Centripetal Force Calculator

The Centripetal Force Calculator determines the inward-directed force required to keep an object moving along a circular path. In any form of circular motion, whether a car rounding a curve, a satellite orbiting Earth, or a ball on a string, a net force must act continuously toward the center of the circle. Without this centripetal force, the object would fly off in a straight line due to its inertia, as described by Newton's first law.

This calculator supports two standard formulations. The linear velocity form uses $$F_c = \frac{mv^2}{r}$$, which is ideal when you know the tangential speed. The angular velocity form uses $$F_c = m\omega^2 r$$, which is convenient when working with rotating systems measured in radians per second. Both expressions are mathematically equivalent since $$v = \omega r$$. The tool also computes the centripetal acceleration $$a_c = v^2 / r$$, which is the acceleration directed toward the center regardless of mass.

Understanding centripetal force is essential in mechanical engineering for designing safe roadways and roller coasters, in aerospace for calculating orbital mechanics, and in everyday physics for analyzing anything that spins, turns, or orbits. The concept was formalized by Christiaan Huygens in 1659 and later incorporated into Newton's laws of motion.