Gear Ratio Calculator

Gear ratio from tooth counts for one or two stages, with output speed and output torque including efficiency.

rpm
%
Lossless is 100%. Well-lubricated spur or helical gear meshes are typically very efficient; use the manufacturer’s figure if known.
Gear ratio (input speed ÷ output speed)
3.00 : 1
Speed reduction: output turns slower with more torque.
Output speed
600.00 rpm
Output torque
30.00 N·m
Output rotation
Opposite to input (one external mesh)
Input power
1.885

Estimate generated with SortedSums: https://sortedsums.com/gear-ratio-calculator/. For informational purposes only; verify before relying on it.

Estimate only. This tool is for informational and educational purposes. Results depend on your inputs and simplifying assumptions, and are not a substitute for professional engineering, design or financial advice. Always verify with a qualified professional and applicable codes before purchasing, building or making decisions.

How it’s calculated

For meshing gears the pitch-line speed is shared, so angular speed is inversely proportional to the number of teeth. In a compound train, gears on the same shaft turn together and the stage ratios multiply. With no losses, power in equals power out (P = τω), so torque is multiplied by the same ratio that speed is divided by.

Gear ratio = ω_in / ω_out = N_driven / N_driver Two stages: ratio = (N2 / N1) × (N4 / N3) Output speed = input speed ÷ ratio Output torque = input torque × ratio × efficiency^meshes

Example: a 20-tooth pinion driving a 60-tooth gear gives a 3 : 1 reduction. At 1,800 rpm input the output turns at 600 rpm, and 10 N·m input becomes 30 N·m output if lossless (28.5 N·m at 95% mesh efficiency).

Assumes external spur/helical meshes with no slip. Idler gears change direction but not the ratio. Check the gears’ and shafts’ torque ratings separately.

Frequently asked questions

Is a 3:1 ratio a reduction or an overdrive?

With ratio defined as input speed ÷ output speed, 3:1 is a reduction: the output turns 3 times slower and (ideally) delivers 3 times the torque.

Do idler gears change the ratio?

No. An idler between driver and driven changes the direction of rotation only; its tooth count cancels out.

Why is output torque lower than ratio × input?

Every mesh loses a little power to friction. Multiply by the efficiency once per mesh.

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Sources

Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.

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