The centripetal force formula
Centripetal force keeps an object moving in a circle and points toward the center: F = m·v² ÷ r, where m is mass, v is velocity, and r is the radius. A 2 kg object at 10 m/s on a 5 m radius needs 40 N. Force grows with the square of speed. To find the object's momentum, use the momentum calculator.
The formula follows from Newton's second law: an object circling at constant speed still accelerates because its direction changes, and that centripetal acceleration is a = v² ÷ r.
How to use this calculator
Enter the mass in kilograms, the velocity in meters per second, and the radius of the circle in meters. The result is force in newtons (N). Radius must be greater than zero. Because velocity is squared, doubling speed quadruples the force. See also the pressure calculator.
Convert km/h to m/s (divide by 3.6) first, or the newton figure will be badly off. Centripetal force is not an extra force on a free-body diagram — it is the net inward force that tension, friction or gravity must supply.
Worked example
A 2 kg ball swings at 10 m/s on a 5 m string: 2 × 10² ÷ 5 = 2 × 100 ÷ 5 = 40 N. Double the speed to 20 m/s and the force jumps to 160 N, four times as large, because force depends on velocity squared.
That squared dependence is the practical takeaway: a string that snaps above 100 N holds at 10 m/s but fails well before 20 m/s. The force depends on the square of the speed, so an accurate velocity matters more than anything else in the formula.
Frequently asked questions
- How do I calculate centripetal force?
- Multiply mass by velocity squared, then divide by the radius: F = m·v² ÷ r.
- Why must the radius not be zero?
- Dividing by zero is undefined, so the force has no value when radius is zero.
- Which way does centripetal force point?
- Toward the center of the circular path, perpendicular to the velocity.
- What happens if velocity doubles?
- The force quadruples, because it depends on the square of velocity.
- Is centrifugal force the same thing?
- No. Centripetal force is a real inward force supplied by a string, road friction or gravity, while centrifugal force is an apparent outward push felt only in the rotating frame of the object itself. In a ground-based frame there is no outward force — only the inward one this calculator returns.