🎡 Centripetal Force Calculator
Find the centripetal force needed for circular motion (F = mv²/r), or solve for mass, speed or radius.
Centripetal force F
40 N
Centripetal force F = m·v²/r; centripetal acceleration a = v²/r points toward the centre. 🔒 Computed in your browser.
How the centripetal force calculator works
An object moving in a circle needs a centre-directed (centripetal) force F = mv²/r, producing acceleration a = v²/r. Enter any three of force, mass, speed and radius and the tool solves for the fourth. Since the linear speed v = ωr for a rotation rate ω (in radians per second), the force can equally be written F = mω²r, convenient when you know the angular speed rather than the linear speed.
Centripetal force isn’t a new kind of force. It’s whatever provides the inward pull (tension, gravity, friction). There is no outward “centrifugal force” in an inertial frame.
Frequently asked questions
How do I calculate centripetal force?
F = mv²/r, where m is mass, v speed and r the radius. A 2 kg object at 10 m/s on a 5 m radius needs F = 2 × 100 / 5 = 40 N inward.
What is centripetal acceleration?
The centre-directed acceleration of circular motion: a = v²/r (= ω²r). It changes the direction of velocity, not its magnitude.
What provides the centripetal force?
Some real force directed toward the centre, string tension for a whirled ball, gravity for an orbit, friction for a car cornering. Centripetal is the role, not the type.
Is centrifugal force real?
In an inertial frame, no, the outward feeling is inertia resisting the inward acceleration. “Centrifugal force” only appears as a fictitious force in a rotating reference frame.
How does speed affect the force?
Force scales with v², so doubling the speed quadruples the centripetal force needed, which is why cornering fast requires so much more grip.
Worked example: a car cornering
A 1000 kg car takes a 50 m-radius bend at 20 m/s. F = mv²/r = 1000 × 20² / 50 = 8000 N of inward force, supplied by friction between the tyres and the road.
Can I use the radius and rotation rate instead of speed?
Yes. With angular speed ω in radians per second, the centripetal force is F = mω²r and the acceleration a = ω²r, because the linear speed v = ωr.
What units does the formula use?
SI throughout: force in newtons, mass in kilograms, speed in metres per second and radius in metres. Keep them consistent and the force comes out in newtons.
What is the period of the circular motion?
The time for one full circle is T = 2πr/v = 2π/ω. Combined with F = mv²/r, a shorter period, faster rotation, at the same radius means a larger centripetal force is required.
Why do you feel pushed outward on a fast bend?
Your body’s inertia tries to keep it moving in a straight line, so it presses against the door that is pushing you inward. The real force is inward (centripetal); the outward feeling is inertia, not a separate force.