# Bike Gear Ratio Calculator

> Computes a bicycle gear's ratio, gear inches, metres of development and gain ratio from chainring and cog teeth and the wheel size (ISO rim diameter plus tyre width), and the speed that gear gives at a chosen cadence.

- Calculator id: `bike-gear-ratio` · Category: Sports & Fitness (`fitness`) · Tool name: `calculate_bike_gear_ratio`
- Canonical page: https://tttkmbb.com/fitness/bike-gear-ratio · This document: https://tttkmbb.com/fitness/bike-gear-ratio.md · JSON definition: https://tttkmbb.com/fitness/bike-gear-ratio.json

## Purpose

Computes a bicycle gear's ratio, gear inches, metres of development and gain ratio from chainring and cog teeth and the wheel size (ISO rim diameter plus tyre width), and the speed that gear gives at a chosen cadence.

**Use when:** You want to compare gears or drivetrains (gear inches, development), or know how fast a given chainring/cog combination rolls at a cadence.

**Do not use when:** You already know the gear ratio and wheel circumference and only need speed (use cadence-to-speed), or you need engine or machine gearing rather than bicycle gearing.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `chainring_teeth` | integer | teeth | required | Number of teeth on the front chainring. (min 10, max 90) |
| `cog_teeth` | integer | teeth | required | Number of teeth on the rear sprocket (cog). (min 6, max 60) |
| `rim_diameter_mm` | number | mm | optional, default 622 | ISO 5775 bead-seat diameter: 622 for 700C / 29", 584 for 650B / 27.5", 559 for 26", 406 for 20" BMX. (min 200, max 700) |
| `tire_width_mm` | number | mm | optional, default 25 | Nominal tyre width (e.g. 25 for 700×25C, 54 for 29×2.1"); wheel diameter = rim + 2 × tyre width. (min 15, max 130) |
| `cadence_rpm` | number | rpm | optional, default 90 | Pedal revolutions per minute for the speed output. (min 1, max 250) |
| `crank_length_mm` | number | mm | optional, default 170 | Crank arm length, used only for the gain ratio. (min 100, max 220) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `gear_ratio` | number |  | chainring_teeth / cog_teeth: wheel revolutions per pedal revolution. |
| `gear_inches` | number | in | Wheel diameter in inches × gear ratio (equivalent penny-farthing wheel diameter). |
| `development_m` | number | m | Distance travelled per pedal revolution = π × wheel diameter × gear ratio. |
| `gain_ratio` | number |  | Sheldon Brown's crank-independent measure: (wheel radius / crank length) × gear ratio. |
| `wheel_diameter_mm` | number | mm | rim_diameter_mm + 2 × tire_width_mm. |
| `wheel_circumference_mm` | number | mm | π × wheel diameter (use as wheel_circumference_mm in cadence-to-speed). |
| `speed_kmh` | number | km/h | development_m × cadence_rpm × 60 / 1000. |
| `speed_mph` | number | mph | Same speed in miles per hour. |

## Formula

`wheel_diameter = rim_diameter_mm + 2 × tire_width_mm; gear_ratio = chainring_teeth / cog_teeth; gear_inches = wheel_diameter / 25.4 × gear_ratio; development_m = π × wheel_diameter / 1000 × gear_ratio; gain_ratio = (wheel_diameter / 2) / crank_length_mm × gear_ratio; speed_kmh = development_m × cadence_rpm × 60 / 1000`

Wheel diameter from bead-seat diameter plus twice the nominal tyre width is the convention of Sheldon Brown's gear calculator; real rolling diameter differs by 1–2 % with tyre casing, pressure and load. Internally geared hubs would need their stage ratio applied to gear_ratio.

## Data Sources

- Sheldon Brown – Bicycle Gear Calculator (gear inches, metres of development, gain ratio) — https://www.sheldonbrown.com/gear-calc.html (reference, retrieved 2026-09-24)
- Wikipedia – ISO 5775 tyre and rim designations (bead seat 622 mm = 700C/29", 584 mm = 650B/27.5", 559 mm = 26") — https://en.wikipedia.org/wiki/ISO_5775 (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/bike-gear-ratio?chainring_teeth=…&cog_teeth=…`
- `POST https://tttkmbb.com/api/v1/calculate/bike-gear-ratio` 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/bike-gear-ratio · OpenAPI operationId `calculate_bike_gear_ratio` 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": "bike-gear-ratio", "inputs": {…}}`

## Example

- 50 × 25 on 700×25C at 90 rpm: inputs `{"chainring_teeth":50,"cog_teeth":25,"rim_diameter_mm":622,"tire_width_mm":25,"cadence_rpm":90}` → `{"gear_ratio":2,"gear_inches":52.9,"development_m":4.222,"gain_ratio":3.953,"wheel_diameter_mm":672,"wheel_circumference_mm":2111,"speed_kmh":22.8,"speed_mph":14.17}`
- 53 × 11 on 700×23C at 100 rpm: inputs `{"chainring_teeth":53,"cog_teeth":11,"tire_width_mm":23,"cadence_rpm":100}` → `{"gear_ratio":4.818,"gear_inches":126.7,"development_m":10.111,"gain_ratio":9.466,"speed_kmh":60.67,"speed_mph":37.7}`

```
GET https://tttkmbb.com/api/v1/calculate/bike-gear-ratio?chainring_teeth=50&cog_teeth=25&rim_diameter_mm=622&tire_width_mm=25&cadence_rpm=90
```

## Limitations

You already know the gear ratio and wheel circumference and only need speed (use cadence-to-speed), or you need engine or machine gearing rather than bicycle gearing. Wheel diameter from bead-seat diameter plus twice the nominal tyre width is the convention of Sheldon Brown's gear calculator; real rolling diameter differs by 1–2 % with tyre casing, pressure and load. Internally geared hubs would need their stage ratio applied to gear_ratio. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What are typical gear-inch ranges?**

Road bikes span roughly 30–130 gear inches; mountain bikes 18–100; a single-speed commuter is usually 65–75 gear inches.

**Why gain ratio instead of gear inches?**

Gear inches ignore crank length. Gain ratio (distance the bike moves per distance the pedal moves) compares bikes with different cranks fairly; a gain ratio of 4 means the bike travels 4 m per metre of pedal travel.

## Related

- [Cadence to Speed Calculator](https://tttkmbb.com/fitness/cadence-to-speed.md) — Speed from cadence when the ratio and wheel circumference are already known.
- [FTP Power Zones Calculator](https://tttkmbb.com/fitness/ftp-power-zones.md) — Power targets to pair with gearing choices.
- [Speed Converter](https://tttkmbb.com/conversion/speed.md) — Convert the resulting speed to other units.