Circular Motion Calculator
Centripetal acceleration, force and period for an object moving in a circle — plus the g-force it experiences.
The inward pull that keeps something going round.
How the circular motion calculator works
Moving in a circle at constant speed still means accelerating, because the direction keeps changing. That acceleration points to the centre and equals v²/r; the force producing it is mv²/r.
There is no outward "centrifugal force" in an inertial frame — what a passenger feels on a roundabout is their own inertia resisting the inward push from the seat.
Formula: a = v²/r; F = mv²/r; T = 2πr/v
Worked examples
| Inputs | Centripetal force | Note |
|---|---|---|
| 1,000 kg at 15 m/s on a 50 m radius | 4,500 N | 4,500 N, 0.46 g |
| Twice the speed | 18,000 N | four times the force |
| Half the radius | 9,000 N | double the force |
FAQFrequently asked questions
Is centrifugal force real?
Not in an inertial frame. The only real force is the inward (centripetal) one; the outward feeling is inertia. In a rotating reference frame it is a useful fiction.
Why do tight corners feel so much stronger?
Because force is inversely proportional to radius. Halving the corner radius doubles the force at the same speed.
How fast can a car corner?
About √(μgr). On dry tarmac with μ ≈ 0.7 and a 50 m radius, roughly 18.5 m/s or 67 km/h — before any banking.
What is 1 g sideways?
A cornering force equal to the car's weight. Road cars manage around 0.9 g; racing cars with aerodynamic downforce exceed 3 g.
Does mass change the maximum cornering speed?
No, in the simple model — mass cancels between the required force and the available friction. Real tyres do lose grip as load rises.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.