Angular Velocity Calculator

Angular velocity (ω) measures how fast an object rotates around a central point. It describes the rate of change of the angular position — essentially how many radians, degrees, or revolutions an object covers per unit of time. The standard SI unit is radians per second (rad/s).

Use the formula ω = Δα / t, where Δα is the change in angle (in radians) and t is the time taken (in seconds). For example, if an object rotates 360° (2π radians) in 2 seconds, its angular velocity is π rad/s ≈ 3.1416 rad/s.

Angular velocity relates to linear (tangential) velocity by the formula ω = v / r, where v is the linear speed and r is the radius of the circular path. For instance, an object moving at 10 m/s along a circular path of radius 5 m has an angular velocity of 2 rad/s.

They share the same formula and unit (rad/s), but conceptually differ. Angular velocity describes the rate of rotation of a physical object and has a direction (it is a vector). Angular frequency refers to the rate of oscillation in wave or periodic motion and is a scalar quantity.

Multiply RPM by 2π and divide by 60: ω (rad/s) = RPM × 2π / 60. For example, a motor spinning at 60 RPM has an angular velocity of 60 × 2π / 60 = 2π ≈ 6.2832 rad/s.

Earth completes one full rotation (2π radians) in approximately 24 hours (86,400 seconds). Its angular velocity is therefore ω = 2π / 86400 ≈ 7.27 × 10⁻⁵ rad/s, or about 0.0042 degrees per second.

No — that would give units of m²/s, which is not angular velocity. The correct relationship is ω = v / r (linear velocity divided by radius). The product v × r is not a standard physical quantity for angular motion.

Tangential (linear) velocity v is the speed along the circular path, measured in m/s. Angular velocity ω is the rate of rotation, measured in rad/s. They are related by v = ω × r, where r is the radius of the circular path.