Anything moving in a circle is being pulled toward the centre — and from the rotating point of view, it feels pushed outward with a force of mv²/r. This centrifugal force calculator computes that force from mass, speed and radius (or from angular velocity), together with the centripetal acceleration it corresponds to and the g-force equivalent that engineers and racing drivers actually quote.
The Formula, Twice Over
In speed form: F = mv²/r. In angular form: F = mω²r, with ω the angular velocity in rad/s (and v = ωr connecting the two). The page’s default — a 2 kg mass at 10 m/s on a 5 m radius — gives F = 2 × 100 ÷ 5 = 40 N, an acceleration of 20 m/s², just over 2 g. Both forms are printed by the calculator so you can start from whichever your problem states: a tachometer’s rpm (convert: ω = rpm × 2π/60), a lap time, or a road speed. The units are honest SI throughout — kilograms, metres, seconds — because centrifugal folklore in mixed units is how centrifuge rotors get oversped.
Centrifugal vs Centripetal: One Force, Two Frames
The pedantic point, made once and then used freely: in an inertial frame there is no outward force — there is the inward centripetal force (from the rope, the road’s friction, the tube wall) bending the velocity toward the centre, and inertia doing the rest. In the rotating frame — the driver’s seat, the spinning station, the centrifuge tube — an outward “centrifugal” pseudoforce of exactly mv²/r balances the books and predicts everything correctly within that frame. Engineers design in the rotating frame constantly (it is where the stresses live), which is why this page carries the name on the tin. The magnitude is not in dispute between the frames; only the bookkeeping is.
The v² Tyranny
Everything dramatic about circular motion comes from the square. Double the speed and the force quadruples; halve the radius and it doubles. A car cornering at 20 m/s on a 50 m bend pulls 8 m/s² (0.8 g, near the tyre limit); the same bend at 28 m/s needs 1.6 g and leaves the road. A washing machine’s spin at 15 rev/s flings water outward at hundreds of g — on purpose. A laboratory centrifuge at 10,000 rpm with a 10 cm rotor generates over 11,000 g, which is why its manual speaks of RCF (relative centrifugal force, exactly the g-multiple this calculator reports) rather than rpm: different radii at the same rpm are different machines.
Where the Number Works
Road and rail design (banking angles chosen so the required friction stays sane at the design speed — the angle-of-banking sibling problem), centrifuge specification and sample prep (RCF converts to rotor speed for your rotor radius via this formula), amusement-ride certification, satellite and space-station artificial gravity (ω²r budgeted against motion sickness at low rpm, which forces big radii), and motorsport, where lateral g is the lap time. In each the workflow is identical: geometry and speed in, force and g out, compare against the material or human limit.
Earth Gets a Vote
The planet itself runs this calculation on you: at the equator, Earth’s rotation (ω = 7.29 × 10⁻⁵ rad/s, r = 6.37 × 10⁶ m) produces ω²r ≈ 0.034 m/s² of centrifugal acceleration — about 0.35 percent of g, quietly subtracted from your weight and one reason g is smaller at the equator than at the poles (the bulge the same effect created does the rest). Small, but geodesy measures it, rocket ranges exploit it (equatorial launches borrow the 465 m/s of tangential speed), and it is the correct first answer to “why is the Earth not a sphere.”
Common Mistakes
Entering diameter where radius belongs — a clean factor-of-two error. Feeding rpm into the ω slot without the 2π/60 conversion (the calculator accepts rpm only via its printed conversion, and shows you the rad/s it used). Believing centrifugal force can be “turned off” separately from the rotation. And applying mv²/r to non-circular paths pointlessly: on curves of varying radius the formula still works instantaneously — with r the local radius of curvature — which is how road engineers use it on clothoid bends.
Related Tools
The mechanics bench continues in the Physics Calculators hub — the Tension Calculator supplies the rope that provides this force in the classic demo, and the Speed of Sound Calculator covers straight-line wave motion.
Frequently Asked Questions
How do you calculate centrifugal force?
F = mv²/r with speed, or F = mω²r with angular velocity. A 2 kg mass at 10 m/s on a 5 m radius experiences 40 N — an acceleration of 20 m/s², about 2 g.
Is centrifugal force real?
It is a pseudoforce: absent in inertial frames, where the inward centripetal force and inertia explain everything, but fully valid and indispensable inside the rotating frame, where stresses, sensations and engineering all live. Its magnitude, mv²/r, is frame-independent fact.
What is RCF in a centrifuge?
Relative centrifugal force — the acceleration in multiples of g: RCF = ω²r ÷ 9.81. It, not rpm, is the transferable specification, because two rotors at the same rpm but different radii produce different RCF. This calculator outputs the g-multiple directly.
Why does doubling speed quadruple the force?
The speed enters squared — kinetic direction changes twice as fast and each change is twice as large. It is why modest speed increases on the same bend overwhelm tyres that felt comfortable slightly slower.
How do I convert rpm to angular velocity?
ω (rad/s) = rpm × 2π ÷ 60. A 3,000 rpm shaft spins at about 314 rad/s. Enter speed mode with v = ω × r, or use the angular mode of this calculator directly.
Does centrifugal force affect my weight at the equator?
Slightly: Earth’s rotation supplies about 0.034 m/s² outward at the equator, roughly a third of a percent of g — one reason measured gravity is lower there than at the poles.