🎡 Centripetal Acceleration Calculator

Anything moving in a circle is accelerating — even at constant speed — because acceleration is a change in velocity and velocity includes direction. The centripetal acceleration points toward the centre of the circle and has magnitude a = v²/r (from linear speed v and radius r) or a = 4π²r/T² (from rotation period T). The force that produces it, F = m·a, is the centripetal force: friction on a corner, tension in a string, or gravity in orbit.

Why it matters in daily life: a car rounding a corner needs friction to provide this force, and the required force grows with the square of speed — twice the speed, four times the force. That quadratic growth is why cornering at high speed is so dramatically more dangerous than a moderate speed.

The calculator accepts two input styles: linear speed (m/s, km/h or mph) plus radius, or rotation period (seconds per turn) plus radius. It computes a = v²/r in m/s², converts to multiples of standard gravity (divide by 9.80665), and optionally derives the period from a given RPM. If you enter a rotating mass, it also reports the centripetal force F = m·a in newtons.

The derived g-force reading (multiples of Earth gravity) is the figure pilots, racing engineers and ride designers quote, and the centripetal force for your mass tells you what your body experiences. Pair the result with our acceleration calculator for linear motion or the speed converter to switch units before computing.

1. Choose the input mode: linear speed, or rotation period / RPM.
2. Enter the speed (or period) and its unit.
3. Enter the radius of the circular path and its unit.
4. Optionally enter a rotating mass to get the centripetal force.
5. Click Calculate to see acceleration in m/s², g-force and the derived force.

Why is something moving at constant speed still accelerating?

Speed is only the magnitude of velocity; velocity is a vector that also includes direction. Uniform circular motion constantly changes direction, so the velocity vector keeps turning — an acceleration. The acceleration is perpendicular to the motion, toward the centre.

What does 1 g feel like?

1 g is 9.80665 m/s² — your normal weight. Fighter pilots train to about 9 g, where a 70 kg pilot effectively weighs 630 kg. At 4–5 g (a large roller coaster loop) blood pools in the legs and vision starts to grey without a suit.

Why does doubling speed quadruple the force?

Because acceleration scales as v². The tyres (or the string, or gravity) must supply four times the force at twice the speed for the same radius. This is why safe cornering speed is so sensitive — and why speed limits drop sharply on sharp curves.

Is the centripetal force a new kind of force?

No — it is the name for whatever real force happens to pull toward the centre: friction for a car, tension for a ball on a string, gravity for a satellite, the normal force at the top of a loop. 'Centrifugal force' is a fictitious force that appears only in a rotating frame of reference.

How is the ISS still 'weightless' if gravity is still 0.88 g there?

Weightlessness is not zero gravity — at ISS altitude gravity is about 88% of the surface value. The crew and station are in free fall, both accelerating toward Earth at the same rate, so nothing pushes against anything. They are effectively falling around the planet forever.

What is the difference between period, frequency and RPM?

Period T is seconds per revolution; frequency f = 1/T is revolutions per second; RPM is revolutions per minute (f × 60). The calculator accepts any of them and converts to the centripetal acceleration formula that matches your data.

Remember the direction: centripetal acceleration always points toward the centre, never along the motion — it changes only the direction of velocity, not its magnitude. In a car corner, all four tyres together must supply F = m·v²/r through friction; wet roads halve the available friction, so the safe speed drops by about 30%. The apparent outward 'centrifugal force' you feel in a corner is an inertial effect of your body continuing straight — there is no real force pushing you out. For orbit problems, set the centripetal force equal to the gravitational force from our gravitational force calculator and solve for speed. When measuring radius on a roller coaster, use the radius at the point of interest — loops are not perfect circles, and the bottom of a loop is where g-force peaks.