Gear Ratio Calculator

How to use the Gear Ratio Calculator

1. 1Enter the teeth on the driving gear, the teeth on the driven gear and the input speed.
2. 2Pick the units or options from the menus if the gear ratio tool offers them.
3. 3Read the gear ratio in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the gear ratio

Bicycles, clocks, gearboxes, winches and robots all use gear ratios. Makers choose the ratio of a motor gearbox to get the speed and the pulling power they need, and bike riders compare the chainring and sprocket to choose an easy climbing gear.

For a train of several gear pairs, multiply the ratios together. Each meshing pair also reverses the direction of rotation, so an even number of pairs gives output in the same direction as the input.

How the gear ratio is worked out

Gear ratio = driven teeth ÷ driving teeth. Output speed = input speed ÷ ratio. Output torque = input torque × ratio, less friction losses. A 20-tooth gear driving a 60-tooth gear has a ratio of 3 : 1. At 1,500 rpm in, the output turns at 500 rpm with three times the torque. Swap them and the 60-tooth gear drives the 20-tooth one: 600 rpm becomes 1,800 rpm with one third of the torque.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Speed, torque and ratio
• Reduction or overdrive label
• Whole teeth only

Mistakes to avoid with gear ratio

The tooth counts must be whole numbers, and both gears must share the same tooth size, or they would not mesh. The torque figure is the ideal one; real gear pairs lose a few percent to friction. The result for chains and belts is the same, using the number of teeth on the sprockets or pulleys.

On phone and computer

On a phone, type into the boxes one after another and read the gear ratio underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the gear ratio move. The gear ratio calculator works the same on both. Use Torque Calculator for the turning force, Speed Calculator for the final speed, Horsepower Calculator for power, and Torque Converter for unit changes.

Features

• Multiply ratios for gear trains
• Direction flips at each mesh
• Friction costs a few percent
• Clear messages when the gear ratio inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions