Angular Velocity Calculator Formula

Understand the math behind the angular velocity calculator. Each variable explained with a worked example.

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Formulas Used

Angular Velocity

omega = angle_rad / time

Revolutions per Minute

rpm = (angle_rad / time) * 60 / (2 * pi)

Variables

VariableDescriptionDefault
angle_degAngle of Rotation(degrees)360
timeTime(s)2
angle_radDerived value= angle_deg * pi / 180calculated

How It Works

Angular Velocity

Angular velocity quantifies how fast an object rotates.

Formula

omega = theta / t

where theta is the angle in radians and t is time. One full revolution is 2*pi radians.

Worked Example

A wheel completes one full rotation (360 degrees) in 2 seconds.

angle_deg = 360time = 2
  1. 01Convert 360° to radians: 360 * pi / 180 = 2*pi rad
  2. 02omega = theta / t = 2*pi / 2 = pi rad/s
  3. 03omega = 3.1416 rad/s
  4. 04RPM = omega * 60 / (2*pi) = 30 RPM

Ready to run the numbers?

Open Angular Velocity Calculator