Chain Drive Speed Calculator
Calculate driven sprocket RPM, chain speed, and ratio for a roller chain drive.
Used for motorcycles, bicycles, conveyors, and industrial drives.
Chain Drive Speed Ratio
Chain drives transmit power between two toothed sprockets connected by a roller chain. Unlike belts, they cannot slip, so the speed ratio is exactly the ratio of teeth counts.
Formula
N₂ = N₁ × (T₁ / T₂)
Where:
- N₁ = drive sprocket RPM
- N₂ = driven sprocket RPM
- T₁ = drive sprocket teeth
- T₂ = driven sprocket teeth
Chain Speed
V_chain = N₁ × T₁ × pitch / 60 (m/s, with pitch in m)
Standard ANSI / ISO chain pitches:
- 1/4" = 6.35 mm (cycle, light machinery)
- 3/8" = 9.525 mm (motorcycle)
- 1/2" = 12.7 mm (most automotive cam, industrial)
- 5/8" = 15.875 mm (heavy industrial)
- 3/4" = 19.05 mm (very heavy)
Worked Example: Motorcycle 15/45
A motorcycle with a 15-tooth countershaft sprocket and 45-tooth rear sprocket at 5000 RPM countershaft:
- N₂ = 5000 × (15 / 45) = 1667 RPM (rear wheel)
- Speed ratio: 3:1
A 17-inch rear wheel turning at 1667 RPM gives a road speed of about 135 km/h — typical for a sport bike at high gear, mid-rev.
Torque Relationship
T₂ = T₁ × (T₂_teeth / T₁_teeth) × η
Chain drives have very high efficiency, typically 96–99%, so torque amplifies almost directly with the gear ratio.
Common Sprocket Ratios
| Ratio | Use Case |
|---|---|
| 1:1 | Direct drive |
| 2:1–3:1 | Most motorcycles, ATVs |
| 3:1–6:1 | Bicycles in low gear |
| 4:1–8:1 | Conveyors, light industrial |
| 8:1–15:1 | Wood chippers, augers |
Chain Length
L ≈ 2 × C / pitch + (T₁ + T₂) / 2 + ((T₂ − T₁) / (2π))² × pitch / C
where L is in pitches and C is center distance. The total physical length is L × pitch, and you should round up to an even number of pitches.
Polygon Effect
Chains do not roll perfectly smoothly — they engage sprockets in discrete steps. This causes a small periodic speed variation called the polygon effect, especially with sprockets under ~17 teeth. Using larger sprockets (≥ 19 teeth) on the smaller side smooths the drive significantly.
Caveats
Roller chains stretch over time as the pins and bushings wear, slowly increasing their effective pitch. A chain replaced when its overall length grows by ~1% — about 1 link in 100 — extends sprocket life dramatically. Lubrication and proper alignment are far more important to chain life than slight ratio adjustments.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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