What Is Centripetal Force?
Centripetal force is the net inward force required to keep an object moving along a circular path. Without it, the object would fly off in a straight line according to Newton's first law. It always points toward the center of the circle and depends on the object's mass, its speed, and the radius of the curve. This calculator is a universal physics tool — it works with any consistent SI inputs.
How to Use This Calculator
Enter the object's mass in kilograms, its tangential velocity in meters per second, and the radius of the circular path in meters. The calculator returns the centripetal force in newtons (N) along with the centripetal acceleration in meters per second squared (m/s²).
The Formula Explained
The centripetal force is given by $$F = \frac{m \cdot v^{2}}{r}$$ where \(m\) is mass, \(v\) is speed, and \(r\) is the radius. Because velocity is squared, doubling the speed quadruples the force needed. A tighter curve (smaller \(r\)) also demands more force. The related centripetal acceleration is $$a = \frac{v^{2}}{r}$$ so \(F = m \cdot a\), consistent with Newton's second law.
Worked Example
A 2 kg ball is whirled in a circle of radius 4 m at 5 m/s. Then $$F = \frac{2 \times 5^{2}}{4} = \frac{2 \times 25}{4} = \frac{50}{4} = 12.5 \text{ N}.$$ The centripetal acceleration is $$a = \frac{25}{4} = 6.25 \text{ m/s}^{2}.$$
FAQ
Is centripetal force a new kind of force? No. It is the name for whatever real force (tension, gravity, friction, normal force) acts inward to maintain circular motion.
What is the difference between centripetal and centrifugal force? Centripetal force is the real inward force. Centrifugal "force" is an apparent outward force felt only in a rotating reference frame.
What units should I use? Use kilograms, meters per second, and meters to get force in newtons (SI units).
