Centripetal Force Calculator

Enter mass, tangential speed, and radius to calculate inward acceleration, force, angular speed, and RPM.

Mass

Tangential speed

Radius

—centripetal m/s²

—force N

—angular rad/s

—RPM

—a = v²/r · F = mv²/r

These are idealized classical-physics calculations. Real systems can differ because of air resistance, friction, deformation, measurement uncertainty, non-constant forces, or other effects not included in the selected model.

Physics model preflight

Check the governing model before trusting the number

uniform circular motion

aᶜ = v²/r · Fᶜ = mv²/r

Reading the current native inputs…

Radius must be positive; entered speed is tangential speed magnitude. This is an idealized educational model: unit consistency and valid inputs do not guarantee that omitted effects are negligible in a real system.

State the model before trusting the number

Classical formulas are only as good as their assumptions and units. Air resistance, damping, deformation, non-constant forces and measurement uncertainty are not silently invented when the selected model does not include them.

Governing physics model

aᶜ = v²/r · Fᶜ = mv²/r — uniform circular motion.

How to verify the result

The force divided by mass should equal v²/r. Doubling speed should quadruple centripetal acceleration and force.

Domain and assumption boundary

Radius must be positive; entered speed is tangential speed magnitude. The calculator does not silently add drag, damping, deformation, varying fields, relativistic effects, measurement uncertainty, or geometry that the selected model does not contain.

Practical guide and verification

Identify the radial force, not a new kind of force

Centripetal force is the net inward force required for circular motion, F = m v² / r. Depending on the setup, tension, friction, gravity, a normal force or a combination of forces can supply that radial net force. Do not add a separate “centripetal force” on top of those physical forces in a free-body diagram.

Square the speed only after unit conversion

Because speed is squared, a unit mistake has an amplified effect. Convert mph, km/h or other speed units into the unit system used by the force equation before squaring, and keep the radius in a compatible length unit.

Use radius of the actual path

The radius belongs to the trajectory of the object or its center of mass, not necessarily the diameter of a wheel, turn or apparatus. If a problem supplies diameter, convert it to radius explicitly before substituting.

Check limiting friction or tension separately

The required inward force may exceed what tires, a string, a track or another constraint can supply. Compare the calculated requirement with the available friction, tension or structural limit when the question is about whether the motion is feasible rather than only what force would be required.

Verify with radial acceleration

Calculate a = v²/r independently and then multiply by mass. The result should match F = m v²/r after unit conversion. This two-step route provides a useful dimensional and arithmetic check without changing the underlying physical model.