Calculate driven sprocket RPM from tooth counts and drive speed, or the teeth needed for a target speed, with optional chain speed and wheel top speed.

Find output rotational speed from the two tooth counts and drive speed.

Chain pitch, torque and wheel speed

Adds mean chain speed and pitch diameters. Equal pitch does not establish chain/sprocket compatibility.

Blank omits torque. Zero is valid. Output torque assumes no losses.

Blank omits road speed. Assumes the wheel turns directly with the driven sprocket, with no slip.

Sprocket Speed Formula

The sprocket speed calculator finds the output speed of a chain-driven system from the input speed and the tooth counts of the driving and driven sprockets. In most applications, this is used for rotational speed such as RPM or rad/s.

V₂ = V₁ × (T₁) / (T₂)

Where:

  • V1 = input speed of the driving sprocket
  • T1 = number of teeth on the driving sprocket
  • T2 = number of teeth on the driven sprocket
  • V2 = output speed of the driven sprocket

This relationship comes from the fact that both sprockets share the same chain motion, so rotational speed changes in inverse proportion to sprocket size. A larger driven sprocket turns more slowly, while a smaller driven sprocket turns more quickly.

Rearranged Forms

If you know any three values, you can solve for the fourth:

V₁ = V₂ × (T₂) / (T₁)
T₁ = (V₂ × T₂) / (V₁)
T₂ = (V₁ × T₁) / (V₂)

How to Use the Calculator

  1. Select the value to solve for, then enter the three displayed known values.
  2. Use positive whole tooth counts for known sprockets.
  3. Select rotational-speed units and choose Calculate.
  4. For a tooth-count solve, compare the exact fractional requirement with the nearest whole count and its achieved driven speed.
  5. Optionally expand the advanced settings for chain pitch, ideal torque, or wheel speed. Wheel speed assumes direct coupling to the driven sprocket with no further gearing or slip.

The ratio formula uses rotational speed: RPM, revolutions per second, or radians per second. Linear chain speed is a separate optional result, calculated from chain pitch, tooth count, and rotational speed; m/s and ft/s are not rotational-speed input units.

What the Tooth Ratio Means

Drive Setup Effect on Output Speed Ideal Torque Result
Driving sprocket has more teeth than the driven sprocket Output rotates faster than input Higher speed, lower output torque
Driving sprocket has fewer teeth than the driven sprocket Output rotates slower than input Lower speed, higher output torque
Both sprockets have the same number of teeth Output speed matches input speed No ratio change

Example: Finding Output Speed

A driving sprocket has 15 teeth, the driven sprocket has 45 teeth, and the input speed is 180 RPM.

V₂ = 180 × (15) / (45)
V₂ = 60 RPM

The output sprocket turns at 60 RPM. In the ideal lossless model, the 45:15 tooth ratio multiplies output torque by 3; real losses reduce the available torque.

Example: Finding the Required Driven Sprocket

Suppose the input speed is 240 RPM, the driving sprocket has 12 teeth, and you want an output speed of 120 RPM. Solve for the driven sprocket tooth count.

T₂ = (240 × 12) / (120)
T₂ = 24

You would need a 24-tooth driven sprocket to cut the speed in half.

Practical Notes

  • Tooth count controls speed ratio: doubling the driven tooth count halves the output speed if the input speed stays the same.
  • Ideal speed and torque trade off: neglecting losses, output torque equals input torque multiplied by the driven-to-drive tooth ratio.
  • Ideal calculation: the formula assumes proper chain engagement, no slip, and negligible losses.
  • Real systems vary: wear, chain stretch, friction, shock loads, and alignment issues can affect actual performance.
  • Use whole tooth counts: sprocket teeth are discrete. The calculator’s illustrative comparisons do not establish availability, chain compatibility, load capacity, or safe design; verify real components separately.

Common Questions

Does a smaller driven sprocket increase speed?
Yes. If the input speed stays constant, reducing the number of teeth on the driven sprocket increases output rotational speed.
Does a larger driven sprocket reduce speed?
Yes. A larger driven sprocket turns more slowly because each revolution requires more chain travel.
Can this ratio be used for bicycles, conveyors, and machinery?
Yes. The same tooth-ratio principle applies anywhere a chain transfers motion between sprockets.
What if both sprockets are the same size?
The speed ratio is unchanged, so the output speed equals the input speed.

When This Calculator Is Most Useful

This calculator is helpful when sizing chain drives, checking drivetrain changes, estimating output shaft speed, selecting replacement sprockets, or comparing how different tooth counts affect machine performance. It is especially useful during early design and troubleshooting, when you need a quick ratio-based answer before moving on to torque, power, or pitch-line velocity calculations.