π Centripetal Force Calculator
Calculate Fc = mvΒ²/r for circular motion.
How to Use This Calculator
This calculator finds the inward force needed to keep a mass moving in a circle. Enter the mass, the speed, and the radius of the circular path.
Enter the mass in kilograms.
Enter the speed in meters per second. This is the tangential speed along the circle.
Enter the radius of the circular path in meters, measured to the center of the circle.
Click Calculate. The required centripetal force appears in newtons, always directed toward the center.
The Centripetal Force Formula
Anything moving in a circle is constantly changing direction, which means it is constantly accelerating toward the center. Newton's second law says acceleration needs force, so circular motion always requires an inward, or centripetal, force. The v^2 term is the key insight: force grows with the square of speed. Drive twice as fast around the same curve and you need four times the grip.
Centripetal force is not a new kind of force. It is a job description. Whatever real force happens to point inward, friction, tension, gravity, or a push from a banked road, plays the centripetal role. If the available inward force falls short, the object cannot hold the circle and drifts outward along a tangent.
Worked Example
Where This Comes Up
Road engineers use this formula to set speed limits on curves and to design banking: tilt the road so part of the normal force points inward and the tires do less work. Centrifuges in labs and hospitals spin samples at thousands of rpm to separate blood or purify chemicals, generating forces thousands of times gravity. Satellites stay in orbit because gravity supplies exactly the centripetal force their circular path demands.
The most common mistake is forgetting that velocity is squared. Students often double the speed and expect double the force, then wonder why their answer is off by a factor of two. The other trap is the radius: for a car on a curve it is the radius of the road's arc, for a whirling ball it is the string length, and mixing up diameter with radius halves or doubles the answer.
Frequently Asked Questions
What provides the centripetal force in real situations?
It depends on the setup: friction between tires and road for a turning car, tension in the string for a whirling ball, gravity for an orbiting satellite, and the normal force on a banked curve.
What happens if the centripetal force suddenly disappears?
The object moves in a straight line tangent to the circle at that instant, following Newton's first law. This is why a car slides straight off an icy curve instead of following it.
What is the difference between centripetal and centrifugal force?
Centripetal force points inward and is the real net force needed for circular motion. Centrifugal force is the outward sensation you feel inside a turning car: an apparent effect of your inertia in the rotating reference frame, not a real force.
Why does doubling the speed quadruple the force?
Speed is squared in F = mv^2/r. Twice the speed means four times the inward force, which is why highway curves have strict speed limits.
Can I use angular velocity instead of speed?
Yes. Since v = wr, the formula becomes F = mw^2r. Use w in radians per second.