Output speed, tooth count and sprocket diameters for roller chain drives.
Example Result
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A chain drive changes speed by the ratio of its tooth counts. Put a 17-tooth sprocket on a 1,750 rpm motor and a 51-tooth sprocket on the shaft, and the shaft turns at 583 rpm with about three times the torque. This calculator does that sum, works backwards to the tooth count you need for a target speed, and gives the pitch, outside and bottom diameters of a sprocket for a chosen chain size.
Choose Output speed, Teeth for a speed, or Sprocket diameters.
Enter the driver speed and tooth counts, or the chain number and teeth.
Press Calculate.
For two chain stages, multiply the ratios, or run the calculator twice.
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A 17T to 51T drive at 1,750 rpm gives 583.3 rpm, a ratio of 3:1. An input of 20 N·m at about 98% efficiency gives roughly 58.8 N·m. Power falls slightly, and it is torque that rises. The gear ratio calculator uses the same arithmetic for gears, and the pulley speed calculator for belts, where slip makes the ratio less exact.
The average ratio of a chain is exact, but the instantaneous speed is not. The chain wraps the sprocket as a polygon, so it pulses slightly, by about 1.7% with 17 teeth and more with fewer teeth.
| Symbol | Meaning |
|---|---|
| N₁, N₂ | Teeth on the driver and driven sprockets |
| n₁, n₂ | Driver and driven speed, rpm |
| i | Reduction ratio, N₂ ÷ N₁ |
| T₁, T₂ | Input and output torque |
1Target 480 rpm from 1,450 rpm with a 19-tooth driver.
N₂ = 19 × 1,450 ÷ 480 = 57.4
57 teeth gives 483.3 rpm (+0.7%); 58 teeth gives 475.0 rpm (−1.0%)
Teeth are whole numbers, so check both neighbours. Where two stages are needed, multiply the ratios: 3:1 then 4:1 gives 12:1, so 1,750 rpm becomes 145.8 rpm. Keep the small sprocket reasonably large, since few teeth means rough running and fast wear. Many designs start from about 17 teeth.
Pitch diameter is p ÷ sin(180° ÷ N). Outside diameter is approximately p × (0.6 + cot(180° ÷ N)), and bottom diameter is pitch diameter minus the roller diameter. Outside diameter varies by maker, so use the catalogue value to check clearance. For #40 chain, p = ½ in (12.7 mm) and the roller is 0.312 in (7.92 mm). In this drive the chain moves at 17 × 0.5 × 1,750 ÷ 12 = 1,240 ft/min (6.3 m/s). For chain length and pull, go on to the chain drive speed calculator.
| Teeth | Pitch dia. | Outside dia. | Bottom dia. |
|---|---|---|---|
| 17 | 2.721 in (69.1 mm) | 2.975 in (75.6 mm) | 2.409 in (61.2 mm) |
| 51 | 8.122 in (206.3 mm) | 8.407 in (213.5 mm) | 7.810 in (198.4 mm) |
It assumes two sprockets on parallel shafts, in steady running. It does not rate the chain for power or wear, so use the maker's tables. Shaft load and keys need checking too: the shaft diameter calculator sizes the shaft for the output torque, and the keyway dimension calculator picks the key. A chain drive needs a guard. Moving chain and sprockets can trap fingers and clothing.
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