Almighty Calculator

Pulley and Sprocket RPM Calculator

Driven RPM = driver RPM × driver size ÷ driven size, using pulley diameters or sprocket tooth counts.

RPM
Motor or engine speed.
in or teeth
Pulley diameter (any unit) or sprocket teeth. Use the same unit for the driven size.
in or teeth
Used when finding the driven speed.
RPM
Used when finding the driven size.
Driven speed
875RPM
Driven size8 in or teeth
Speed ratio (driver : driven)2 :1
Ideal torque multiplication2 ×

The driven shaft turns slower than the driver, so it gains torque.

Show the math

Driven speed = driver RPM × driver size ÷ driven size
= 1,750 × 4 ÷ 8 = 875 RPM
Speed ratio = 1,750 ÷ 875 = 2 : 1

Rounded the same way as the result above.

How it works

A belt or chain moves at one speed around both wheels, so the speed of each shaft times the size of its pulley is the same. That is why a small pulley driving a big one slows the shaft down and a big one driving a small one speeds it up.

For belts, use pulley diameters, measured at the pitch line for a precise answer. For chains, use tooth counts of the two sprockets. The same size ratio gives the same speed ratio. Ideal torque changes by the opposite ratio; friction and slip reduce real output.

N₂ = N₁ × D₁ ÷ D₂ D₂ = N₁ × D₁ ÷ N₂ Speed ratio = N₁ ÷ N₂

Worked example

A 1,750 RPM motor with a 4 in pulley driving an 8 in pulley:

  1. Driven speed = driver RPM × driver size ÷ driven size
  2. = 1,750 × 4 ÷ 8 = 875 RPM
  3. Speed ratio = 1,750 ÷ 875 = 2 : 1
InputValue
FindDriven speed
Driver speed1750 RPM
Driver size4 in or teeth
Driven size (find speed)8 in or teeth
Target driven speed (find size)875 RPM
ResultValue
Driven speed875 RPM
Driven size8 in or teeth
Speed ratio (driver : driven)2 :1
Ideal torque multiplication2 ×

Assumptions and limits

  • No belt slip. Real V-belts slip a little, so measured speed can be slightly lower.
  • Belt drives use the pitch diameter, which is slightly less than the outside diameter of a V-belt pulley. Enter the value you have consistently for both wheels.
  • A single stage. For a compound drive, apply each stage in turn.

Common questions

How do I calculate pulley speed?

Multiply the driver RPM by the driver pulley diameter and divide by the driven pulley diameter.

How do I pick a pulley for a target RPM?

Use the “Driven size for a target speed” option: it gives the driven size from the driver speed, driver size, and target speed.

Does it work for sprockets?

Yes. Enter tooth counts instead of diameters; the ratio is the same.

Why does the speed drop when torque rises?

Power is torque times speed. A slower shaft carries more torque for the same power, ignoring losses.

Sources

  • Belt and chain drive kinematics: driver speed × driver size = driven speed × driven size (no-slip assumption), as in standard machine design texts.

Updated 2026-09-30