Centripetal Force & Acceleration Calculator

Anything moving in a circle needs an inward force pulling it toward the centre. That force is F = mv²/r, where m is mass in kilograms, v is the speed along the circle in m/s, and r is the radius in metres. Result is in newtons. A 1500 kg car taking a 50 m bend at 15 m/s needs F = 1500 × 225 / 50 = 6750 N of friction or banking. Lose that friction on ice and the car keeps going straight — Newton's first law in action. Always check that v is the tangential speed, not RPM.

Pop in the speed v and the radius r, and the calculator returns centripetal acceleration using a = v²/r in m/s². If you also give the mass, it can multiply through to get force F = ma. For a stone on a 0.8 m string whirled at 4 m/s, a = 16 / 0.8 = 20 m/s², roughly two g. The acceleration always points toward the centre, even though the stone's speed never changes — direction-changing counts as acceleration too. Useful for circular motion problems and amusement-park ride design questions.

When a question gives you angular velocity ω instead of linear speed v, use F = mω²r. This drops out of substituting v = ωr into F = mv²/r and simplifying. Keep ω in rad/s, r in metres, m in kilograms, and the force comes out in newtons. A 0.2 kg ball spinning at 10 rad/s on a 0.5 m string needs F = 0.2 × 100 × 0.5 = 10 N to stay in its circle. The two formulas describe the same physics — pick whichever matches the data you're handed.

Centripetal force grows with the square of speed. Double the speed and you need four times the force to keep the object moving in the same circle. Triple it and you need nine times. That's why a car taking a turn at 60 km/h handles fine, but the same turn at 120 km/h can throw it off the road — the tyres can't supply four times the friction. This square-law relationship explains banked tracks, racing crashes, and why washing machines vibrate so violently at high spin speeds.

Centripetal force is the real, inward force that actually keeps an object moving in a circle — friction, tension, gravity, whatever supplies the pull. Centrifugal force is the apparent outward push you feel inside a rotating frame, like being shoved against the car door on a sharp bend. It isn't a true force; it's an artefact of viewing the motion from a non-inertial frame. From outside the rotation, only centripetal force exists. From inside, you have to invent centrifugal force to make Newton's laws work. One is physics, the other is bookkeeping.

Rearrange a = v²/r to get r = v²/a when you know the linear speed and the inward acceleration. If you have angular velocity instead, use r = a/ω². Suppose a satellite has acceleration 9 m/s² and orbital speed 7800 m/s — then r = 7800² / 9 ≈ 6.76 million metres, close to Earth's radius. This kind of reverse calculation is bread and butter for orbital mechanics, particle accelerator design, and even figuring out the radius of a curve from a car's lateral g-force reading.

Centripetal acceleration is acceleration just like any other, so it carries the standard unit of m/s² in SI. The corresponding force, when multiplied by mass in kilograms, comes out in newtons. People sometimes get spooked because nothing's speeding up or slowing down, but a change in direction is still an acceleration. So a steady 9.8 m/s² inward acceleration is essentially one g of sideways pull. Mixing centimetres or kilometres into your radius will quietly mess up the units, so always convert to metres before computing.