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.
Why the angle matters more than people expect
Only the component of force perpendicular to the handle actually turns the bolt. Pull at 45° instead of square and you lose 29% of your torque for the same effort. Pull straight along the handle and you get nothing at all: sin(0°) = 0, and you are just trying to stretch the wrench. This is why a breaker bar is used with the body weight square to the bar, and why an awkward angle in an engine bay costs real leverage.
Radius is not always the lever arm
The two are separate inputs here on purpose. Radius is where you want the tangential speed, say the rim of a wheel or the tip of a turbine blade. The lever arm is where a force is applied to create torque, which might be a completely different distance from the same axis. A 0.3 m wrench turning a bolt on a 0.02 m radius shank uses both numbers, and they are not interchangeable.
Fill in the inputs you know. The calculator computes the remaining quantities. Radius and at least one of v, ω, or RPM are needed for the velocity conversions. Force, lever arm, and the angle are needed for torque.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.