This all-in-one online Centripetal Force Calculator performs calculations using the formula that relates the centripetal force that acts on an object to the mass of this object, its velocity, and the radius of curvature of its trajectory. Both linear (tangential) velocity and angular velocity can be used. You can enter the values of any three known parameters in the fields of the calculator and find the missing parameter.
Fc = m·v2/r = m·ω2·r
Centripetal Force Formula
The centripetal force is the force that causes a body to move along a curved path. Its direction is always orthogonal to the motion of the body and directed toward the instantaneous center of curvature of the trajectory.
The magnitude of the centripetal force acting on an object can be expressed by the following formula:
$$F_{c} = \frac{m \cdot v^2}{r},$$
where
\(F_{c} \ \) is the magnitude of the centripetal force,
\(m \ \) is the mass of the object,
\(v \ \) is the magnitude of the tangential velocity of the object,
\(r \ \) is the radius of curvature if the path.
The best-known example involving a centripetal force is when a body moves at a constant speed along a circular path. The centripetal force is directed at right angles to the instantaneous velocity vector of the body along the radius towards the center of the circular trajectory.
In this case, the centripetal force can be expressed in terms of the angular velocity \(\omega\) of the body relative to the center of the circle. The angular velocity (we use here actually its magnitude – the angular speed) is related to the tangential velocity by the formula:
$$v=\omega \cdot r,$$
so the centripetal force formula will look like this:
$$F_{c} = m \cdot \omega^2 \cdot r.$$
Angular velocity is a quantity with dimension T−1. The SI unit is s−1 or Hz. Other common units are rad/s (radians per second) and rpm (revolutions per minute).
Our Centripetal Force Calculator uses both centripetal force formulas for your convenience.
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