Centripetal Force Calculator
Any object moving in a circle is constantly changing direction. Changing direction means accelerating, even at steady speed, and that acceleration always points toward the centre of the circle. The force responsible for that inward acceleration is called the centripetal force. It is not a new kind of force by itself but whatever real force happens to provide the inward pull: the tension in a string spinning a ball, the friction between tyres and road as a car corners, gravity holding a satellite in orbit, or the track pushing on a rollercoaster car. The size of the centripetal force is given by F = mv2 / r, where m is mass, v is tangential speed, and r is the radius of the circle. Crucially, speed enters as a square, so doubling the speed quadruples the force required to hold the same radius. That is why cornering fast is so much more demanding than cornering slowly, and why running off the road is the most common cause of high-speed crashes. This calculator returns everything you need for circular motion analysis from three inputs: mass, speed, and radius. It gives the centripetal force in newtons, the centripetal acceleration in m/s2, the angular velocity in radians per second, and the period of one full circle in seconds. Results update as you type. The default example uses a 1,000 kg car travelling at 20 m/s around a bend with a 50 m radius, giving a centripetal force of 8,000 N and an acceleration of 8 m/s2. Use this tool for physics homework, vehicle dynamics, or orbital and engineering problems.
F = mv²/r. Centripetal acceleration = v²/r. Force grows with the square of speed. Rounded for display.
How it works
Centripetal force: F = mv²/r. Centripetal acceleration: a = v²/r, directed toward the centre. Angular velocity: ω = v/r in radians per second. Period: T = 2πr/v, the time for one complete revolution. Because speed appears squared, the centripetal force is very sensitive to speed changes.
Worked example
A 1,000 kg car travels at 20 m/s around a circular bend of radius 50 m. Centripetal force = 1,000 times 20 times 20 / 50 = 8,000 N. Centripetal acceleration = 400 / 50 = 8.00 m/s². Angular velocity = 20 / 50 = 0.40 rad/s. Period = 2π times 50 / 20 = 15.71 s. These match the default values pre-filled above.
Related calculators
- Angular Velocity Calculator: convert RPM to rad/s and find linear speed.
- Gravitational Force Calculator: gravity as the centripetal force in orbits.
- Torque Calculator: rotational force from lever arm and angle.
- Force Calculator: net force from mass and acceleration.