Centripetal Force Calculator

What Is Centripetal Force?

Centripetal force is the real inward force that keeps an object moving along a curved or circular path. Without centripetal force, an object in motion would travel in a straight line, according to Newton's first law of motion (the law of inertia).

Different types of forces can act as centripetal force depending on the situation. For a car turning on a road, it is the friction between the tires and the pavement. For a satellite orbiting Earth, it is gravity. For a ball on a string, it is the tension in the string.

How to Calculate Centripetal Force

Centripetal Force Formula

The formula to calculate centripetal force is:

Where:

• F = centripetal force (N)
• m = mass of the object (kg)
• v = speed of the object (m/s)
• r = radius of the circular path (m)

You can also express this using angular velocity: F = mω²r, where ω is in rad/s.

Worked Example: Car on a Curve

Let's calculate the centripetal force for a 1,500 kg car traveling at 20 m/s (about 45 mph) around a curve with a 50-meter radius.

F = 1,500 × 20² / 50
F = 1,500 × 400 / 50
F = 12,000 N

The centripetal acceleration in this case is v²/r = 400/50 = 8 m/s², which is about 0.82 g of lateral force. This centripetal force must be provided entirely by the friction between the tires and the road surface.

Centripetal Force vs. Centrifugal Force

Centripetal force and centrifugal force have the same magnitude but act in opposite directions. Centripetal force is the real inward force, while centrifugal force is the apparent outward force felt in a rotating reference frame. Use our centrifugal force calculator to find the outward force.