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Shaft Speed (RPM) Calculator

Work out shaft speed (rpm) instantly with clear inputs, formula shown and shareable results.

About Shaft Speed (RPM) Calculator

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.

Formulas

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

Worked example

With the default values below, Shaft Speed (RPM) Calculator returns Shaft speed required of 254.65. Change any input above and every figure here is recalculated in your browser.

Inputs used

Required linear speedminimum 0.1 fpm
400 fpm
Roller or drum diameterminimum 0.1 in
6 in
Gear reduction ratiominimum 0.1
1.5

Results

Shaft speed required
254.65 rpm
Motor speed required
382.0 rpm
Angular velocity
26.667 rad/s
Surface speed in metric units
2.032 m/s

Step by step

  1. 1Values used
  2. 2Shaft speed
  3. 3Motor speed
  4. 4Shaft speed required= 254.65 rpm
  5. 5Motor speed required= 382.0 rpm
  6. 6Angular velocity= 26.667 rad/s
  7. 7Surface speed in metric units= 2.032 m/s

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Shaft Speed (RPM) figure worked out?

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.

Does belt or material thickness matter?

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.

What values do I need to enter?

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.

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