 36,
      "stage4Efficiency": 98,
      "stage5Driver": 12,
      "stage5Driven": 36,
      "stage5Efficiency": 98
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "driverTeeth"
      ],
      "msg": "Input should be a valid number, unable to parse string as a number",
      "input": "abc"
    }
  ]
}

An input sent as text. Nothing was counted.

{
  "detail": "More than 120 requests in 60 seconds from this address.",
  "errorKind": "rate_limited",
  "limit": 120,
  "windowSeconds": 60,
  "upgradeUrl": "https://rftools.io/pricing/"
}

Too many requests in a minute, with Retry-After.

Same inputs on the calculator pageGear Ratio Calculator, at these values