Tangential Velocity Calculator

What is Tangential Velocity?

Tangential velocity is the linear speed of an object moving along a circular path. It is called "tangential" because the velocity vector is always tangent to the circle at any point, perpendicular to the radius. The formula for tangential velocity is $v = 2\pi r / T$, where $r$ is the radius of the circular path and $T$ is the period (the time for one complete revolution). For related circular motion tools, try our Centripetal Force Calculator and Speed Calculator.

Tangential velocity can also be expressed in terms of angular velocity: $v = \omega r$, where $\omega$ is the angular velocity in radians per second. This relationship shows that points farther from the center of rotation move faster than points closer to the center, even though they share the same angular velocity.

How to Use the Tangential Velocity Calculator

This calculator solves the equation $v = 2\pi r / T$ for any of the three variables. Select what you want to calculate, enter the known values with their units, and the result updates automatically. The calculator also displays the angular velocity $\omega$ for reference.

• Solve for Tangential Velocity: Enter the radius of the circular path and the period of one revolution. The calculator gives the linear speed in your chosen unit.
• Solve for Radius: Enter the tangential velocity and period to find the radius of the circular path.
• Solve for Period: Enter the radius and tangential velocity to find the time for one complete revolution.

Applications of Tangential Velocity

Tangential velocity appears throughout science and engineering. In aerospace engineering, it is used to compute the orbital speed of satellites and spacecraft given their orbital radius and period. For a satellite in low Earth orbit at 7,000 km radius moving at 7,500 m/s, the orbital period is about 98 minutes.

In automotive engineering, tangential velocity helps estimate tire tread speed from wheel radius and rotation rate. Industrial engineers calculate belt speeds on pulley systems. In sports science, it measures the speed of a hammer-throw weight at the end of the wire. Astronomers compare the equatorial rotational speeds of planets using their radius and rotation period.

Tangential Velocity vs Angular Velocity

A common point of confusion is the difference between tangential velocity and angular velocity. Tangential velocity $v$ is a linear speed with units of m/s, km/h, or mph. It describes how fast a point on the rim is moving along the circle. Angular velocity $\omega$ is the rate of angular displacement with units of rad/s or degrees/s.

The two are related by $v = \omega r$. A point near the rim of a spinning disk has a larger tangential velocity than a point near the center, even though both have the same angular velocity. The period $T$ and angular velocity are reciprocals scaled by $2\pi$: $\omega = 2\pi / T$.