Gear Ratio Calculator
Gear ratio, output speed and torque multiplication from tooth counts, plus spur gear dimensions from module
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Calculates the gear ratio, whether it is a reduction or a speed increase, the output speed and the direction of rotation from tooth counts, and finds spur gear pitch diameters and centre distance from the module or diametral pitch. It also covers bicycle gearing and wheel speed.
How to use
- On "Gear ratio", enter the "Input speed", "Driving gear teeth" and "Driven gear teeth" to see the ratio and "Output speed".
- For a compound train, press "Add stage". Enter the number of idler gears if there are any between a pair.
- On "Spur gear dimensions", enter the module (or diametral pitch) and both tooth counts to see the diameters and centre distance. Below, you can find tooth pairs for a given centre distance and ratio.
- On "Chain, bicycle and wheel speed", enter chainring and cog teeth and the wheel diameter to get the distance per pedal turn and the speed.
How it works
- Gear ratio = driven gear teeth ÷ driving gear teeth, and output speed = input speed ÷ ratio. For a compound train, the stage ratios are multiplied.
- Torque multiplication is the ideal value without losses; real gearboxes deliver less. Gear strength, life and efficiency are not calculated.
- Dimensions are for standard spur gears without profile shift (20° pressure angle, ISO 53 basic rack). A warning about undercut appears below about 17 teeth.
Questions and answers
- How do I calculate a gear ratio?
- Divide the driven gear's teeth by the driving gear's teeth. A 20-tooth gear driving a 60-tooth gear gives a 3 : 1 reduction, so 1,500 rpm in becomes 500 rpm out.
- How much torque does a 3 : 1 reduction give?
- Three times the input torque if there are no losses. In practice friction makes it somewhat less.
- Does an idler gear change the ratio?
- No. Its tooth count cancels out. Each idler only reverses the direction of the output.
- How do I find the centre distance of two gears?
- Centre distance = module × (teeth 1 + teeth 2) ÷ 2. With module 2 and gears of 20 and 40 teeth, the pitch diameters are 40 mm and 80 mm and the centre distance is 60 mm.