Gear Ratio Calculator

Formula

• Gear ratio = Driven teeth ÷ Driver teeth
• Output RPM = Input RPM ÷ Gear ratio
• Output torque = Input torque × Gear ratio × Efficiency

About this calculator

Part of our Mechanical Calculators collection. Beams, bolts, springs, gears, bearings, and core ME calculations.

How it works

Gear ratio equals driven teeth divided by driver teeth. Output speed equals input speed divided by the ratio. Output torque equals input torque times the ratio times efficiency. Use this for first-pass drive sizing before detailed gear design.

Enter your values in the inputs above and click CALCULATE. Results appear on the right without a page reload. No login and no server upload.

Worked example

A 20-tooth pinion drives a 60-tooth gear at 1450 rpm with 10 N·m input torque and 100% efficiency.

1. Ratio = 60 ÷ 20 = 3.0
2. Output RPM = 1450 ÷ 3 = 483 rpm
3. Output torque = 10 × 3 = 30 N·m

Result: Gear ratio 3.0, output 483 rpm, output torque 30 N·m, speed reduction 66.7%.

When to use

• First-pass check of a two-gear speed reducer
• Verifying replacement gear tooth counts
• Estimating output torque before motor sizing

Limitations

• Single gear pair only (no multi-stage trains yet)
• Spur/external gears with parallel shafts assumed
• Does not check tooth bending or contact stress

FAQ

What does a 3:1 gear ratio mean?

The driver turns three times for every one turn of the driven gear. Output speed is one-third of input speed, and ideal output torque is three times input torque.

Which gear teeth count goes first?

This calculator uses driven teeth divided by driver teeth. Driver is the input gear; driven is the output gear.

How does efficiency affect torque?

Output torque equals input torque times the ratio times efficiency. At 95% efficiency, some torque is lost to friction and heat.