Centripetal Force Calculator

Frequently Asked Questions

What is centripetal force?

The inward force that keeps an object moving on a circular path: F = m·v²/r = m·ω²·r.

Is centrifugal force real?

No - it is an apparent force felt in a rotating frame. The real force is the inward centripetal force.

What does this calculator give?

Centripetal force, centripetal acceleration, and the speed for a given radius and mass.

Why do tight turns feel stronger?

Force scales with v²/r, so halving the radius or doubling the speed sharply increases the required force.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

Any object moving in a circle is constantly accelerating toward the center, even at constant speed, because its direction keeps changing. The centripetal (center-seeking) acceleration is aᶜ = v² ÷ r and the inward force required is F = m · v² ÷ r, where m is mass (kg), v is tangential speed (m/s), and r is the radius of the turn (m). For a vehicle rounding a curve, the ideal banking angle that lets the road's normal force alone supply this force - needing zero friction - is θ = arctan(v² ÷ (r·g)). This calculator returns the force in N and kN, the acceleration in m/s² and as multiples of g, the angular speed ω = v ÷ r, and the ideal banking angle.

Worked Example: A Car on a Highway Curve

A 1200 kg car takes a curve of radius r = 80 m at v = 25 m/s (90 km/h). Acceleration aᶜ = 25² ÷ 80 = 625 ÷ 80 ≈ 7.81 m/s², about 0.80 g sideways. The required force F = 1200 × 7.81 ≈ 9,375 N (≈9.4 kN) - all of it supplied by tire friction on a flat road. The ideal banking angle is θ = arctan(625 ÷ (80 × 9.80665)) = arctan(0.797) ≈ 38.6°. A road banked at that angle would let the car hold the curve at 25 m/s even on ice; flatter banking means friction must make up the difference.

Real-World Uses

Highway & racetrack design: set superelevation (banking) for the design speed.

Roller coasters & aviation: compute the g-forces riders and pilots experience in loops and banked turns.

Centrifuges: the same aᶜ = ω²r drives separation forces of thousands of g.

Orbital mechanics: gravity supplies the centripetal force keeping satellites in orbit.

Common Mistakes

Centripetal force is not a new, separate force - it is the net inward force, supplied by friction, tension, gravity, or a normal force depending on the situation. "Centrifugal force" is the apparent outward push felt in the rotating frame, not a real force in the inertial frame. Because force scales with v², doubling speed quadruples the force and acceleration - a frequent underestimate. The ideal banking angle depends only on speed and radius, not on the vehicle's mass.

Limitations & Related

The model assumes uniform circular motion: constant speed, constant radius, and a single resultant force directed exactly at the center. Real curves have varying radius (clothoid transitions), and real driving adds tangential acceleration when speeding up or braking, requiring vector addition of both components. The ideal-banking result ignores friction entirely; a real road is designed for a range of speeds, with friction covering the rest. It also assumes a point mass - vehicle weight transfer, suspension roll, and tire grip limits matter in practice. Related tools include the angular-velocity and gravitational-force calculators.

Centripetal Force Calculator

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