Centripetal Force Calculator

How it works

1. 1Enter the mass of the object and the radius of the circular path.
2. 2Choose “Linear speed” and enter the tangential speed v, or “Angular speed” and enter ω in rad/s.
3. 3The calculator applies F = mv²/r (linear) or F = mω²r (angular) and shows the centripetal force.

Use cases

• Designing banked curves and roundabouts to find the required friction or banking angle.
• Engineering centrifuges and rotating machinery where loads depend on centripetal force.
• Physics coursework on planets, satellites, and any object in uniform circular motion.

Frequently asked questions

What is the formula for centripetal force?

F = mv²/r when you know the linear speed v, or equivalently F = mω²r when you know the angular speed ω in rad/s. For example, a 2 kg object at 10 m/s on a circle of radius 5 m experiences F = 2 × 10² ÷ 5 = 40 N.

In which direction does centripetal force act?

Centripetal force always points toward the centre of the circular path — it is the net inward force that continuously redirects the object’s velocity without changing its speed. When a car turns, road friction provides this inward force.

How do I convert between linear and angular speed?

Linear speed v (m/s) and angular speed ω (rad/s) are related by v = ω·r. For a 0.5 m radius wheel spinning at 20 rad/s, the rim moves at v = 20 × 0.5 = 10 m/s, giving the same centripetal force either way.