Centripetal Acceleration Calculator (a = v\u00B2 / r)

This centripetal acceleration calculator uses a equals v squared over r, the acceleration that points toward the centre of a circular path. Choose the unknown and enter the others; the calculator solves for the acceleration, the speed or the radius. Anything moving in a circle is constantly changing direction, which is an acceleration even at steady speed, and that acceleration is directed inward toward the centre. It grows with the square of the speed and shrinks with a larger radius, which is why tight, fast corners feel so strong. Use SI units. The formula, a worked example and the assumptions are below.

Centripetal acceleration (m/s\u00B2)

Speed (m/s)

Radius (m)

Solve for

Value

Result

The formula

Centripetal acceleration is a = v squared / r, where v is the speed and r is the radius of the circular path. Rearranged: v = the square root of (a r) and r = v squared / a. It points toward the centre.

Worked example

An object moving at 10 m/s around a circle of radius 5 m has a centripetal acceleration of a = 100 / 5 = 20 m/s squared. Solve for a with v = 10, r = 5 to confirm.

Frequently asked questions

What is centripetal acceleration?

The inward acceleration of an object moving in a circle, equal to v squared over r, caused by the constant change in direction.

Why is there acceleration at constant speed?

Because velocity includes direction. Going around a circle the direction changes constantly, which is an acceleration.

How do I get the centripetal force?

Multiply by the mass: F = m times v squared over r. See the centripetal force calculator.

Who this calculator is for

This calculator is for physics students, teachers and engineers.

What this calculator assumes

You enter SI units as labelled.
One variable is solved from the others.
Results are rounded for display.

Formula and sources

Related calculators

Kinetic Energy Calculator: energy of motion.
Momentum Calculator: mass times velocity.
Projectile Motion Calculator: range and height.

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