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Gear ratios


Equation

A gear ratio compares how many times one gear turns relative to another.

It’s written as a fraction:

Calculating Gear Ratios

Gear Ratio = Number of teeth on output gear ÷ Number of teeth on input gear


So, if a gear with 10 teeth (input) turns a gear with 20 teeth (output):

Gear Ratio = 20⁄10 = 2⁄1

This means:

  • The input gear must spin 2 times for the output gear to spin once
  • The output gear spins slower, but with more torque


Likewise, if the input gear has 20 teeth and the output has 10 teeth:

Gear Ratio = 10⁄20 = 1⁄2

This means:

  • The output gear spins twice as fast, but with half the torque

Gear Ratio Efficiency

  • Higher ratio (>1) = more torque, less speed
  • Lower ratio (<1) = more speed, less torque

Gear Ratios Media

  • Two meshed spur gears showing tangent contact between their pitch circles, each illustrated with broken blue lines; the gear on the left has 10 teeth and the gear on the right has 15 teeth.

  • Spur gear tooth dimensions and how they are measured:t = tooth thickness, along the pitch circle*p = circular pitch, along the pitch circle*a = addendum, radially*b = dedendum, radiallyIn this example, the gear has 20 teeth.

  • Two meshing gears transmit rotational motion; note difference in rotational speeds is equal to the reciprocal of the ratio between the number of teeth on the two gears

  • Two meshed spur gears, with a 2:1 ratio

  • Gear train with an idler gear in the middle which does not affect the overall gear ratio but reverses the direction of rotation of the gear on the right.

  • 2 gears and an idler gear on a piece of farm equipment, with a ratio of 42:13 = 3.23:1

  • Two sets of gears. z1=14 (red); z2=42 (blue); z3=14 (yellow); z4=28 (green).

  • Bicycle with toothed belt drive to transmit torque from crank to rear sprocket

  • Cutaway illustration of gears of an automotive transmission

  • Valve timing gears on a Ford Taunus V4 engine — the small gear is on the crankshaft, the larger gear is on the camshaft. The crankshaft gear has 34 teeth, the camshaft gear has 68 teeth and runs at half the crankshaft RPM.(The small gear in the lower left is on the balance shaft.)

References


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