Calculate tangential speed, rotational speed, or radius from the other two values using v = ωr. Enter rotational speed in RPM or rad/s; this tool reports nonnegative magnitudes.

Calculate v = ωr. Enter speed magnitudes; radius is the distance from the axis, not the diameter.

RPM means revolutions per minute; rad/s means radians per second.

Optional settings

Tangential Velocity Formula

The following equation relates tangential speed magnitude to angular speed in radians per second and radius in meters. The calculator also rearranges it to solve angular speed or radius. See OpenStax’s angular and tangential speed relationship.

Vt = w × r
  • Where Vt is the tangential speed magnitude (m/s)
  • w is the angular speed magnitude (rad/s)
  • r is the nonnegative radius from the rotation axis (m)

To calculate tangential speed, choose Tangential speed, enter the radius, select RPM or rad/s for rotational speed, and select Calculate. The calculator converts RPM to rad/s using ω = RPM × 2π / 60, then multiplies by radius. For the inverse modes, ω = v / r and r = v / ω.

What is a Tangential Velocity?

Definition:

Tangential velocity is the instantaneous velocity directed along the tangent to a circular path. This calculator returns its nonnegative speed magnitude, without determining direction. Radius zero represents a point on the axis.

How to Calculate Tangential Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate tangential speed. In inverse calculations, zero speed at zero radius leaves rotational speed undetermined; two zero speeds leave radius undetermined. A nonzero tangential speed with a zero radius or zero rotational speed has no finite solution.

First, determine the angular speed. In this example, it is 5 rad/s. Choose Tangential speed and select rad/s beside Rotational speed.

Next, determine the radius. For this problem, the radius is found to be 7 m.

Finally, enter 5 rad/s and 7 m, then select Calculate. The tangential speed magnitude is:

Vt = w * r

Vt = 5*7

Vt = 35 m/s. This is also 126 km/h.