Centrifugal Force Calculator

What the centrifugal force calculator does

When something spins, anything riding along with it seems to be flung outward. This calculator works out the size of that apparent outward force, the centrifugal force, from the mass, the radius of rotation, and the rotational speed. As with the others, you can solve instead for the mass, the radius, or the speed when you know the force.

Below is what centrifugal force really is, how it differs from centripetal force, the equations behind it, and a worked example.

How to use it

1. Choose what to calculate: the force, the mass, the radius, or the speed.
2. Pick how you are giving the speed, as an angular velocity in radians per second or a tangential velocity in metres per second, and enter the values requested.
3. Press Calculate for the result, or Reset to clear it.

What centrifugal force is

Centrifugal force is the outward push you seem to feel when you are part of a spinning system. Sitting in a car that swings hard around a bend, you feel thrown toward the outer door. On a fast roundabout, you feel pulled away from the middle. That sensation of being pushed outward is what we call centrifugal force, and the word means center-fleeing.

What is interesting is what is really happening. In the everyday sense, nothing is actually pushing you outward. Your body, like anything in motion, simply wants to keep going in a straight line, and the spinning seat or car is forcing it to curve instead. The outward feeling is your own inertia resisting that curve. Physicists call centrifugal force a fictitious or pseudo-force for exactly this reason: it is real to feel, but it is the felt effect of inertia inside a rotating frame, not a push from anything. The calculator gives its magnitude, the size of that apparent outward effect.

Centrifugal versus centripetal

The two words are easy to mix up, and the difference comes down to point of view. Centripetal force is the real, inward force that actually keeps an object moving in a circle, supplied by gravity, friction, tension, or a push. Centrifugal force is the apparent, outward force you seem to feel when you yourself are going around. They have the same size and point in opposite directions, but they belong to different frames of reference.

Picture the car on the bend from two viewpoints. Standing at the roadside, you see only the inward centripetal force: the door pushing the passenger inward, bending their path into the curve. Sitting inside the car, the passenger instead feels an outward centrifugal force pinning them to the door. Both descriptions are useful, but only the inward one corresponds to an actual push. The outward one is the convenient way to describe how things behave from inside the spin, where inertia shows up as an outward force. An observer who is not rotating never sees it at all.

The equations it uses

Because the centrifugal force has the same magnitude as the centripetal force, it uses the same relationship. With the tangential speed v it is:

F = m v² ÷ r

And with the angular velocity ω, the rate of spin in radians per second, it is:

F = m r ω²

Here m is the mass and r is the distance from the axis of rotation. The calculator accepts whichever measure of speed you have and rearranges the same formula to solve for mass, radius, or speed as needed. The only thing that changes between this and the centripetal case is the direction you assign to the force, and the frame you are describing it from.

Where it is put to work

Although centrifugal force is an apparent effect, treating it as a force is genuinely useful, because for anyone or anything inside a rotating system it behaves exactly like one. Engineers lean on it constantly. A centrifuge spins samples so that the apparent outward force drives denser material to the bottom of the tube, separating blood, isolating particles, or enriching materials. A spin dryer flings water out through the drum holes the same way.

The idea reaches further than machines. A spinning space station could create artificial gravity by rotating, so that the outward effect presses inhabitants against the outer wall and mimics standing on a floor. Designers of fast roads and fairground rides bank the curves precisely to work with this apparent force rather than against it. In all these cases, calculating the centrifugal force tells you how strong that outward effect will be, which is what this tool provides.

Units and precision

The calculator works in SI units: mass in kilograms, radius in metres, tangential velocity in metres per second or angular velocity in radians per second, and the force in newtons. The relationship is exact, so the result is as precise as the inputs; it assumes steady rotation at a constant rate. Results are shown to several decimal places.

A worked example

Take a 2 kilogram mass rotating at the end of an arm 1.5 metres long, moving at 10 metres per second.

The centrifugal force is F = mv²/r = (2 × 10²) ÷ 1.5 ≈ 133 newtons, the apparent outward force felt by the rotating mass. It is exactly equal to the inward centripetal force holding the mass on its path; the two are the same number seen from opposite frames. Spin it faster and the effect climbs steeply, since the speed enters squared.

Questions people ask

Is centrifugal force a real force?

Not in the everyday sense. It is a fictitious or pseudo-force, an apparent outward effect felt only in a rotating frame, caused by inertia. An observer who is not rotating sees only the real inward centripetal force.

What is the difference between centrifugal and centripetal force?

Centripetal is the real inward force that keeps an object moving in a circle; centrifugal is the apparent outward force you feel when you are inside the rotation. Same magnitude, opposite direction, different frames of reference.

How do you calculate centrifugal force?

With the same formula as centripetal force: F = mv²/r using tangential speed, or F = mrω² using angular velocity. Only the assigned direction differs.

Why do I feel pushed outward when a car turns?

Your body wants to keep moving straight, and the car forces it to curve. The outward feeling is your inertia resisting that curve. The door actually pushes you inward; the outward push is the felt effect, not a real force.

References

A quick note on where the physics comes from. The treatment of centrifugal force as a fictitious force in a rotating frame, with the same magnitude as the centripetal force, is standard mechanics, described in the Wikipedia article on centrifugal force and in OpenStax's University Physics. The SI units follow the US National Institute of Standards and Technology.

1. Wikipedia, Centrifugal force. https://en.wikipedia.org/wiki/Centrifugal_force
2. OpenStax, University Physics Volume 1, Section 6.3, Centripetal Force. https://openstax.org/books/university-physics-volume-1/pages/6-3-centripetal-force
3. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811