Centripetal Force Calculator
Enter a mass, a speed, and a radius to get the inward force in newtons that holds an object on its circular path — and see why the force climbs with the square of speed.
Use SI units
Mass in kilograms, speed in metres per second, and radius in metres give the force in newtons — divide km/h by 3.6 to get m/s before you start.
What is centripetal force?
The inward force of circular motion
Centripetal force is the net inward force that keeps an object moving along a circular path instead of flying off in a straight line. It always points toward the centre of the circle, and it grows with the object's mass, with the square of its speed, and inversely with the radius of the circle. The centripetal force calculator turns three measurements — the mass in kilograms, the speed in metres per second, and the radius in metres — into the force in newtons. It is the number behind a car holding a corner, a ball whirled on a string, and a satellite kept in orbit by gravity.
Enter a mass in kilograms, a speed in metres per second, and a radius in metres to get the centripetal force in newtons instantly.
Centripetal force is the mass multiplied by the speed squared, divided by the radius of the circle.
F = m × v² ÷ rThe speed is squared, so it dominates the result: a small change in speed produces a large change in the force. The radius works the other way — a larger circle needs less force for the same speed. Use kilograms, metres per second, and metres, and the force comes back in newtons.
Suppose a 2 kg object is swung at 5 m/s on a circle of radius 10 m.
Square the speed
5² = 25 — the squared speed that drives the force.
Multiply by the mass
2 × 25 = 50 — mass times speed squared.
Divide by the radius
50 ÷ 10 = 5 N — the centripetal force pulling the object toward the centre.
The centripetal force (5 N for the example above) is the net inward pull that must act on the object to keep it on its circular path, always directed toward the centre. It is not a new or extra force you add on — it is whatever real force is already doing the job, whether that is the tension in a string, the friction between tyres and road, or gravity holding a moon in orbit. The crucial insight is that the force scales with the square of speed: double the speed from 5 to 10 m/s and the centripetal force jumps fourfold, from 5 to 20 N, while doubling the radius only halves it. That is exactly why cars need so much more grip to corner quickly, why a faster spin strains a string far more, and why tightening a turn (a smaller radius) demands more force. Mass matters too, but only in direct proportion — speed is the lever that moves the result the most.
The formula is exact, but a couple of practical points are worth keeping in mind.
Uniform circular motion and consistent units
This calculator gives the centripetal force for an object in uniform circular motion — constant speed on a circle of fixed radius. It does not cover changing speed, elliptical orbits, or relativistic effects. Keep your units consistent — kilograms for mass, metres per second for speed, and metres for the radius — or the newtons will be wrong: convert km/h to m/s by dividing by 3.6 before you enter the speed.