⭕ Centripetal Force Calculator
F = mv²/r — Circular motion solver for force, mass, speed, or radius.
Result
How to Use This Calculator
Select the variable you want to find from the dropdown, then enter the three remaining values. You can solve for centripetal force F, mass m, speed v, or radius r. When you solve for F, the calculator also gives you centripetal acceleration, angular velocity, and the period of circular motion.
Choose what to solve for: Force (N), Mass (kg), Speed (m/s), or Radius (m).
Enter mass in kilograms. For a 500 g ball on a string, enter 0.5.
Enter tangential speed in m/s. This is the speed along the circular path, not the angular velocity.
Enter the radius of the circular path in metres. Click Calculate to get your answer plus the bonus outputs.
Centripetal Force Formula
F is force in newtons, m is mass in kilograms, v is tangential speed in m/s, and r is the radius in metres. Notice that force grows with the square of speed: doubling your speed on a circular track requires four times the friction to stay on the curve. That is why cars on motorway on-ramps are speed-limited.
Worked Examples
Where This Comes Up in Real Life
When a car corners, friction between tyres and road is the centripetal force. At 60 km/h (16.7 m/s) on a 40 m radius bend, a 1200 kg car needs F = 1200 × 16.7² / 40 = 8,337 N of friction. If the road is wet and friction cannot supply this, the car slides wide. Banked roads tilt so that the normal force from the road surface contributes to centripetal force, reducing how much grip is needed.
Satellites in circular orbits are in continuous free fall around the Earth. Gravity provides the centripetal force. For the ISS at about 400 km altitude, the required speed to stay in orbit works out to about 7,660 m/s. A centrifuge in a laboratory spins biological samples at thousands of RPM to create large centripetal accelerations that separate particles by density far faster than gravity alone could manage.
Frequently Asked Questions
What is centripetal force?
Centripetal force is the net force directed toward the center of a circular path that keeps an object moving in a circle. It is not a separate type of force — it's provided by tension, gravity, friction, or normal force.
What is the centripetal force formula?
F = mv²/r, where m is mass (kg), v is tangential speed (m/s), and r is radius of the circular path (m).
What is centripetal vs centrifugal force?
Centripetal force is real — it acts toward the center. Centrifugal force is a fictitious force felt in the rotating reference frame, acting outward.
How is centripetal force related to angular velocity?
F = mω²r, where ω is angular velocity in rad/s. Also: v = ωr, so both formulas are equivalent.
What provides centripetal force in everyday examples?
Car turning: friction. Satellite orbit: gravity. Carnival ride: normal force and tension. Electron in orbit: electric force.