Enter the teeth on two gears, a known ratio, or the input and output speeds, and get the gear ratio, the output speed and the output torque. Add a second stage for a two-stage reducer and an efficiency to allow for losses. It is the standard gear relationship; nothing is looked up from a table.
Worked example
These are example values. Change any entry above and press Calculate to run your own numbers.
Gear ratio
3 : 1
What it does
Speed reduction: the output turns 3 times slower and, ideally, with 3 times the torque.
Output speed
583.33 rpm
Output torque
28.5 N·m (21.021 lbf·ft)Input torque x ratio x efficiency
Input power
1.833 kW (2.458 hp)
Output power
1.741 kW (2.335 hp) Input power x efficiency; the rest is lost as heat
Speed is divided by the ratio and torque is multiplied by it, so power is conserved apart from the losses set by the efficiency you enter.
How it works
A gear ratio tells you how a gear pair or a gearbox trades speed for torque. The output turns slower than the input by the ratio, and, apart from losses, produces more torque by the same factor. The same arithmetic applies to chain sprockets and belt pulleys, using tooth counts or diameters.
The formulas
Gear ratio = driven gear teeth ÷ driver gear teeth
Gear ratio = input speed ÷ output speed
Output speed = input speed ÷ ratio
Output torque = input torque × ratio × efficiency
Two stages: overall ratio = stage 1 ratio × stage 2 ratio
Power (kW) = torque (N·m) × speed (rpm) ÷ 9,549
Frequently asked questions
How do you calculate a gear ratio?
Divide the number of teeth on the driven (output) gear by the number of teeth on the driver (input) gear. A 20-tooth driver turning a 60-tooth gear is a 3 : 1 ratio. For a gearbox you can also divide the input speed by the output speed: 1,750 rpm in and 350 rpm out is 5 : 1.
Does a higher gear ratio mean more torque?
Yes, at the cost of speed. A 3 : 1 reduction turns the output at one third of the input speed and, ideally, multiplies the torque by three. Power stays the same apart from losses, which is why the calculator multiplies torque by the efficiency you enter. The strength of the gears still limits the torque you can use, so the gearbox rating governs, not this formula.
How do I find the ratio of a two-stage gearbox?
Multiply the ratio of each stage. A 3 : 1 first stage followed by a 4 : 1 second stage gives 12 : 1 overall, so a 1,200 rpm input becomes 100 rpm at the output.
What efficiency should I use?
It depends on the gear type, the ratio and the load, and the manufacturer's datasheet is the right source. Spur and helical gear sets generally lose less than worm gears, and worm gear efficiency falls as the ratio rises. Enter 100 for an ideal figure, then lower it to see how losses reduce the output torque and power.
Does the output turn in the same direction as the input?
A single external gear pair reverses the direction of rotation. An idler gear between them restores it without changing the ratio. Planetary and some in-line gearboxes are built to keep input and output rotation the same. Check the gearbox drawing when direction matters.
Can I use this for chains, belts and pulleys?
Yes. Use the sprocket tooth counts or the pulley diameters in place of gear teeth: the ratio is driven size divided by driver size, and the speed and torque relationships are the same. Belt slip and chain losses reduce the real result slightly.
