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engineering

RPM Calculator

Find a shaft or wheel’s rotational speed from its surface speed and diameter.

Rotational speed
954.93 rpm
rpm = v ÷ (π · D) × 60. At 10 m/s on a 200 mm diameter shaft.
Angular velocity
100 rad/s
Shaft diameter
200 mm

How it works

  1. 1Enter the surface (linear) speed at the rim of the shaft or wheel.
  2. 2Enter the outer diameter of the shaft or wheel.
  3. 3The calculator computes angular velocity (ω = v / r), then returns RPM = ω × 60 / (2π).

Use cases

  • Finding the spindle RPM of a grinding wheel given its required surface cutting speed.
  • Checking conveyor roller RPM from belt speed and roller diameter.
  • Setting lathe chuck speed when a target surface finish speed is specified.

Frequently asked questions

What is the formula for RPM from surface speed?

RPM = v ÷ (π · D) × 60, where v is surface speed in m/s and D is diameter in metres. For example, 10 m/s on a 200 mm wheel gives ω = 10 / 0.1 = 100 rad/s ≈ 955 rpm.

What is surface speed?

Surface speed (peripheral or cutting speed) is the linear speed of a point on the rim of a rotating shaft or wheel. It relates to RPM by v = π · D · n / 60.

Why does diameter matter for RPM?

A larger wheel covers more distance per revolution, so it needs fewer revolutions per minute to keep the same rim speed. Same RPM but a larger diameter means a faster rim speed.

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