Centripetal Force
Calculate centripetal force, velocity, or radius for uniform circular motion using F = mv²/r, with clear step-by-step formulas.
Key formula
F = mv^2 / r
How do you calculate centripetal force?
For uniform circular motion, F = m v² / r. Multiply mass by speed squared, then divide by radius. Rearrange to v = √(F r / m) or r = m v² / F when force is given. Report force in newtons toward the centre of the circle.
About this tool
Centripetal force is the inward force that keeps an object on a circular path. This page keeps F = mv²/r visible so you can solve for force, speed, or radius without losing the unit and direction checks that usually cost marks.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: 2.0 kg at 4.0 m/s, r = 2.0 m
F = m v² / r = (2.0)(4.0)² / 2.0 = (2.0)(16) / 2.0 = 16 N toward the centre. Check: a = v²/r = 8 m/s², then F = ma = 16 N.
Example 2: find speed from 45 N
A 5.0 kg mass needs F = 45 N on a 5.0 m radius. v = √(F r / m) = √(45 × 5.0 / 5.0) = √45 ≈ 6.71 m/s. Check: (5)(45)/5 = 45 N.
Example 3: convert km/h first
A 0.50 kg ball on a 1.0 m string at 36 km/h. First v = 36 / 3.6 = 10 m/s. F = (0.50)(10)² / 1.0 = 50 N. Using 36 m/s wrongly would give about 648 N.
Frequently asked questions
What is the formula for centripetal force?
F = m v² / r for uniform circular motion. Mass m is in kg, speed v in m/s, radius r in m, and F in newtons toward the centre. Equivalently F = m a with a = v²/r.
Is centripetal force a new kind of force?
No. It is the net inward force requirement. Friction, tension, gravity, or a normal force (or a combination) can supply it. The formula tells you how large that inward net force must be.
What is the difference between centripetal and centrifugal?
In the inertial lab frame used in most school problems, the object needs an inward centripetal force. “Centrifugal force” is a fictitious outward force that appears in rotating frames — do not add both in the same free-body diagram.
How do I convert km/h for circular motion?
Divide km/h by 3.6 to get m/s before substituting into F = mv²/r. Leaving km/h in the formula inflates v² and the force.
Can I use F = m ω² r instead?
Yes when angular speed ω (rad/s) is given: F = m ω² r, and v = ω r. Use F = mv²/r when the problem gives linear speed.