Calculate angular velocity in rad/s from an angle and time, from revolutions per minute (rpm), or from linear speed and radius.
Last updated: November 8, 2026
ω = θ ÷ t, ω = 2π × rpm ÷ 60, ω = v ÷ r
Angular velocity (ω) is the angle a rotating object sweeps per unit of time, measured in radians per second: • ω = θ ÷ t (θ in radians; 360° = 2π rad) • ω = 2π × rpm ÷ 60 • ω = v ÷ r (linear speed ÷ radius) • Frequency f = ω ÷ 2π, period T = 1 ÷ f Example: a wheel making one full turn (360°) every 2 seconds has ω = 2π ÷ 2 = π ≈ 3.14 rad/s. That is 30 revolutions per minute and 0.5 Hz. 60 rpm equals 2π ≈ 6.28 rad/s. The calculation assumes a steady rotation.
Common questions about angular velocity
Multiply by 2π and divide by 60. For example, 3,000 rpm = 3,000 × 2π ÷ 60 ≈ 314 rad/s.
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One full turn = 360°.
In seconds.