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ChainSprocketCalc

Sprocket Ratio Calculator for Compound Chain Drives

Add up to three chain stages and get the total ratio, output speed, ground speed and estimated launch thrust, with a hunting-tooth check on the first stage.

Presets

Chain Stages

Stage 1: 5:1
Driver (Nin)
T
Driven (Nout)
T
Input RPM
Gearbox ratio

Vehicle & thrust (optional)

Engine torque
Nm
Total weight
kg
Rear tire diameter (0 = none)
in

Total Sprocket Ratio

5:1

Overall final drive:5:1

Output Shaft Speed

720rpm

Efficiency:96% (1 stage)

Top Ground Speed

23.6mph

Metric:38 km/h

Wheel Torque

57.6Nm

After chain losses

Tractive Force

412.3N

At the tire contact

Launch Thrust

0.323G

Thrust ÷ weight

Estimates, not measurements

Thrust uses peak engine torque at the wheel and ignores traction limits, clutch slip, rolling and air resistance. Chain speed is 2250 ft/min at the first stage; chain makers pick a lubrication method from chain size and rpm, and speed alone points to: Type C: Forced-Feed Oil Stream Lubrication (High Speed).

Stage 1 hunting-tooth matrix (GCD 12)

Select a cell to load those tooth counts. GCD 1 pairs spread wear across more tooth pairs, which is a screening aid rather than a guarantee.

Ratio and common divisor for tooth counts around stage 1
Driver \ Driven58T59T60T61T62T
10T
11T
12T
13T
14T

How to Calculate a Compound Chain Ratio

Each chain stage multiplies the ratio by its driven-to-driver tooth count. When the target is a speed rather than a ratio, solve for the missing sprocket with the missing tooth sprocket size solver.

The formulas

Total = (N₂ / N₁) × (N₄ / N₃) × …
Output rpm = Input rpm / (Total × Gearbox)
Speed (mph) = Output rpm × tire Ø (in) / 336.1
N1
= driver teeth, N₂ the driven teeth of the same stage
Gearbox
= gearbox or CVT reduction, 1 if none

Worked example: mini bike

  1. Stage 1: 30 / 10 = 3.000:1
  2. Stage 2: 54 / 14 = 3.857:1
  3. Total = 11.57:1
  4. At 3600 rpm: 311 rpm out
  5. On a 14.5 in tire: 13.4 mph

Chain Speed and Efficiency

Chain speed is the driver sprocket's teeth × pitch × rpm, and it matters for lubrication and noise. Roller chain drives are commonly estimated at about 96% efficiency per stage, so each extra stage costs a few percent of output torque. To check speeds against a vehicle, use the sprocket speed calculator.

Why efficiency compounds

Two stages at 96% give about 92% overall (0.96 × 0.96), and three give about 88%. This calculator applies that to wheel torque.

Lubrication

Higher chain speeds call for oil bath or oil stream lubrication rather than manual oiling. Manufacturers choose the method from chain size and sprocket rpm, so use their chart for the final decision.

Sprocket Ratio FAQ

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