Centripetal Acceleration Calculator
Enter a speed and a radius to get the centripetal acceleration in metres per second squared — the inward pull that keeps an object on its circular path.
Speed and radius in, acceleration out
Enter the velocity and the radius of the circle and the calculator returns the centripetal acceleration (v²/r) in metres per second squared.
Use SI units
Velocity in metres per second and radius in metres give acceleration in m/s² — divide km/h by 3.6 to get m/s before you start.
What is centripetal acceleration?
The inward acceleration of circular motion
This centripetal acceleration calculator finds the inward acceleration that keeps an object moving along a circular path. Whenever something travels in a circle — a car rounding a bend, a satellite orbiting the Earth, a ball on a string — its direction is constantly changing, and a change in direction is a change in velocity, which means it is accelerating. That acceleration always points toward the centre of the circle, which is why it is called centripetal ("centre-seeking"). It depends only on how fast the object moves and how tight the circle is: the speed in metres per second and the radius in metres become the acceleration in metres per second squared.
Enter a speed in metres per second and a radius in metres to get the centripetal acceleration in m/s² instantly.
Centripetal acceleration is the velocity squared divided by the radius of the circular path. The velocity is squared, so it dominates the result, while a larger radius softens the turn and lowers the acceleration.
a = v² ÷ rWork the worked example through step by step. Suppose an object moves at 10 m/s around a circle of radius 2 m. First square the velocity: 10² = 100, the squared speed that drives the acceleration. Then divide by the radius: 100 ÷ 2 = 50 m/s². That inward acceleration — about five times the pull of Earth's gravity — is what bends the object's straight-line motion into a circle. Keep the units consistent (metres per second and metres) and the answer comes back in m/s².
The acceleration you get is the rate at which the object's velocity is turning toward the centre, not a change in how fast it is going. An object can circle at a perfectly steady speed and still have a large centripetal acceleration, because acceleration measures any change in velocity — and direction is part of velocity. Two levers control the size of the result. Speed is squared, so doubling it from 10 to 20 m/s quadruples the acceleration, from 50 to 200 m/s². Radius works the other way: it sits in the denominator, so halving the circle from 2 m to 1 m doubles the acceleration at the same speed. That is why a tight, fast corner presses you hardest into your seat, and why designers widen high-speed bends to keep the inward acceleration — and the force it demands — within comfortable, safe limits. Multiply this acceleration by the object's mass and you get the centripetal force in newtons.
The formula is exact for uniform circular motion, but a couple of practical points are worth keeping in mind.
Uniform circular motion and consistent units
This calculator gives the centripetal acceleration for motion in a circle of fixed radius at a given speed. It does not include any tangential acceleration from speeding up or slowing down, and it assumes a true circular path rather than a changing curve. Keep your units consistent — metres per second for velocity and metres for the radius — or the result will be wrong: convert km/h to m/s by dividing by 3.6 before you enter the speed.