Centripetal Force Calculator
Calculate the centripetal force and acceleration required to keep an object moving in a circular path. Useful for designing roads, roller coasters, satellites, and rotating machinery.
Last updated: September 2026
Formula below · 2 sources (NIST, Wikipedia) · Updated Sep 2026
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About this calculator
For an object of mass m moving at tangential velocity v along a circular path of radius r, the centripetal force directed toward the center is: F = m·v²/r. The corresponding centripetal acceleration is a = v²/r. The net inward force is always m·v²/r; the context option shows what the road or track must supply. On a horizontal circle that is m·v²/r itself. On a road banked at θ, part of it comes from the tilted normal force, and the side friction the tyres must provide along the surface is F = m·(v²/r)·cosθ − m·g·sinθ (negative means the car would slide down-slope without friction). At the bottom of a vertical loop the seat or track pushes up with N = m·v²/r + m·g. Angular velocity ω relates to tangential velocity by v = ω·r, allowing conversion between rotational and linear quantities. This inward force is not a separate physical force—it is the net result of friction, normal force, gravity, or tension depending on the scenario.
How to use
A 1,200 kg car travels at v = 25 m/s around a flat circular bend of radius r = 80 m. Step 1 – choose Horizontal circle. Step 2 – F = m·v²/r = 1200 × 625 / 80 = 750,000 / 80 = 9,375 N. Step 3 – centripetal acceleration a = v²/r = 625 / 80 ≈ 7.81 m/s². Step 4 – on a road banked at 10° the tyres need only F = 9,375 × cos(10°) − 1,200 × 9.81 × sin(10°) = 9,233 − 2,044 ≈ 7,189 N of side friction: banking reduces the lateral friction demand on the tires.
Frequently asked questions
What is the difference between centripetal force and centrifugal force?
Centripetal force is a real inward force that continuously redirects an object toward the center of its circular path—without it, the object would fly off in a straight line. Centrifugal force is a fictitious outward force that appears only in a rotating (non-inertial) reference frame, such as the feeling of being pushed outward in a turning car. In an inertial frame of reference used by this calculator, only centripetal force exists as a physical quantity.
How does banking angle affect the centripetal force needed on a curved road?
Banking a road tilts the normal force so that a component of it points toward the center of the curve, reducing reliance on tire friction. The centripetal force contribution from the normal force is N·sin(θ), while the vertical balance gives N·cos(θ) = mg. At the ideal banking angle for a given speed, no friction is needed at all. This calculator models the cosine correction factor to help engineers determine safe speeds for banked curves.
Why does centripetal force increase with the square of velocity?
Because kinetic energy and momentum both grow with velocity, the rate at which an object's direction must change to maintain a circular path scales with v². Doubling the speed requires four times the centripetal force (F ∝ v²) to maintain the same radius. This is why highway on-ramps have speed limits and why high-speed centrifuges can exert thousands of times the force of gravity on their contents with modest increases in rotational rate.