Centripetal Acceleration Calculator (a = v² / r)

This centripetal acceleration calculator works out any one of three related values in a = v squared / r, the equation describing the inward acceleration of an object travelling in a circle. Anything moving along a curved path is constantly changing direction, and because velocity is a vector that includes direction as well as speed, that change counts as an acceleration even when the speed itself never varies. This acceleration always points toward the centre of the circle, which is why it is called centripetal, and it grows quickly with speed, since it depends on speed squared, while shrinking as the radius gets larger, explaining why sharp, fast bends feel so much stronger than gentle ones. To use the calculator, choose which quantity to solve for from the dropdown, either the acceleration, the speed or the radius, then enter the other two values in SI units: metres per second for speed and metres for radius. The calculator returns the solved value in a labelled result showing which quantity was worked out, updating live as you adjust the inputs. It suits physics students checking homework, teachers building worked examples, and engineers running quick circular-motion checks on vehicles, machinery or orbital paths. Results are rounded for display, so keep extra decimal places in mind for precise engineering work, and remember the formula assumes steady circular motion at a constant radius.

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Centripetal acceleration (m/s²)

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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