Calculates the center-directed force needed to keep an object moving along a circular path at a given speed and radius.
How it works
Mass is multiplied by velocity squared, then divided by the radius of the circular path.
What this does not include
This does not include centrifugal “force,” which is a fictitious force that only appears in the rotating object’s own reference frame — this calculator computes the real, center-directed force.
How to use this calculator
- Enter the object’s mass, velocity, and the radius of its circular path.
A worked example
A 2 kg mass moving at 5 m/s in a 1 m radius circle: force = mv²/r = 2 × 5² ÷ 1 = 50 N.
A 1 kg mass at 10 m/s in a 2 m radius: force is also 50 N — a different mass, speed, and radius combination landing on the identical force.
What the variables mean
| Variable | Meaning |
|---|---|
| Mass | Mass of the moving object |
| Velocity | Speed along the circular path |
| Radius | Radius of the circular path |
Edge cases worth knowing
Force scales with the square of velocity, not linearly. Doubling the speed on the same circular path quadruples the required centripetal force — a key reason sharp turns feel so much more forceful at higher speeds.
A radius of zero makes the force infinite, which has no physical meaning — the calculator declines to show a result for that case.
Frequently asked questions
Why does force increase so quickly with speed?
Because velocity is squared in the formula — doubling the speed quadruples the required centripetal force for the same radius.
What provides centripetal force in real life?
It depends on the situation — tension in a string for a swung ball, friction between tires and road for a turning car, or gravity for an orbiting satellite.
What happens if the centripetal force suddenly disappears?
The object stops moving in a circle and instead travels in a straight line, tangent to the circle at the point it was released.
