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.