Gear Ratio Calculator

Gears trade speed for turning force, and the gear ratio is exactly how much. A reduction, more teeth out than in, slows the output and multiplies the torque by the same number. This gives you the ratio from the two tooth counts, and if you add an input speed and torque, the output speed and the torque at the other end.

The ratio is just the tooth counts

Divide the driven gear's teeth by the driving gear's teeth and you have the ratio. Sixty teeth driven by twelve is five to one, a reduction. The output turns once for every five turns of the input, and in exchange the output carries five times the torque. If the driven gear has fewer teeth than the driving one, it is an overdrive: faster output, less torque. Pitch diameters give the same ratio if you would rather measure than count.

Speed down, torque up, in step

A gear reduction does not create energy, it trades one thing for another. Slow the output by a factor and you raise its torque by the same factor, less a little to friction. That is the whole reason geared motors exist: a fast, weak motor becomes a slow, strong drive. When you size a drive, decide whether you need speed or force at the output and pick the ratio that gets you there, because you cannot have more of both from the same motor.

Compound trains multiply

One gear pair can only reduce so far before the big gear gets unwieldy. A compound train stacks stages, and the ratios multiply: two three-to-one stages give nine to one, three of them give twenty-seven. That is how a small planetary gearbox packs a large reduction into a short can. To find a train's overall ratio, work out each pair and multiply them together.

Idlers change direction, not ratio

An idler gear between the driving and driven gears flips the output's direction of rotation but does not change the ratio at all, because its teeth cancel out of the math. People add idlers to reverse a wheel's spin or to bridge a gap between two shafts. So count only the input and the final output gear for the ratio, and treat anything in between as there for direction or spacing.

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