Tangential Velocity Calculator
Enter an angular velocity and a radius to get the tangential (linear) velocity in metres per second — and see why a point farther from the axis moves faster.
Angular velocity meets radius
Enter the angular velocity in rad/s and the radius in metres and the calculator returns the tangential velocity (ω × r) in metres per second.
Use radians
Angular velocity must be in radians per second, not revolutions or degrees — multiply rev/s by 2π to get rad/s before you start.
What is tangential velocity?
The speed of a point along its circular path
The tangential velocity calculator turns an angular velocity and a radius into the linear speed of a point on a rotating body. Tangential velocity is how fast that point travels along its circular path, measured along the tangent to the circle. It depends on two things: how quickly the body spins, the angular velocity ω in radians per second, and how far the point sits from the axis, the radius r in metres. Multiply them together and you get the tangential velocity in metres per second — the number behind the rim speed of a wheel, the tip speed of a turbine blade, and the linear pace of any point riding a turntable.
Enter an angular velocity in rad/s and a radius in metres to get the tangential velocity in metres per second instantly.
Tangential velocity is the angular velocity multiplied by the radius — that is the whole formula.
v = ω × rThe angular velocity ω stays the same for every point on a rigid body, but the radius does not — so points farther from the axis cover a longer circle in the same time and therefore move faster. Use radians per second for ω and metres for r and the velocity comes back in metres per second.
Suppose a point sits 2 m from the axis of a body rotating at 10 rad/s.
Note the angular velocity
ω = 10 rad/s — how fast the whole body turns.
Note the radius
r = 2 m — how far the point sits from the axis of rotation.
Multiply them
v = 10 × 2 = 20 m/s — the tangential velocity of that point along its circular path.
The tangential velocity (20 m/s for the point above) is the genuine linear speed of that point as it sweeps around the axis — the speed you would measure if the point flew off on a tangent and travelled in a straight line. The crucial insight is that this speed depends on the radius: points farther from the axis move faster even though every point shares the same angular velocity. That is why the rim of a wheel moves quicker than a spot near the hub, why the tip of a fan blade outruns its root, and why a child at the edge of a merry-go-round whirls faster than one near the centre. If you know the rotation frequency f in revolutions per second instead of ω, the same result follows from v = 2πrf, because ω = 2πf — the two formulas are one and the same. Doubling either the angular velocity or the radius doubles the tangential velocity, since the relationship is a simple product.
The formula is exact, but a couple of practical points are worth keeping in mind.
Radians per second and rigid rotation
This calculator expects the angular velocity ω in radians per second, not revolutions per minute or degrees — convert rev/s to rad/s by multiplying by 2π, and rpm by dividing by 60 first. The result is the tangential velocity for a single radius on a body in rigid rotation, where every point shares the same ω; it does not describe deformable or slipping systems. Keep the radius in metres so the velocity comes back in metres per second.