Work out shaft speed (rpm) instantly with clear inputs, formula shown and shareable results.
A driven roller converts rotation to linear motion at its circumference, so rpm is linear speed times 12 divided by pi times the diameter in inches. Multiplying by the gearbox ratio gives the motor speed to specify, and angular velocity in radians per second is the form needed for torque and inertia calculations.
Shaft speed
rpm = linear speed fpm x 12 / (pi x diameter in)
Motor speed
Motor rpm = shaft rpm x gear ratio; omega = 2 pi rpm / 60
rpm = linear speed fpm x 12 / (pi x diameter in). A driven roller converts rotation to linear motion at its circumference, so rpm is linear speed times 12 divided by pi times the diameter in inches.
Yes. The effective diameter is the roller plus the belt or coil thickness, so a thick belt raises linear speed by a few percent for the same shaft rpm.
This calculator takes 3 inputs: Required linear speed, Roller or drum diameter, Gear reduction ratio. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.