Centripetal force calculator
This centripetal force calculator takes mass and radius plus speed, period or rpm, and gives you the force, acceleration, g-force and the maximum cornering speed on different road surfaces.
Example: Mass m 1,000 kg · Radius r of the circular path 50 m · Known value: Speed v · Speed v 50 km/h → Result: F = 3,858 N (a = 3.858 m/s², about 0.39 g). Source: Wikipedia – Zentripetalkraft: F = m·v²/r = m·ω²·r. Updated: .
How it is calculated
Centripetal force is F = m·v²/r. A 1000 kg car on a 50 m radius curve at 50 km/h needs about 3858 N to stay on the circular path – an acceleration of roughly 0.39 g.
How it is calculated
A mass stays on a circular path only if a force points to the centre. It is F = m·v²/r = m·ω²·r, with acceleration a = v²/r. From the period, v = 2πr/T; from the rotation speed n (per minute), v = 2πr·n/60. The cornering speed limit comes from static friction μ·m·g just providing the centripetal force: v = √(μ·g·r).
Good to know
- The force grows with the square of the speed: twice as fast means four times the force.
- Centripetal force is not a separate force but the resultant of other forces (friction, tension, gravity).
- “Centrifugal force” is a fictitious force in the rotating frame, equal in size but pointing outward.
Frequently asked questions
How do you calculate centripetal force?
F = m · v² / r: mass times speed squared divided by the radius. Alternatively F = m · ω² · r with angular velocity ω.
How do you turn the period into speed?
In one period T the body covers the circumference 2πr, so v = 2πr / T.
How fast can you take a curve?
At most v = √(μ · g · r). With friction 0.8 and a 50 m radius that is about 71 km/h (44 mph); on a wet road (μ = 0.5) about 56 km/h (35 mph).
What is the difference between centripetal and centrifugal force?
Centripetal force really acts towards the centre. Centrifugal force is a fictitious force that appears only in the rotating frame.
Sources and legal basis
- Wikipedia – Zentripetalkraft: F = m·v²/r = m·ω²·r
- NIST – Standard acceleration of gravity g_n = 9,80665 m/s²
- Wikipedia – Haftreibung: static friction coefficients of tyres on road surfaces (guide values)
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