Centripetal Acceleration

a_c = \frac{v^2}{r} = \omega^2 r

Acceleration pointing toward center of circular path.

Variables

a_c

Centripetal acceleration

Toward center

Allowed values: 0 or more

m/s²

Tangential velocity

Speed along circle

m/s

Radius

Radius of path

Allowed values: greater than 0

Angular velocity

Rate of rotation

rad/s

Derivation

From geometry: a_c = v²/r. With v = ωr: a_c = ω²r.

Your notes

0/5000

Check value

Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

v = 2 m/s (Tangential velocity)
r = 3 m (Radius)

Result: a_c = 1.3333333 m/s²

Other mechanics formulas with the same quantities

Angular Velocity (Rotational Motion) shares Angular velocity
Rotational Kinetic Energy (Rotational Motion) shares Angular velocity
Angular Momentum (Rotational Motion) shares Angular velocity
Rolling Kinetic Energy (Rotational Motion) shares Angular velocity

Where this formula is listed

Mechanics formulas, under Rotational Motion, alongside Angular Acceleration, Torque, Moment of Inertia (Point Mass), Newton's Second Law (Rotation) and Rotational Kinematic 1.
In the mechanics list it comes after Linear-Angular Velocity Relation and before Centripetal Force.
Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Centripetal Acceleration formula?

Centripetal Acceleration is written a_c = v²/r = ω²r. Acceleration pointing toward center of circular path. It belongs to Mechanics, under Rotational Motion.

What are the units in a_c = v²/r = ω²r?

In SI units, a_c is centripetal acceleration, measured in m/s²; v is tangential velocity, measured in m/s; r is radius, measured in m; ω is angular velocity, measured in rad/s.

How is the Centripetal Acceleration formula derived?

From geometry: a_c = v²/r. With v = ωr: a_c = ω²r. The result is a_c = v²/r = ω²r.