Centripetal Force Calculator

Calculate the inward force needed to keep a mass moving in a circle.

About Centripetal Force Calculator

Required force rises with the square of speed and falls with radius. Because both the required force and available friction scale with mass, the maximum cornering speed does not depend on mass at all. Cornering speed depends only on grip and radius, which is why a loaded and empty vehicle corner at similar limits but brake very differently.

Formula

Centripetal Force

F = m v² ÷ r; maximum speed = √(μ g r)

r: Radius of the circular path
μ g r: Grip-limited cornering speed, independent of mass

Worked example

With the default values below, Centripetal Force Calculator returns Centripetal Force Required of 9,600.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Massminimum 0 kg: 1,200 kg
Speedminimum 0 m/s: 20 m/s
Radius of the turnminimum 0.01 m: 50 m
Available friction coefficientaccepts 0–3: 0.8

Results

Centripetal Force Required: 9,600.00 N
Centripetal Acceleration: 8.000 m/s2
Maximum Force Friction Can Supply: 9,417.60 N
Maximum Speed Through the Turn: 19.81 m/s
Verdict: Exceeds available grip — the vehicle would slide

Step by step

1Values used
2Centripetal Force
3Centripetal Force Required= 9,600.00 N
4Centripetal Acceleration= 8.000 m/s2
5Maximum Force Friction Can Supply= 9,417.60 N
6Maximum Speed Through the Turn= 19.81 m/s
7Verdict= Exceeds available grip — the vehicle would slide

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Centripetal Force calculated?

F = m v² ÷ r; maximum speed = √(μ g r) Required force rises with the square of speed and falls with radius. Because both the required force and available friction scale with mass, the maximum cornering speed does not depend on mass at all.

Why does Centripetal Force matter?

Cornering speed depends only on grip and radius, which is why a loaded and empty vehicle corner at similar limits but brake very differently.

What values do I need to enter?

This calculator takes 4 inputs: Mass, Speed, Radius of the turn, Available friction coefficient. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.