Anything moving in a circle obeys F = mv²/r. Enter any three of force, mass, velocity, or radius and we'll solve the fourth — from theme park rides to orbital mechanics.
A centripetal force calculator lets you instantly compute the relationship between force, mass, velocity, and radius for any object moving in a circular path, using the formula F = mv²/r. Enter any three of the four values — mass, velocity, radius, or centripetal force — and the calculator solves for the missing one, letting you analyze circular motion for physics problems, vehicle dynamics, or engineering design.
Centripetal force is one of the most important — and most misunderstood — concepts in classical mechanics. It isn't a new type of force on its own; rather, it's the label given to whatever net inward force happens to be causing an object to move in a circle. Gravity provides the centripetal force that keeps planets in orbit, tension provides it for a ball swung on a string, and friction provides it for a car navigating a curve. In every case, the underlying mathematics — F = mv²/r — is the same.
This calculator is useful in many contexts: physics students use it to solve circular motion problems, automotive and civil engineers use it to design safe curve banking and speed limits, ride engineers use it to ensure roller coaster loops are safe at the speeds involved, and astronomers use the same principle (with gravity as the force) to understand orbital mechanics.
A 2 kg object moves in a circle of radius 1.5 meters at a velocity of 5 m/s. Using F = mv²/r: F = (2 × 5²) / 1.5 = (2 × 25) / 1.5 = 33.33 N. This is the net inward force required to keep the object on its circular path at that speed and radius.
The force value this calculator produces represents the total net inward force needed to sustain the specified circular motion — in a real scenario, you'd need to identify which physical force (or combination of forces) is actually supplying it. When comparing your result to the reference table, notice the enormous range: everyday car turns and thrown objects require forces in the thousands of newtons, while planetary orbits involve forces of astronomical scale (made possible by equally astronomical masses), and atomic-scale orbits involve forces many orders of magnitude smaller than everyday intuition would suggest. If your calculated force seems unreasonably large for a given radius and velocity, double check your units — mixing km/h with meters, or centimeters with kilograms, are common sources of large calculation errors in circular motion problems.
Enter any three of mass, velocity, radius, or centripetal force, and leave the fourth blank — the calculator solves for the missing value using F = mv²/r.
| Scenario | Centripetal Force |
|---|---|
| Car turning a highway curve | 4,500 N |
| Roller coaster loop | 12,000 N |
| Olympic hammer throw release | 2,200 N |
| Moon orbiting Earth | 1.980e+20 N |
| Electron orbiting a hydrogen nucleus | 8.200e-8 N |