Gear Ratio Calculator

Enter tooth counts to get the gear ratio, output speed and output torque, for one or two stages.

On the input (motor) shaft.
On the output shaft.
Second Stage (Optional)
For a compound train: a gear on the same shaft as the first driven gear drives a fourth gear.
Spur and helical gears run about 97% to 99%.
Fractions and decimals both work.
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Ratio
Type
Output speed
Output torque
Output direction
Speed multiplier
Written As

Saved Gear Sets

Items you add are saved in this browser.

NameTeethRatioOutput RPMRemove

How to Calculate Gear Ratio

Gear ratio is the driven gear's teeth divided by the driving gear's teeth. A ratio above 1 is a reduction: the output turns slower and with more torque. In a compound train, multiply the ratios of each stage.

Ratio = driven teeth ÷ driving teeth   Compound: ratio₁ × ratio₂
Output RPM = input RPM ÷ ratio   Output torque = input torque × ratio × efficiency

Power (torque times speed) stays the same through ideal gears, less a little friction at each mesh. Two meshing gears turn in opposite directions; each added mesh flips the direction again.

Worked Example

Tips

Ratios are often written as 3:1 for a reduction (three input turns per output turn). An idler gear between two gears changes the direction but not the ratio. Worm gears are far less efficient than spur gears, often 50% to 90%, so enter a lower efficiency for them.