Angular Velocity Calculator
Angular velocity measures how fast an object rotates or revolves. This calculator converts between the three common units (radians per second, RPM, and degrees per second) and optionally calculates the linear (tangential) velocity at a given radius. It also provides the period of rotation.
Angular velocity (ω) describes rotational speed. The SI unit is radians per second (rad/s), where one full revolution equals 2π radians. RPM (revolutions per minute) is common in engineering and everyday use, while degrees per second is intuitive for angles.
The conversions are straightforward: ω (rad/s) = RPM × 2π/60 = deg/s × π/180. When combined with a radius, angular velocity gives the linear (tangential) velocity: v = ωr. A point on the rim of a wheel spinning at 100 RPM with radius 0.3 m moves at v = (100 × 2π/60) × 0.3 ≈ 3.14 m/s.
Angular velocity is fundamental to rotational mechanics, motor specifications, centrifuge calculations, wheel dynamics, and satellite orbits. The period T = 2π/ω gives the time for one complete revolution, useful for determining orbital periods or the cycle time of rotating machinery.