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 is the name given to whatever force (tension, gravity, friction, normal force) acts as the inward force in a given situation.

What is the formula for centripetal force?

F = mv²/r, where F is the centripetal force in Newtons, m is the mass in kilograms, v is the tangential velocity in meters per second, and r is the radius of the circular path in meters.

What units does this calculator use?

The calculator uses SI units: mass in kilograms (kg), velocity in meters per second (m/s), radius in meters (m), and force in Newtons (N). Make sure to convert your values to these units before entering them.

What is centripetal acceleration?

Centripetal acceleration a = v²/r is the acceleration directed toward the center of the circular path. Multiplying it by the mass gives centripetal force: F = ma = mv²/r.

Can I calculate the required velocity or radius instead?

Yes. Rearranging F = mv²/r gives v = √(Fr/m) for velocity and r = mv²/F for radius. The calculator supports all three solve modes — select what you want to find and fill in the other two values.

Centripetal Force Calculator

Name: Centripetal Force Calculator
Availability: InStock
Author: Nham Vu

Calculate centripetal force F = mv²/r for circular motion given mass, velocity, and radius.

Circular Motion Inputs

Fill in any two values and the unknown to solve for.

Solve for

Mass (m)

Velocity (v)

m/s

Radius (r)

Result

Enter values and click Calculate.

Formula Reference

Find Force

F = mv² / r

Find Velocity

v = √(F·r / m)

Find Radius

r = mv² / F

Summary

Calculate centripetal force F = mv²/r for circular motion given mass, velocity, and radius.

How it works

Enter the mass of the object in kilograms.
Enter the velocity (tangential speed) of the object in meters per second.
Enter the radius of the circular path in meters.
Click Calculate to apply the formula F = mv²/r.
The result is displayed in Newtons along with the step-by-step breakdown.

Use cases

Physics homework and exam preparation for circular motion problems.
Engineering design of curves, bends, and roundabouts for vehicles.
Calculating tension in a string for an object in horizontal circular motion.
Determining the normal force on a car navigating a banked curve.
Aerospace and orbital mechanics concepts involving centripetal acceleration.
Lab calculations to verify experimental circular motion setups.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu