Centripetal force calculator
Centripetal force, acceleration, angular velocity and period of revolution.
Fill in the fields and the result will appear here automatically.
Find the magnitude of the net inward force for uniform circular motion. Mass and radius are positive; speed is a nonnegative magnitude in m/s. Doubling speed requires four times the radial force. The result does not determine tyre grip, rope strength or a safe driving speed.
How it works
Formula and logic
F = m × v² ÷ r. Acceleration is v² ÷ r, angular velocity is v ÷ r, and the period of one revolution is 2πr ÷ v.
Example
A 1,200 kg car at 15 m/s on a 40 m radius needs 6,750 N towards the centre.
Fields and units
- Mass — kg
- Speed along the circle — m/s
- Radius — m
How to use
- — Enter the mass of the moving body in kilograms.
- — Enter its speed along the circle in metres per second.
- — Enter the radius of the circle in metres.
- — Compare the force against what the tyres, rope or track can actually supply.
- — At speed 0, force and angular speed are 0; no finite revolution period exists. A negative input does not encode clockwise motion here.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: radial force in circular motion
- Limitation
- Uniform circular motion; force means the net radial component. Available force and material limits must be checked separately.
FAQ
Is centripetal force a separate kind of force?
No. It is a role, not a source. Friction, tension, gravity or the track surface provides it; the formula says how much is needed, not where it comes from.
What about centrifugal force?
An inertial frame needs a net inward force. A rotating frame can use an outward centrifugal inertial force; it is not an additional external interaction. Weight, normal force and other force components may still be present.
Why does the speed matter so much more than the radius?
Speed enters squared and radius only to the first power. Twice the speed needs four times the force; half the radius needs only twice.
Is the period shown for a stationary body?
No. At zero speed a revolution never completes, so the row is omitted rather than shown as an unbounded number. The force itself is legitimately zero.