Gear Ratio Output Torque

Q: How do you calculate Gear Ratio Output Torque?

Use the formula τout = τin × N × η. A gear train multiplies torque by the gear ratio N while dividing speed by the same ratio, with efficiency losses reducing the actual output. Enter the values you know in the calculator above and it solves for the remaining variable.

Q: What is the formula for Gear Ratio Output Torque?

The Gear Ratio Output Torque formula is τout = τin × N × η, where τout—Output torque (N·m); τin—Input torque from motor (N·m); N—Gear ratio (output teeth / input teeth); η—Gear train efficiency (0 to 1).

τout = τin × N × η

Quick answer

This calculator solves τout = τin × N × η for Output Torque. With Input Torque 2.2 N·m, Gear Ratio 0.5, Efficiency 1.1, the result is 1.21 N·m. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Input Torque

Gear Ratio

Efficiency

Output Torque (N·m)

—

Formula

τout = τin × N × η

Description

A gear train multiplies torque by the gear ratio N while dividing speed by the same ratio, with efficiency losses reducing the actual output. A gear ratio of 10:1 means the output shaft rotates 10 times slower but with 10 times more torque (minus losses). The output speed is ωout = ωin / N. Gear efficiency depends on the type: spur gears 95-98%, helical gears 96-99%, worm gears 50-90% (highly dependent on lead angle), planetary gears 90-97% per stage. Multi-stage gearboxes multiply both ratios and efficiencies.

Variables

τout — Output torque (N·m)
τin — Input torque from motor (N·m)
N — Gear ratio (output teeth / input teeth)
η — Gear train efficiency (0 to 1)

Practical Notes

Backlash (the play between gear teeth) affects positioning accuracy and is critical for servo applications. Zero-backlash gearboxes (harmonic drives, cycloidal reducers) are used in robotics. For high reduction ratios, multi-stage planetary gearboxes or harmonic drives (100:1+ in a single stage) are preferred over spur gear trains. Always account for the reflected inertia: J_reflected = J_load / N².

Symbols and units

Symbol	Meaning	Default unit	Accepted units
tauOut	Output Torque	N·m	N·m, mN·m
tauIn	Input Torque	N·m	N·m, mN·m
N	Gear Ratio	—	—
eta	Efficiency	—	—, %

Step by step

1. What you know: Input Torque 2.2 N·m, Gear Ratio 0.5, Efficiency 1.1
2. The relation: τout = τin × N × η
3. Substitute: tauIn = 2.2 N·m, N = 0.5, eta = 1.1
4. Result: Output Torque = 1.21 N·m

Worked examples

Minimum range

Given: Input Torque 11 mN·m, Gear Ratio 0.025, Efficiency 5.5 %

Result: Output Torque = 0.01513 mN·m

Low range

Given: Input Torque 110 mN·m, Gear Ratio 0.25, Efficiency 0.55

Result: Output Torque = 15.13 mN·m

Typical

Given: Input Torque 2.2 N·m, Gear Ratio 0.5, Efficiency 1.1

Result: Output Torque = 1.21 N·m

High range

Given: Input Torque 110 N·m, Gear Ratio 0.8, Efficiency 1.76

Result: Output Torque = 154.9 N·m

Maximum range

Given: Input Torque 1100 N·m, Gear Ratio 8, Efficiency 17.6

Result: Output Torque = 154900 N·m

Solving for each variable

Solve for Output Torque

Input Torque 11 mN·m, Gear Ratio 0.025, Efficiency 5.5 % → 0.01513 mN·m

Solve for Input Torque

Output Torque 5 mN·m, Gear Ratio 0.025, Efficiency 5.5 % → 3.636 N·m

Solve for Gear Ratio

Output Torque 5 mN·m, Input Torque 11 mN·m, Efficiency 5.5 % → 8.264

Solve for Efficiency

Output Torque 5 mN·m, Input Torque 11 mN·m, Gear Ratio 0.025 → 18.18

How Output Torque changes with Input Torque

Input Torque (input)	Output Torque (result)
0.22 N·m	121 mN·m
0.55 N·m	0.3025 N·m
1.1 N·m	0.605 N·m
1.65 N·m	0.9075 N·m
2.2 N·m	1.21 N·m
3.3 N·m	1.815 N·m
4.4 N·m	2.42 N·m
8.8 N·m	4.84 N·m
15.4 N·m	8.47 N·m
22 N·m	12.1 N·m

The same result in other units

Unit	Value
N·m	1.21
mN·m	1210

Embed this calculator

Paste this into any page. It keeps working when this page updates, and credits the source.

<iframe src="https://vbatpower.com/embed/gear-ratio/" width="100%" height="460" style="border:1px solid #1f2a37;border-radius:12px" loading="lazy" title="Gear Ratio Output Torque"></iframe>
<p><a href="https://vbatpower.com/formulas/gear-ratio/">Gear Ratio Output Torque</a> Calculator by vbatpower.com</p>

Frequently asked questions

How do you calculate Gear Ratio Output Torque?

Use τout = τin × N × η. With Input Torque 2.2 N·m, Gear Ratio 0.5, Efficiency 1.1, Output Torque works out to 1.21 N·m.

How do you calculate output torque = motor torque × gear ratio × η?

Rearrange for Output Torque: with Input Torque 110 mN·m, Gear Ratio 0.25, Efficiency 0.55, Output Torque is 15.13 mN·m.

What is the formula for Gear Ratio Output Torque?

The formula is τout = τin × N × η. A gear train multiplies torque by the gear ratio N while dividing speed by the same ratio, with efficiency losses reducing the actual output.

How do you find Input Torque when you know the other values?

Rearrange for Input Torque: with Output Torque 5 mN·m, Gear Ratio 0.025, Efficiency 5.5 %, Input Torque is 3.636 N·m.

How do you find Gear Ratio when you know the other values?

Rearrange for Gear Ratio: with Output Torque 5 mN·m, Input Torque 11 mN·m, Efficiency 5.5 %, Gear Ratio is 8.264.

What units does Gear Ratio Output Torque use?

Output Torque is shown in N·m, mN·m. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Motors & Mechanical formulas →

Motor Mechanical Power Motor Torque Motor Speed Gear Ratio Output Torque Back-EMF Voltage Motor Efficiency Rotational Dynamics Stepper Motor Step Angle

Need more features?

Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.

Try the App