Sprocket Calculator

Inputs

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Teeth on the driver (input) sprocket — e.g. the front/engine sprocket.
Teeth on the driven (output) sprocket — e.g. the rear/wheel sprocket.
Speed of the driver sprocket.
rpm
ANSI 40 = 12.7 mm (1/2 in)
mm

Results

Default result
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Sprocket ratio(i)
3
Pass

3.00:1 — reduction (torque up, speed down).

driven ÷ driver (n:1).

Also computed

Driven speed(n₂)333.3rpm

Chain speed(v)3.175m/s

Pitch-line speed of the chain.

Driver pitch diameter(PD₁)61.08mm

Driven pitch diameter(PD₂)182.1mm

Method notes 5 notes
  • Ratio i = driven teeth ÷ driver teeth. Driven speed = driver × N₁/N₂.
  • Chain (pitch-line) speed v = N₁ · p · n₁ / 60000 (p in mm, n₁ in rpm) → m/s.
  • Pitch diameter PD = p / sin(180°/N) is theoretical (the pitch circle the chain rollers sit on), not the tip diameter.
  • A smaller driver / larger driven sprocket raises the ratio: more torque, lower output speed. For top speed do the reverse.
  • Keep at least ~17 teeth on the small sprocket for smooth running and good chain life.

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