Centripetal Force Calculator
The curve's bill: F = mv²/r toward the centre, g-quoted for the body and translated into the friction budget the road must quietly supply.
Centripetal Force Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Uniform circular motion — constant speed on a fixed radius
- Flat-road friction budget; banking not modelled
In short: A 1,000 kg car taking a 50 m curve at 20 m/s (72 km/h) needs F = mv²/r = 8,000 N pointing at the curve's centre — an acceleration of 8.000000 m/s², or 0.815773 g, felt entirely as the seat pushing you sideways (that push is what everyone misnames centrifugal). The friction card is the driver's reading: the road must supply μ ≥ 0.815773, inside the commonly cited 0.7–0.9 dry-rubber band but with little spare — and wet asphalt ends the argument. The speed enters SQUARED: the same curve at 40 m/s bills 32,000 N, four times. Period of one lap: 15.707963 s, or 3.819719 rpm.
Formula
a = v²/r · F = m·v²/r · ω = v/r · T = 2πr/v · flat-road μ ≥ v²/(r·g)
Centripetal means centre-seeking: to bend a mass's path, something must push it toward the curve's centre — friction, a banked road, a string, a seat. The acceleration changes DIRECTION, not speed, which is why it can be steady forever at constant speed: the work-page's 90° case running in a circle.
Worked Example
- Enter the mass, the tangential speed and the curve radius.
- Read the force and its g-quote — what the body feels.
- Read the friction budget before driving the curve for real: the road supplies this force or the curve does not happen.
- Double the speed on the square card to see why curves punish pace quadratically.
Defaults: 8,000 N inward (0.815773 g) at 20 m/s on r = 50 m; needs μ ≥ 0.815773. At 10 m/s the same curve asks a = 2.000000 m/s² — quarter the bill, since the speed halved and squared.
Strengths & Limits Of This Model
Where this engine is strong
- Friction budget translated into the μ the road must supply
- g-quote and rpm from the same three inputs
Where it stops
- No banked-curve geometry
- No vertical loops or varying radius
Practical Use Cases
Driving
curve speeds against the friction budget
Amusement
g's on a loop, priced honestly
Teaching
why 'centrifugal' is the seat, not a force
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Centripetal Force Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
If I'm pushed outward in the curve, why is the force inward?
The push you feel outward is the seat or door pushing INWARD on you, transmitting the centre-seeking force your body would rather not follow. 'Centrifugal force' names that sensation, not a force on the free-body diagram — in the ground frame only the inward push exists, and this page prices it.
Why does the speed enter squared?
Because bending the path twice as fast demands four times the acceleration: a = v²/r. It is the kinetic-energy square arriving from the side — the same quadratic that quadruples braking distances also quadruples the curve bill. The square card computes your own doubling.
What supplies the force on a flat road?
Friction between tyres and asphalt — nothing else is pushing toward the centre. That is why the budget card matters: the curve demands μ ≥ v²/(r·g), and when demand outruns the surface, the vehicle departs tangentially, still obeying Newton honestly.
What do banked curves change?
They let the road's NORMAL force carry part of the centripetal bill, so grip is spent last. That is why highway curves are banked and why velodromes are absurdly steep: geometry buys friction a rest. The flat-road budget here is the worst-case, unguarded reading.
Does mass matter to the friction budget?
Not to the BUDGET: v²/(r·g) has no mass in it, because the demanded force and the available friction both scale with weight. The lorry and the bicycle need the same μ for the same curve and speed — the force card differs, the verdict does not.
What is the period card telling me?
How long one lap takes at this speed and radius (2πr/v = 15.707963 s here), and its rpm cousin. Fast laps shrink it linearly in speed, which is how centrifuges and fairground loops choose their spin rates.
Why does the page refuse a zero radius?
Because v²/r with r = 0 is a corner, and corners demand an unbounded acceleration — the mathematics says so and every crashed kart agrees. Curves need radius; give the page one and it prices the bend honestly.
How does this tie back to work at 90°?
Perfectly: the centripetal force is ALWAYS perpendicular to the motion, so it does zero work — which is exactly why the speed stays constant while the direction turns. Circular motion is the suitcase theorem, sustained.