# Gear Ratio and Speed Calculator

> Computes vehicle road speed in km/h and mph from engine rpm, transmission gear ratio, final-drive ratio and tire diameter (or tire code), plus the overall ratio, wheel rpm, speed per 1000 rpm and, optionally, the engine rpm at a given road speed.

- Calculator id: `gear-ratio-speed` · Category: Engineering & Automotive (`engineering`) · Tool name: `calculate_gear_ratio_speed`
- Canonical page: https://tttkmbb.com/engineering/gear-ratio-speed · This document: https://tttkmbb.com/engineering/gear-ratio-speed.md · JSON definition: https://tttkmbb.com/engineering/gear-ratio-speed.json

## Purpose

Computes vehicle road speed in km/h and mph from engine rpm, transmission gear ratio, final-drive ratio and tire diameter (or tire code), plus the overall ratio, wheel rpm, speed per 1000 rpm and, optionally, the engine rpm at a given road speed.

**Use when:** You want to know how fast a vehicle travels at a given rpm in a given gear, what rpm it turns at highway speed, or how a tire or final-drive change shifts the gearing.

**Do not use when:** You need bicycle gearing (chainring/cog teeth and cadence), or torque and power at the engine (use horsepower-torque-rpm).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `engine_rpm` | number | rpm | required | Engine (or motor) crankshaft speed in revolutions per minute. (> 0, max 30000) |
| `gear_ratio` | number |  | required | Ratio of the selected gear (e.g. 3.5 first gear, 1.0 direct, 0.75 overdrive); use 1 for a direct-drive EV reduction already included in final_drive_ratio. (> 0, max 50) |
| `final_drive_ratio` | number |  | required | Differential / axle ratio (e.g. 3.73). (> 0, max 50) |
| `tire_diameter_mm` | number | mm | optional | Overall tire diameter in millimetres (inches × 25.4). Give either tire_diameter_mm or tire_code. (> 0, max 3000) |
| `tire_code` | string |  | optional | Metric tire size such as 225/45R17, used to compute the diameter instead of tire_diameter_mm. |
| `speed_km_h` | number | km/h | optional | Optional road speed; enables the engine rpm at that speed in the same gear. (> 0, max 600) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `overall_ratio` | number |  | gear_ratio × final_drive_ratio (engine revolutions per wheel revolution). |
| `wheel_rpm` | number | rpm | engine_rpm / overall_ratio. |
| `tire_diameter_mm` | number | mm | Overall tire diameter. |
| `tire_circumference_m` | number | m | π × diameter. |
| `speed_km_h` | number | km/h | wheel_rpm × circumference × 60 / 1000. |
| `speed_mph` | number | mph | speed_km_h / 1.609344. |
| `km_h_per_1000_rpm` | number | km/h | Road speed gained per 1000 engine rpm in this gear. |
| `mph_per_1000_rpm` | number | mph | Same in mph. |
| `rpm_at_speed` | number | rpm | Engine speed needed for the given road speed in this gear (only when speed_km_h is given). |

## Formula

`overall_ratio = gear_ratio × final_drive_ratio; wheel_rpm = engine_rpm / overall_ratio; speed_km_h = wheel_rpm × π × tire_diameter_mm / 1000 × 60 / 1000; rpm_at_speed = engine_rpm × speed_km_h / speed_km_h_computed`

Assumes no tire slip and the unloaded nominal diameter; the loaded rolling circumference is typically 2–3 % smaller, so real speeds are slightly lower. Transfer-case low range multiplies the overall ratio further.

## Data Sources

- Wikipedia – Gear train (gear ratio) — https://en.wikipedia.org/wiki/Gear_train (reference, retrieved 2026-09-24)
- Wikipedia – Tire code — https://en.wikipedia.org/wiki/Tire_code (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/gear-ratio-speed?engine_rpm=…&gear_ratio=…&final_drive_ratio=…`
- `POST https://tttkmbb.com/api/v1/calculate/gear-ratio-speed` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/gear-ratio-speed · OpenAPI operationId `calculate_gear_ratio_speed` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "gear-ratio-speed", "inputs": {…}}`

## Example

- 3000 rpm, 1:1 gear, 3.73 final drive, 634.3 mm tire, rpm at 100 km/h: inputs `{"engine_rpm":3000,"gear_ratio":1,"final_drive_ratio":3.73,"tire_diameter_mm":634.3,"speed_km_h":100}` → `{"overall_ratio":3.73,"wheel_rpm":804.29,"tire_circumference_m":1.9927,"speed_km_h":96.16,"speed_mph":59.75,"km_h_per_1000_rpm":32.05,"rpm_at_speed":3120}`
- 2500 rpm in 0.8 overdrive, 4.10 final drive, 205/55R16: inputs `{"engine_rpm":2500,"gear_ratio":0.8,"final_drive_ratio":4.1,"tire_code":"205/55R16"}` → `{"overall_ratio":3.28,"tire_diameter_mm":631.9,"speed_km_h":90.79,"speed_mph":56.41}`

```
GET https://tttkmbb.com/api/v1/calculate/gear-ratio-speed?engine_rpm=3000&gear_ratio=1&final_drive_ratio=3.73&tire_diameter_mm=634.3&speed_km_h=100
```

## Limitations

You need bicycle gearing (chainring/cog teeth and cadence), or torque and power at the engine (use horsepower-torque-rpm). Assumes no tire slip and the unloaded nominal diameter; the loaded rolling circumference is typically 2–3 % smaller, so real speeds are slightly lower. Transfer-case low range multiplies the overall ratio further. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Where do I find the gear and final drive ratios?**

In the vehicle's technical specifications or workshop manual; the axle ratio is often on a door or axle tag. Automatic transmissions with torque converters slip below lock-up, so real rpm is higher at low speed.

**How do bigger tires change the result?**

Speed scales with tire diameter: a 3 % larger tire gives 3 % more speed at the same rpm and 3 % lower rpm at the same speed, like a numerically lower final drive.

## Related

- [Tire Size Calculator](https://tttkmbb.com/engineering/tire-size.md) — Tire diameter from the sidewall code.
- [Horsepower, Torque and RPM Calculator](https://tttkmbb.com/engineering/horsepower-torque-rpm.md) — Engine power and torque at the rpm.
- [Speed Converter](https://tttkmbb.com/conversion/speed.md) — Convert road speed between units.