Speed ratio, output speed and torque multiplication for a two-gear drive from the tooth counts and input speed.
Page last changed 2026-10-19 · based on n/a — standard engineering relationships, no single governing revision
Quick Answer
Gear ratio is N_driven ÷ N_driver. A 12-tooth driver into a 36-tooth gear gives a 3:1 reduction — output speed is one third and output torque three times the input (ignoring losses). Power is unchanged.
Gear Ratio and Output
The Formulas Used
Gear ratio: i = n₂ ÷ n₁ (driven teeth ÷ driver teeth) Output speed: n_out = n_in ÷ i Output torque: T_out = T_in × i × η where η is the drive efficiency
Torque Multiplies, Power Does Not
A gear pair trades speed for torque. Whatever the ratio, the power through the drive is unchanged — that is the conservation of energy. A 3:1 reduction gives three times the torque at one third the speed, and the product is the same.
That is why a gearbox cannot create capacity, only reshape it. If a motor is too small for a load, gearing it down will let it move a heavier load slower, but it cannot make the job go faster. And because every stage has losses — typically 1 to 3% per mesh for spur gears — a multi-stage box delivers slightly less power out than in, never more.
Frequently Asked Questions
How do I calculate gear ratio?
Divide the driven gear's tooth count by the driver's. A 12-tooth driver into a 36-tooth gear is 36/12 = 3, written 3:1. Output speed is input speed divided by the ratio, and output torque is input torque multiplied by it.
Does a gearbox increase power?
No. It trades speed for torque, and the product — power — is unchanged apart from losses. A reduction gear gives more torque at lower speed; the power output is always slightly less than the input because of friction in the mesh and bearings.
What is the difference between a gear ratio and a gear train?
A gear ratio describes one pair of gears. A gear train is several pairs in series, and the overall ratio is the product of the individual ratios. Idler gears in a train change the direction and the spacing but not the overall ratio.
How do I work out compound gear ratios?
Multiply the individual stage ratios. A 3:1 stage followed by a 4:1 stage gives 12:1 overall. Compound trains are used when a single pair would need an impractically large gear — the same ratio is achieved in a much smaller envelope.
What efficiency should I assume?
About 98–99% per mesh for spur gears, 95–98% for helical, and lower for worm drives — a single-start worm can be under 50%. Add bearing losses of about 1% per shaft. A multi-stage gearbox's overall efficiency is the product of the stage efficiencies.
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