Centripetal Force Calculator
F = mv²/r, with the g-force it works out to.
Work out Centripetal Force. F = mv²/r, with the g-force it works out to. Names the counter-intuitive bit rather than hiding it.
Centripetal force
8,000 N
8 m/s² — 0.816 g
The force points inward, towards the centre. There is no outward centrifugal force in an inertial frame — what a passenger feels pressed against the door is their own inertia trying to continue in a straight line while the car turns underneath them. Force scales with the square of speed, so taking a bend twice as fast needs four times the grip. That is why cornering accidents cluster at high speed rather than spreading evenly, and why the advisory sign on a slip road is a genuine limit rather than a suggestion. On a flat road the force must come entirely from friction, which is why the same bend that is trivial when dry becomes impossible in ice.
How the Centripetal Force Calculator works
Enter mass, speed and turn radius for the inward force needed to hold something in a circle, plus the acceleration expressed in g. Force scales with the square of speed, which is why cornering goes wrong so suddenly.
Also known as: centripetal acceleration calculator · circular motion calculator · f = mv2/r calculator · g force calculator
Frequently asked questions
How do I calculate centripetal force?
F = mv²/r — mass times speed squared, divided by the radius of the turn. A 1,000 kg car at 20 m/s round a 50 m bend needs 8,000 N.
Is centrifugal force real?
Not in an inertial frame. The only real force is centripetal, pointing inward. What a passenger feels pushing them outward is their own inertia continuing straight while the car turns underneath them.
Why is cornering so much harder at speed?
Because the force needed grows with the square of speed. Taking the same bend twice as fast requires four times the grip, so a corner that is comfortable at 30 is impossible at 60.
What provides the centripetal force on a car?
Friction between tyres and road, on a flat bend. That is why the same corner becomes impossible in ice — the required force has not changed, but the available friction has collapsed.
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