What this calculator does
Centrifugal force is the outward push you feel when a car corners hard or a washing machine spins on high. This calculator works out its size from mass, speed and the radius of the circular path, using the same formula, F = mv²/r, that governs circular motion generally.
The confusing part is that centrifugal force is not a real force in the usual sense: it only appears if you do the physics from inside the rotating object, treating it as if it were standing still. From outside, watching from a fixed point, the only real force acting is centripetal force, pulling inward and keeping the object on its circular path. Centrifugal force is what that inward pull feels like from the rotating passenger’s point of view, equal in size but pointing the other way.
The formula
Centrifugal force is calculated the same way as centripetal force: mass times speed squared, divided by radius. The result also equals mass times angular velocity squared times radius, which is the same number reached a different way.
| Term | Meaning |
|---|---|
| Centripetal force | The real, inward force (from friction, tension, gravity or a normal force) that keeps an object moving in a circle rather than a straight line. |
| Centrifugal force | The apparent outward force felt in the rotating object’s own frame of reference, equal in magnitude to the centripetal force but pointing outward. |
| ω (angular velocity) | Speed divided by radius, in radians per second: how fast the object sweeps around the circle. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the object moving in a circle. |
| Speed (m/s) | Its speed along the circular path. |
| Radius (m) | The radius of the circle it is travelling on. |
When to use it
Explaining why passengers slide in a turn
A passenger in a cornering car feels pushed toward the outside of the bend. That sensation is centrifugal force in the car’s rotating frame; from the road’s point of view, it is really the car (via friction from the tyres, a real centripetal force) turning underneath the passenger’s own straight-line inertia.
Sizing a centrifuge or spin-dryer drum
Lab centrifuges and washing machine spin cycles are rated by the outward force (or the equivalent g-force) reached at a given radius and speed, which is exactly this calculation.
Understanding orbital and rotational mechanics
In problems that are easier to analyse from a rotating frame, such as an object on a spinning platform or a satellite in a co-rotating reference frame, centrifugal force is the standard way to account for the rotation without switching back to an external, non-rotating viewpoint.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does centrifugal force change with speed?
A fixed mass and radius, across a range of speeds.
| Speed | Centrifugal force (apparent, outward) | In g |
|---|---|---|
| 2 m/s | 10.000 N | 0.510 g |
| 4 m/s | 40.000 N | 2.039 g |
| 5 m/s | 62.500 N | 3.187 g |
| 8 m/s | 160.000 N | 8.158 g |
| 10 m/s | 250.000 N | 12.746 g |
| 15 m/s | 562.500 N | 28.680 g |
How does centrifugal force change with radius, at a fixed speed?
A fixed mass and speed, across a range of radii.
| Radius | Centrifugal force (apparent, outward) | Angular velocity |
|---|---|---|
| 0.2 m | 250.000 N | 25.000 rad/s |
| 0.4 m | 125.000 N | 12.500 rad/s |
| 0.8 m | 62.500 N | 6.250 rad/s |
| 1.2 m | 41.667 N | 4.167 rad/s |
| 2 m | 25.000 N | 2.500 rad/s |
| 3 m | 16.667 N | 1.667 rad/s |
Questions
Is centrifugal force a real force?
Not in the way gravity or friction are real forces. It is a pseudo-force, or fictitious force, that only needs to be included in the maths when working in a rotating reference frame. Viewed from outside the rotation, no outward force actually exists; only the inward centripetal force is real.
Why do the numbers come out identical to centripetal force?
Because both describe the same physical situation from opposite viewpoints, using the same formula, F = mv²/r. The magnitude is identical by construction; only the direction and the question of whether the force is "real" differ between the two framings.
What is an everyday example of centrifugal force?
Water flung outward and off a spinning bicycle wheel, wet clothes pressed against the outer drum of a washing machine on spin cycle, and the sensation of being pushed sideways in a car taking a corner are all commonly described using centrifugal force, since they are all experienced from within the rotating system.
How does this relate to g-force?
The acceleration figure this calculator reports can be converted to a multiple of standard gravity (g), which is the more familiar way rotational forces are described in contexts like theme park rides, motorsport and centrifuge training.
For the same physics described from the fixed, non-rotating point of view, see the centripetal force calculator. To express the resulting acceleration as a multiple of gravity, use the g-force calculator.