Chain Drive Speed Calculator

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

Road speed from that is a common place to go wrong. A “17-inch wheel” is a 17-inch rim, and the bike rolls on the tyre, not the rim. A 180/55-ZR17 rear has a 99 mm sidewall, so the rolling diameter is 431.8 + 2 × 99 = 630 mm, and the circumference is 1.98 m rather than the 1.36 m the bare rim would give.

At 1667 RPM that works out to 1667 × 1.98 × 60 ÷ 1000 ≈ 198 km/h, not the 135 you get from the rim alone. Using rim diameter understates road speed by about a third, and it is the single most common error in gearing arithmetic.

Torque Relationship

τ₂ = τ₁ × (T₂ / T₁) × η

Here τ is torque and T is still the tooth count, so the driven shaft gains torque in exactly the proportion it loses speed.
Chain drives run at 96–99% efficiency, so η barely dents that.

Common Sprocket Ratios

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 the sprocket in discrete steps, the way a chain wraps a polygon rather than a circle. 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. Replace the chain once its overall length has grown by about 1%, which is roughly one link in a hundred.
Doing it at that point rather than later extends sprocket life dramatically, because a stretched chain rides high on the teeth and files them into hooks. Lubrication and proper alignment are far more important to chain life than slight ratio adjustments.