Centripetal Acceleration Calculator
Calculate the centre-seeking acceleration of an object moving in a circle from its speed and radius.
How it works
a = v² / r · ω = v / r · T = 2π·r / v
An object moving in a circle at steady speed is still accelerating because its direction constantly changes, and that acceleration points straight toward the centre. Its size grows with the square of speed and shrinks as the circle widens. Unlike centripetal force, this figure does not depend on the object’s mass — it is purely geometric.
Worked example
A point moving at 15 m/s around a 50 m radius has a = 15² ÷ 50 = 4.5 m/s², an angular speed of 15 ÷ 50 = 0.3 rad/s, and completes a lap every 2π × 50 ÷ 15 ≈ 20.9 s.
Sources: Centripetal force — Wikipedia
Frequently asked questions
How is centripetal acceleration different from centripetal force?
Acceleration is v²/r and depends only on speed and radius. Force is mass times that acceleration, so it also depends on how heavy the object is. Multiply this result by the mass to get the force.
Does it point outward or inward?
Always inward, toward the centre of the circle. The outward "centrifugal" sensation is inertia felt in the rotating frame, not a real acceleration of the object.
Why does doubling the speed quadruple it?
Because acceleration depends on v squared. At twice the speed the object changes direction twice as often and each change is twice as large, so the acceleration rises fourfold.
Related calculators
Educational estimate. Check the formula and units for your exact case.