Rotational Motion Calculator
Convert between angular velocity, linear velocity, and radius.
Calculate torque from force and lever arm length.
Covers key rotational mechanics formulas.
Rotational motion mirrors linear motion — every linear quantity has a rotational equivalent.
Angular velocity (ω) measures how fast something rotates, in radians per second:
ω = v / r = 2πf = 2π × RPM / 60
Where v is the linear (tangential) speed at the edge, r is the radius, f is frequency in Hz (revolutions per second), and RPM is revolutions per minute.
Period: T = 1/f = 2π/ω — the time for one complete revolution.
Torque (τ) is the rotational equivalent of force:
τ = F × r × sin(θ)
Where F is the applied force, r is the length of the lever arm (distance from pivot to point of force application), and θ is the angle between the force vector and the lever arm. For a perpendicular force (θ = 90°), sin(θ) = 1 and τ = F × r.
A wrench example: a 20 N force applied at 0.3 m from a bolt center, perpendicular to the wrench handle, gives τ = 20 × 0.3 × 1 = 6 N·m.
Fill in the inputs you know. The calculator computes the remaining quantities. Radius and at least one of v, ω, f, or RPM are needed for the velocity conversions. Force and lever arm are needed for torque.