PhysicsCalcs
Forces

Centripetal Force Calculator

Calculate centripetal force (mv\u00B2/r), acceleration, speed, radius, or mass for circular motion. Supports angular velocity (\u03C9) and RPM inputs.

Interactive calculator

Centripetal Force Calculator

Calculate centripetal force, acceleration, speed, radius, or mass for circular motion. Supports angular velocity and RPM modes.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Select what to find: force, acceleration, speed, radius, or mass.
  • Enter known values (mass, speed, radius, \u03C9, RPM).
  • Click Calculate for centripetal force and related values.

Table of Contents

Key Takeaways

  • Centripetal force (F = mv²/r) keeps an object moving in a circle.
  • It is always directed toward the centre of the circular path.
  • Centripetal force is not a new type of force — it’s provided by tension, gravity, friction, etc.
  • Centripetal acceleration aᴄ = v²/r changes direction, not speed.
  • Using angular velocity: F = mrω² and v = rω.
  • Centrifugal force is fictitious, appearing only in rotating reference frames.

What Is Centripetal Force?

Centripetal force is the net force directed toward the centre of a circular path that keeps an object moving in a circle. Without it, the object would travel in a straight line (Newton’s first law). It’s not a new kind of force — it’s provided by real forces like gravity, tension, or friction.

F = mv²/r

Fc=mv2/rF_c = mv^2 / r

This relates the centripetal force to the mass, speed, and radius of the circular path. Doubling the speed quadruples the required force.

F = mrω² (Angular Velocity Form)

Fc=mrω2F_c = mr\omega^2

Using angular velocity ω (rad/s) instead of linear speed. Useful for rotating machinery, centrifuges, and orbital calculations. Convert RPM to ω: ω = RPM × 2π/60.

Centripetal vs Centrifugal Force

Centripetal = real inward force (exists in all reference frames).

Centrifugal = fictitious outward force (only appears in a rotating reference frame). When you feel “pushed outward” on a merry-go-round, that’s the centrifugal effect in your rotating frame.

How to Use the Calculator

  1. Choose a calculation mode for your known quantities.
  2. Enter values with units.
  3. Click Calculate.
  4. Review force, acceleration, speed, and radius results.

Example Calculations

Car: 1500 kg, 20 m/s, r = 50 m

F = 1500 × 400 / 50 = 12,000 N = 12 kN

Ball on string: 0.5 kg, 3 m/s, r = 1 m

F = 0.5 × 9 / 1 = 4.5 N

Centrifuge: 0.01 kg, r=0.1 m, 3000 RPM

ω = 314.2 rad/s, F = 0.01 × 0.1 × 314.2² = 987.4 N

Common Mistakes

  • Thinking centripetal force is a separate force (it’s the net radial force).
  • Confusing centripetal (inward) with centrifugal (outward, fictitious).
  • Using diameter instead of radius.
  • Forgetting to convert RPM to rad/s before applying the formula.

Accuracy and Limitations

These formulas assume uniform circular motion (constant speed). For non-uniform circular motion, tangential acceleration must also be considered. The calculator does not account for air drag, friction losses, or elastic effects. Results are for education and estimation.

FAQ

What is centripetal force?›

It’s the net inward force required to keep an object moving along a curved path. For a car on a curve, friction provides it; for a satellite, gravity provides it.

Is centrifugal force real?›

Centrifugal force is a fictitious (pseudo) force that appears in a rotating reference frame. In an inertial frame, only centripetal force exists.

What provides centripetal force?›

Any real force can act as centripetal force: gravity (orbits), tension (ball on a string), friction (car on a curve), normal force (loop-the-loop).

Does centripetal force do work?›

No. Centripetal force is always perpendicular to velocity, so it does zero work. It changes direction, not speed.

How do I convert RPM to angular velocity?›

ω = RPM × 2π/60 rad/s. For example, 60 RPM = 2π rad/s ≈ 6.28 rad/s.

What happens if centripetal force is removed?›

The object moves in a straight line tangent to the circle (Newton’s first law). It does not fly outward.

Sources

  1. OpenStax University Physics – Centripetal Force
  2. HyperPhysics – Centripetal Force
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish