Centripetal Force Calculator
Centripetal force is the inward force that keeps an object on a circular path. Solve for force, mass, speed or radius, enter motion as a tangential speed or an angular velocity (rad/s, rpm, or period), switch between metric and imperial units, and read the result in newtons, pound-force or g-force.
Formula
Worked example
A 1000 kg car cornering at 15 m/s on a 50 m radius curve needs F = m·v²/r = 1000 × 15² ÷ 50 = 4,500 N of inward force, supplied by tyre friction. That is a = 4.5 m/s², about 0.46 g.
What centripetal force means
Any object moving in a circle is constantly changing direction, and changing direction is a form of acceleration even when the speed stays the same. By Newton’s second law, that acceleration requires a net force, and for circular motion that force always points toward the centre of the circle. This is the centripetal force, F = m·v²/r, where m is the mass, v is the tangential speed, and r is the radius. The word centripetal means "centre-seeking"; it is not a new kind of force but the name for whatever real force supplies the inward pull, such as tension in a string, friction between tyres and road, or gravity holding a satellite in orbit.
Tangential speed or angular velocity
You can describe the same motion two ways. If you know the tangential speed v, use F = m·v²/r. If you instead know how fast the object rotates, the angular velocity ω (in radians per second), use the equivalent form F = m·ω²·r, because v = ω·r. This calculator accepts angular velocity in rad/s, rpm or degrees per second and converts internally, then reports the rotation rate in rpm and the time for one full revolution (the period). That makes it just as easy to size the force on a spinning centrifuge, a record on a turntable, or a stone whirled on a string as it is for a car on a bend.
Solving for any variable
Because F = m·v²/r links four quantities, knowing any three gives the fourth. Set "Solve for" to mass, speed or radius and the calculator rearranges the formula: mass m = F÷a, speed v = √(F·r÷m), and radius r = m·v²÷F. The force can be displayed in newtons, kilonewtons, pound-force, kilogram-force or dynes, and the result also appears as a g-force so you can judge how strong the pull feels. Mass, speed and radius each accept metric or imperial units, so you can mix kilograms with miles per hour and feet without converting by hand.
Why speed and radius dominate
The formula depends linearly on mass but on the square of speed, so velocity is by far the most influential input. Doubling the speed of a turning car quadruples the friction the tyres must provide, which is why cornering too fast causes a skid long before a slow turn would. Radius works the opposite way: a tighter circle (smaller r) demands more force for the same speed, while a gentle, wide curve needs less. The related centripetal acceleration, a = v²/r, is independent of mass and is what your body feels as you are pushed against a car door or the wall of a spinning ride. If the supplying force cannot meet the required value, the object stops following the circle and travels off along a tangent.
Centripetal force in everyday situations
| Scenario | Mass (kg) | Speed (m/s) | Radius (m) | Force (N) | g-force |
|---|---|---|---|---|---|
| Car on a gentle curve | 1000 | 15 | 50 | 4500 | 0.46 g |
| Car taking a sharp bend | 1000 | 15 | 25 | 9000 | 0.92 g |
| Cyclist rounding a corner | 80 | 8 | 10 | 512 | 0.65 g |
| Stone on a 1 m string | 0.2 | 6 | 1 | 7.2 | 3.67 g |
Force grows with the square of speed and shrinks as the radius widens (F = m·v²/r).
Frequently asked questions
What is the formula for centripetal force?
Centripetal force is F = m·v²/r, where m is the mass in kilograms, v is the tangential speed in metres per second, and r is the radius of the circular path in metres. If you know the angular velocity ω instead of the speed, the equivalent form is F = m·ω²·r. The result is in newtons and always points toward the centre.
Can this calculator solve for mass, speed or radius?
Yes. Set the "Solve for" menu to the unknown and fill in the other three values. The calculator rearranges the formula automatically: mass m = F÷a, speed v = √(F·r÷m), and radius r = m·v²÷F, where a = v²/r is the centripetal acceleration.
How do I use angular velocity, rpm or period?
Choose to describe motion by angular velocity and enter it in radians per second, rpm or degrees per second. The calculator uses F = m·ω²·r and also reports the rotation rate in rpm and the time for one full revolution. Tangential speed and angular velocity are linked by v = ω·r.
Is centripetal force the same as centrifugal force?
No. Centripetal force is a real, inward force that keeps an object moving in a circle. Centrifugal force is an apparent outward force you seem to feel inside a rotating frame of reference; it is not a true force on the object but a consequence of viewing the motion from a non-inertial, spinning viewpoint.
What supplies the centripetal force in real situations?
It depends on the situation. For a car rounding a bend it is friction between the tyres and the road, for a ball on a string it is the string’s tension, for a satellite it is gravity, and for a charged particle in a magnetic field it is the magnetic force. Centripetal force names the role, not the source.