Formula and Method for Centrifugal Force
Centrifugal force is the outward push felt by an object moving along a curved or circular path, as experienced from inside the rotating frame itself — the shove you feel outward when a car takes a sharp turn, or that presses a passenger against the door of a spinning carnival ride. Viewed from a fixed point outside the rotation, there is no outward force at all; instead a real inward force called centripetal force (string tension, friction, gravity, or a wall) continuously bends the object's path toward the center. Centrifugal force is the mathematically convenient "fictitious" or pseudo-force that appears when the physics is worked out from inside the rotating system, and its magnitude exactly equals the centripetal force: F = m ω² r = m v² / r, where m is mass, ω is angular velocity in radians per second, r is the radius of the circular path, and v is the tangential (linear) speed.
How the calculation works
Enter the object's mass, the radius of its circular path, and its rotational speed in whichever unit is most convenient. The calculator converts mass to kilograms, radius to meters, and rotational speed to radians per second (ω) internally, then computes the tangential velocity v = ω r and the centrifugal force F = m ω² r. It also expresses that force as a multiple of standard gravity (g = 9.80665 m/s²) so you can compare it against familiar references, such as roller coasters (typically 2-4 g) or high-performance aircraft turns (up to about 9 g).
Centrifugal vs. centripetal force
These two forces share the same magnitude but describe the same rotation from opposite reference frames. Centripetal force is real: it is the net inward force that causes circular motion in the first place. Centrifugal force is what an object "feels" inside the rotating frame — it is not applied by any physical agent, which is why physicists label it fictitious, even though the sensation (and the outward reactive force a rotating object exerts back on whatever restrains it, per Newton's third law) is very real.
Common mistakes and real-world uses
- Using diameter instead of radius: since F depends on r, not d = 2r, plugging in a diameter doubles the radius and produces a force twice too large — halve any diameter measurement first.
- Mixing rotational-speed units: 1 rpm is only 2π/60 ≈ 0.1047 rad/s, so feeding an rpm value directly into ω without converting overstates the force by roughly a factor of 36.
- Applications: this formula sizes laboratory and industrial centrifuges, rates amusement-park rides and centrifugal pumps, checks the cornering forces on vehicle tires, and explains how washing-machine drums spin water out of wet clothes.