# Gear Ratio Calculator

> Calculate gear ratio step by step: Ratio = driven teeth ÷ driving teeth.

Page: https://freecalculator.tech/tools/gear-ratio-calculator
Last reviewed: 2026-11-03

## Formula

Ratio = driven teeth ÷ driving teeth. Output torque = input torque × ratio (ideal).

- Tooth counts must be positive whole numbers.
- Ideal gears — no friction losses.
- Idler gears do not change the ratio.
- Ratio = driven teeth ÷ driving teeth. Output torque = input torque × ratio (ideal).
- Inputs used: Driving gear teeth, Driven gear teeth, Input torque (optional).

## Inputs

- Driving gear teeth
- Driven gear teeth
- Input torque (optional)

## Worked example: 12-tooth pinion driving a 36-tooth gear

Speed reduction.
1. Ratio = 36 ÷ 12 = 3 : 1.

## Common questions

### Does a higher ratio mean more torque?

Yes. A 3 : 1 reduction triples torque (minus losses) and cuts speed to a third.

### What about compound gear trains?

Multiply the ratio of each stage together to get the overall ratio.

### Do idler gears matter?

They reverse direction but do not change the overall ratio.

### How do I use the Gear Ratio Calculator?

Enter the required values for Driving gear teeth, Driven gear teeth, Input torque (optional). The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Gear Ratio Calculator use?

Ratio = driven teeth ÷ driving teeth. Output torque = input torque × ratio (ideal). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

### Can the Gear Ratio Calculator be used for exact decisions?

Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.

## Limitations and assumptions

- Single stage.
- Friction losses ignored.
- Does not check gear strength or meshing.
- Results are estimates for planning and learning. Real designs, installations and bids must be checked by a qualified, licensed professional against the codes that apply where you work.
- The result depends on the values you enter for this gear ratio calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- OpenStax (Rice University) — https://openstax.org/details/books/university-physics-volume-1

## Cite this page

- APA: Free Calculator. (2026, November 3). Gear Ratio Calculator. https://freecalculator.tech/tools/gear-ratio-calculator
- MLA: "Gear Ratio Calculator." Free Calculator, 3 Nov. 2026, https://freecalculator.tech/tools/gear-ratio-calculator.
- Link: Gear Ratio Calculator — Free Calculator, https://freecalculator.tech/tools/gear-ratio-calculator