Enter the tangential velocity and the radius at which an object is rotating into the calculator to determine the centripetal acceleration.

Centripetal Acceleration Formula

The following equation is used to calculate the centripetal acceleration of an object in rotation/orbit.

a = V^2/r
  • Where a is the centripetal acceleration m/s^2
  • V is the tangential velocity m/s
  • r is the radius m

To calculate the centripetal acceleration, square the tangential velocity, then divide by the radius.

Centripetal Acceleration Definition

Centripetal acceleration is the rate of change of angular velocity or speed.

Centripetal Acceleration Example

How to calculate the centripetal acceleration

  1. First, measure the velocity

    The key to this step is that the velocity is the tangential velocity. In other words, the velocity is perpendicular to the radius.

  2. Next, determine the radius

    Either calculate or measure the radius of rotation.

  3. Finally, calculate the centripetal acceleration

    Calculate the centripetal acceleration using the velocity and radius from steps 1 and 2 combined with the formula above.


How do you calculate the tangential acceleration from angular acceleration?

To calculate the tangential acceleration from angular acceleration, you multiply the angular acceleration (α) by the radius (R) of the circular path. The formula is a = α * R.

Can angular acceleration be negative?

Yes, angular acceleration can be negative. A negative angular acceleration indicates that the angular velocity of the object is decreasing over time, meaning the object is slowing down in its rotational motion.

How does the radius of rotation affect angular acceleration?

The radius of rotation affects angular acceleration when calculating it through tangential acceleration. A larger radius at a constant tangential acceleration results in a smaller angular acceleration, as the formula α = a / R indicates. Conversely, a smaller radius increases the angular acceleration for the same tangential acceleration.