Centripetal Force Calculator
Find the centripetal force and acceleration that keep a mass moving in a circle, with the speed in revolutions per minute.
The inward pull a turn needs, from speed, mass and radius.
How the centripetal force calculator works
Anything moving in a circle is accelerating toward the center at v² ÷ r, and the force providing that acceleration — string tension, friction, gravity, a banked road — is m v² ÷ r. Tighter turns and higher speeds both need more force: halving the radius doubles it, doubling the speed quadruples it.
The calculator also gives the acceleration in g and the rotational speed in rpm, useful for centrifuges and rides.
Formula: F = m v² ÷ r · a = v² ÷ r
Worked examples
| Inputs | Centripetal force | Note |
|---|---|---|
| 1,000 kg car, 20 m/s, 50 m radius | 8,000 N | 8 kN — 0.82 g |
| 1,000 kg car, 20 m/s, 100 m radius | 4,000 N | double the radius, half the force |
| 0.5 kg on a 1 m string at 4 m/s | 8 N | 8 N tension |
FAQFrequently asked questions
Is centrifugal force real?
It is what you feel in the rotating frame — the tendency to continue in a straight line. In the fixed frame the only real force is the inward centripetal one.
How fast can a car corner?
Friction supplies the centripetal force, up to μmg. So v_max = √(μgr): on dry tarmac (μ ≈ 0.9) a 50 m radius allows about 21 m/s (76 km/h).
Why are roads banked?
So part of the normal force points inward, reducing the friction needed. At the design speed a banked curve needs no friction at all.
What g does a centrifuge reach?
a = ω²r. A 10 cm rotor at 10,000 rpm gives about 11,000 g.
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 Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.