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Centripetal Force Calculator

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Enter mass, velocity, and radius to find the centripetal force keeping an object moving in a circle.

Centripetal Force Calculator

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Centripetal force
40 N
This force always points toward the center of the circular path.

The formula

Centripetal force = (Mass x Velocity^2) / Radius
Example

A 2 kg object moving at 10 m/s on a 5-meter-radius circular path: Fc = (2 x 100) / 5 = 40 newtons.

Step-by-step guide

  1. Enter the object's mass, velocity, and the radius of its circular path.
  2. Read the centripetal force required to maintain that circular motion.

Why circular motion requires constant inward force

An object moving in a circle is constantly accelerating, even at a perfectly constant speed - because acceleration includes any change in direction, not just speed. That constant change in direction requires a continuous inward-pointing force (the centripetal force), without which the object would simply fly off in a straight line, following Newton's first law. This is exactly what you feel as the sideways pull in a car taking a sharp turn - the car's tires provide the centripetal force keeping you moving in a curve rather than straight ahead.

Common mistakes

Forgetting to square the velocity - this is a very common slip that significantly understates the true centripetal force required.
Confusing centripetal force with "centrifugal force" - centripetal force is the real, inward force causing circular motion, while centrifugal force is an apparent, outward-feeling effect experienced only from within the rotating reference frame itself.

Frequently asked questions

What provides the centripetal force in real situations?

It depends on the situation - friction between tires and road for a turning car, tension in a string for a swung ball, or gravity itself for a satellite orbiting a planet. The formula calculates how much force is needed; the source of that force varies by context.

Why does a tighter turn (smaller radius) need more force?

Because radius is in the denominator of the formula - a smaller radius at the same mass and speed means dividing by a smaller number, which increases the required force, matching the everyday experience that sharp turns feel more forceful than gentle curves.

Is centrifugal force real?

It's real as a perceived effect within a rotating frame of reference (like feeling pushed outward in a spinning car), but it's not a true force in the standard sense - what you're actually feeling is your own body's inertia resisting the car's inward centripetal acceleration.

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