Calculate centripetal force for any object in circular motion. Enter the object's mass, radius of circular path, and tangential velocity — and get the centripetal force and centripetal acceleration back instantly. You can also solve for mass, radius, or velocity by switching the solve for option. Also try the Speeds and Feeds Calculator.
Centripetal Force
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Centripetal Acceleration
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Mass
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Radius
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Tangential Velocity
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Centripetal force is the force that acts on any object moving along a curved or circular path, directed toward the center of curvature. The name comes from the Latin 'centrum' (center) and 'petere' (to seek), meaning it is a center-seeking force. Without it, the object would travel in a straight line due to inertia. See also our calculate Mass Moment of Inertia Moment of Inertia (I).
The centripetal force formula is F = mv²/r, where F is the centripetal force in Newtons, m is the mass of the object in kilograms, v is the tangential velocity in m/s, and r is the radius of the circular path in meters. It can also be expressed as F = mω²r using angular velocity ω.
Centripetal force is a real force directed inward toward the center of circular motion, keeping an object on its curved path. Centrifugal force is a fictitious or pseudo-force felt in a rotating reference frame that appears to push objects outward. In an inertial (non-rotating) frame, centrifugal force does not exist — only centripetal force acts.
Centripetal force continuously changes the direction of an object's velocity without changing its speed, keeping it on a circular path. The greater the speed or mass of the object, or the smaller the radius, the larger the centripetal force required. If the force is removed, the object immediately travels in a straight tangential line. You might also find our Rotational Kinetic Energy useful.
Centripetal force is not a fundamental force itself — it is provided by other physical forces depending on the situation. For a satellite in orbit, gravity provides it. For a car rounding a curve, friction between the tires and road provides it. For a ball on a string, string tension provides it.
Earth's centripetal motion around the Sun is caused by gravitational attraction. The Sun's gravity acts as the centripetal force, continuously pulling Earth toward the Sun and keeping it in its nearly circular orbit rather than flying off into space in a straight line.
Centripetal force is proportional to the square of the velocity (F ∝ v²). This means doubling the speed requires four times the centripetal force to maintain the same circular path. This is why cars have speed limits on curves — at high speeds, the friction force may be insufficient to provide the needed centripetal force.
Centripetal force is measured in Newtons (N) in the SI system, the same as any other force. Since F = mv²/r, the units work out as kg × (m/s)² / m = kg·m/s² = N. In some contexts you may also see it expressed in kilonewtons (kN) or pound-force (lbf).