Spur gear calculator
A gear is defined by its module and tooth count; every diameter follows from those two.
mm
degrees
Centre distance
80.000mm
- Gear ratio
- 3.0000
- Pinion pitch diameter
- 40.000
- Wheel pitch diameter
- 120.000
- Pinion outside diameter
- 44.000
- Wheel outside diameter
- 124.000
- Pinion root diameter
- 35.000
- Pinion base circle diameter
- 37.588
- Circular pitch
- 6.2832
- Equivalent diametral pitch
- 12.7000
- Tooth thickness at the pitch line
- 3.1416
Show the working
- Module = 2
- Teeth on the pinion = 20
- Teeth on the wheel = 60
- Pressure angle = 20
- Pinion pitch diameter = 2 * 20 = 40
- Wheel pitch diameter = 2 * 60 = 120
- Pinion outside diameter = 2 * (20 + 2) = 44
- Wheel outside diameter = 2 * (60 + 2) = 124
- Pinion root diameter = 2 * (20 - 2.5) = 35
- Centre distance = 2 * (20 + 60) / 2 = 80
- Gear ratio = 20 > 0 ? 60 / 20 : 0 = 3
- Circular pitch = pi * 2 = 6.283 19
- Equivalent diametral pitch = 2 > 0 ? 25.4 / 2 : 0 = 12.7
- Pinion base circle diameter = 40 * cos(rad(20)) = 37.5877
- Tooth thickness at the pitch line = pi * 2 / 2 = 3.141 59
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- pitch diameter = module x teeth
- outside diameter = module x (teeth + 2)
- root diameter = module x (teeth - 2.5)
- centre distance = module x (teeth1 + teeth2) / 2
Below about 17 teeth at a 20-degree pressure angle the teeth undercut unless the profile is shifted.
Module and diametral pitch are reciprocal: module = 25.4 / DP.