Mechanical Engineering · Worked example

Gear Ratio, Speed, and Torque: A 12-Tooth to 60-Tooth Worked Example

Calculate gear ratio, driven speed, rotation direction, and efficiency-adjusted output torque for a simple external gear pair.

By Neutron Studios LLC7 minute readPublished 2026-08-11Reviewed 2026-08-11

Why this calculation matters

A gear pair trades rotational speed for torque while preserving power only in the ideal lossless limit. Tooth count gives the kinematic ratio directly for gears with compatible pitch.

This example uses a 12-tooth driver and 60-tooth driven gear. It also includes a 90% mesh/drivetrain efficiency so ideal and practical torque are not confused.

What you will calculate

Calculate external gear ratio from tooth count.
Determine output speed and direction.
Distinguish ideal torque multiplication from efficiency-adjusted torque.
Understand what tooth-count arithmetic does not check about actual gear design.

Given values

Driver gear teeth N1 = 12
Driven gear teeth N2 = 60
Input speed n1 = 1500 rpm
Input torque T1 = 2.0 N·m
Overall efficiency for the example η = 90%
Single external gear mesh

Governing equations

Speed ratio

i = N2/N1 = n1/n2

For a simple external pair, tooth count sets the magnitude of the speed ratio.

Output speed

n2 = n1/i

The larger driven gear rotates more slowly.

Ideal torque

T2,ideal = T1 i

Ideal power conservation before losses.

Efficiency-adjusted torque

T2 ≈ T1 i η

A simple aggregate loss model.

Worked solution

1. Calculate the ratio

The driven gear has five times as many teeth as the driver, giving a 5:1 reduction.

i = 60/12 = 5.0

2. Calculate driven speed

A 5:1 reduction divides the 1500 rpm input speed by five, so the driven gear turns at 300 rpm. Because the gears mesh externally, their angular directions are opposite.

n2 = 1500/5 = 300 rpm, opposite direction

3. Calculate ideal and practical torque

Ideal torque multiplication gives 10 N·m. Applying the assumed 90% overall efficiency gives approximately 9 N·m available at the output.

T2,ideal = 2×5 = 10 N·m; T2 ≈ 10×0.90 = 9 N·m

4. Separate ratio math from gear design

The ratio calculation says nothing about tooth bending stress, contact stress, module/diametral pitch, center distance, undercut, lubrication, bearing load, shaft strength, backlash, noise, or dynamic factors. Those belong to the mechanical design stage.

Result

Engineering interpretation

The 12T-to-60T pair provides a 5:1 reduction: 1500 rpm becomes 300 rpm, rotation reverses once, ideal torque rises from 2 to 10 N·m, and the example 90% efficiency gives about 9 N·m output torque.

A multi-stage train multiplies stage ratios, while direction depends on the number of external meshes and any idlers.

Sanity checks

For a reduction gear pair, output speed should decrease as output torque increases.
Ideal input and output mechanical power should match before efficiency is applied.
An idler gear can change direction without changing the magnitude of the overall ratio when used between fixed driver and driven gears.
Compatible pitch/module and center distance must be checked before two gears can physically mesh.

Common mistakes

Inverting N2/N1 and predicting a speed increase instead of reduction.
Forgetting that each external mesh reverses rotation direction.
Multiplying torque by ratio without accounting for losses.
Using tooth count alone as proof that a gearset is mechanically strong enough.

References and model boundaries

Gear kinematic relationships from standard machine-design references.
Strength and durability require geometry, materials, loads, quality, lubrication, and applicable gear-design methods beyond the ratio calculation.

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