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MachineCalcs

Sprocket Calculator

Sprocket ratio from tooth counts, plus the driven RPM, chain (pitch-line) speed and pitch diameters it produces. For roller-chain drives on machines, motorcycles and karts. Metric and imperial.

Inputs

rpm
mm

Results

Sprocket ratio(i) ✓
3

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

driven ÷ driver (n:1).

Driven speed(n₂)
333.3 rpm

Chain speed(v)
3.175 m/s

Pitch-line speed of the chain.

Driver pitch diameter(PD₁)
61.08 mm

Driven pitch diameter(PD₂)
182.1 mm

  • 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.

How it works

The sprocket ratio is the driven tooth count divided by the driver tooth count: i = N₂ / N₁ A ratio above 1:1 is a reduction — the output turns slower than the input but with proportionally more torque. The driven speed is n₂ = n₁ · N₁ / N₂.

The chain travels along the pitch circle at the pitch-line speed v = N₁ · p · n₁ / 60000 (pitch p in mm, n₁ in RPM, result in m/s). Each sprocket's pitch diameter — the circle the chain rollers ride on — is PD = p / sin(180° / N).

Worked example

A 15-tooth driver sprocket driving a 45-tooth driven sprocket is a 3:1 reduction. At 1,000 RPM in, the output turns about 333 RPM. With ANSI 40 chain (12.7 mm pitch) the chain speed is 15 × 12.7 × 1000 / 60000 ≈ 3.18 m/s, and the pitch diameters are ≈ 61 mm (driver) and ≈ 182 mm (driven). Those are the numbers the calculator shows for these inputs.

Frequently asked questions

How do I calculate the sprocket ratio and RPM?
The sprocket ratio is the driven (output) tooth count divided by the driver (input) tooth count: ratio = N₂ / N₁. The driven speed is n₂ = n₁ · N₁ / N₂. For example 45 driven teeth over 15 driver teeth is a 3:1 reduction, so 1,000 RPM in turns the output at about 333 RPM.
What sprocket ratio do I need for more top speed?
For more top speed, lower the ratio: use a larger front (driver) sprocket or a smaller rear (driven) sprocket. That turns the wheel faster per engine revolution. The trade is less torque, so acceleration drops. A smaller front / larger rear sprocket does the opposite — more torque and quicker acceleration, less top speed.
What is the chain or pitch-line speed?
It is how fast the chain travels along the sprocket pitch circle: v = N₁ · p · n₁ / 60000, with the pitch p in mm and n₁ in RPM, giving metres per second. It governs wear and lubrication — most roller chain is rated to roughly 5–8 m/s before special provisions are needed.
How do I calculate a sprocket pitch diameter?
PD = p / sin(180° / N), where p is the chain pitch and N the tooth count. The pitch diameter is the circle the chain rollers sit on — it is theoretical and slightly smaller than the tip (outside) diameter you measure across the teeth.
What are the common ANSI roller-chain pitches?
ANSI 40 (#40) is 12.7 mm (1/2 in), the most common general-purpose size. ANSI 35 is 9.525 mm (3/8 in), ANSI 50 is 15.875 mm (5/8 in), ANSI 60 is 19.05 mm (3/4 in), and ANSI 80 is 25.4 mm (1 in). Bicycle/kart chain is typically #35, #40 or #41.
Does this work in metric and imperial?
Yes — enter the chain pitch in mm or inches and read pitch diameters in mm or inches and chain speed in m/s or ft/min. Toggle SI/Imperial in the header.

Method & assumptions

  • No chain slip — a roller chain engages the teeth positively, so the speed ratio is exactly N₁/N₂.
  • Pitch diameter PD = p / sin(180°/N) is theoretical (the pitch circle), slightly less than the measured tip diameter.
  • Keep at least ~17 teeth on the small sprocket for smooth running and good chain life.

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