Centripetal Force Calculator
Find the force keeping an object in circular motion.
Results update as you type.
How it works
Any object moving in a circle needs a force directed toward the center to keep it on its curved path, and this calculator finds that centripetal force. You enter the object's mass, its speed, and the radius of the circle, and it returns the centripetal force and the centripetal acceleration. The force equals mass times velocity squared divided by radius, so it grows with the square of the speed: double the speed and the force quadruples, which is why taking a corner twice as fast demands four times the grip. It also increases as the radius shrinks, so a tighter turn needs more force. Centripetal force is not a new kind of force but the net inward force provided by something physical: tension in a string swinging a ball, friction between tires and road on a curve, gravity holding a planet in orbit, or the track pushing a roller-coaster car. The centripetal acceleration, velocity squared over radius, points inward too and is what changes the object's direction without changing its speed. Engineers, physics students, and designers of vehicles, rides, and machinery use this to ensure paths can supply enough force safely. Enter the mass, velocity, and radius to compute the centripetal force.
F = m·v² / r
Centripetal force equals the mass of an object times the square of its speed divided by the radius of its circular path. It always points toward the center of the circle. The centripetal acceleration is the speed squared over the radius. A faster speed or tighter radius sharply increases the force required to maintain circular motion.
Source:Classical mechanics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter mass, velocity and radius.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Centripetal force updates instantly as you type — no button to press.
Frequently asked questions
What is centripetal force?
Centripetal force is the net inward force that keeps an object moving along a circular path, directed toward the center of the circle. It is not a separate force but is supplied by physical sources like tension, friction, or gravity. Without it, the object would fly off in a straight line by inertia.
How do you calculate centripetal force?
Multiply the object's mass by the square of its speed, then divide by the radius of the circular path. So a 2-kilogram object moving at 3 meters per second in a 1.5-meter circle needs 12 newtons of force. The calculator computes both the force and the centripetal acceleration from your inputs.
Why does speed have such a big effect?
Centripetal force depends on the square of the speed, so doubling the speed quadruples the required force. This is why cornering at high speed is so demanding and why speed limits on curves matter: a small increase in speed needs a large increase in the friction or grip available to hold the turn.
What provides the centripetal force in real situations?
It varies with the situation. For a car rounding a bend, friction between the tires and road provides it; for a planet orbiting the sun, gravity does; for a ball on a string, the string's tension does; and for a roller coaster, the track pushes inward. Centripetal force is always some real force acting toward the center.
What is the difference between centripetal and centrifugal force?
Centripetal force is the real inward force that keeps an object in circular motion. Centrifugal force is the apparent outward force felt by an object in a rotating frame, which is a fictitious force arising from inertia, not a real push outward. This calculator computes the real, inward centripetal force.