Centripetal Acceleration Calculator
Find the centripetal (radial) acceleration of an object in uniform circular motion from either its linear speed or its angular speed and the radius of the path.
Input type
m/s
m
Directed toward the centre of the circle
- 1
Speed squared (v²)
10² = 100 - 2
Centripetal acceleration (a = v² ÷ r)
100 ÷ 5 = 20
How does this calculator work?
Centripetal acceleration is the inward acceleration in circular motion, a = v²/r = ω²·r. Enter the linear speed v (m/s) or angular speed ω (rad/s) plus the radius r (m), and the calculator returns a in m/s². It also converts between v and ω and shows the result in g-units.
Formula
How this is calculated
Centripetal acceleration is the inward (radial) acceleration that keeps an object moving along a circular path. Pick whether you know the linear speed v (m/s) or the angular speed ω (rad/s), then enter the radius r in metres. In linear mode the calculator uses a = v² / r; in angular mode it uses a = ω² · r. The two forms are equivalent because v = ω · r.
The result a is reported in m/s² and always points toward the centre of the circle, perpendicular to the velocity. The tool also shows the complementary speed (it converts v to ω, or ω to v, using v = ω · r) and expresses the acceleration in multiples of standard gravity g = 9.80665 m/s² so you can gauge the felt force. The area curve plots how acceleration grows with the chosen speed from zero up to your entered value, showing the quadratic dependence.
Assumptions: motion is uniform circular motion (constant speed, constant radius) so there is no tangential acceleration. Radius must be positive; in linear mode a zero radius is undefined (division by zero) and returns no result. This radial acceleration does not include gravity or any other external accelerations.
Frequently asked questions
Because a = v² / r, doubling the speed quadruples the required inward acceleration for the same radius. The velocity vector must change direction faster when the object moves faster, and that rate of change scales with v².
Centripetal acceleration is the real inward acceleration a = v²/r that a net force provides. Centrifugal "force" is an apparent outward effect felt in the rotating (non-inertial) frame; it is not a separate physical force in the inertial frame.
Use v = ω · r, where v is in m/s, ω in rad/s and r in metres. So ω = v / r. This calculator does the conversion automatically and reports both values.
Also known as
TG we-Calculate Editorial Team. (2026). Centripetal Acceleration Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/centripetal-acceleration-calculator
TG we-Calculate Editorial Team. "Centripetal Acceleration Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/centripetal-acceleration-calculator.
TG we-Calculate Editorial Team, "Centripetal Acceleration Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/centripetal-acceleration-calculator
@misc{wecalculate_centripetal_acceleration_calculator, title = {Centripetal Acceleration Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/centripetal-acceleration-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?