Circular Motion Calculator - Period & Force Solver

A circular motion calculator is a uniform circular motion physics tool that takes the period, radius, and mass of an object on a circular path and returns its linear speed, angular velocity, frequency, centripetal acceleration, centripetal force, and g-force in one view, so you can read every standard UCM quantity without rearranging formulas.

• • Roundabout and traffic-circle physics: Estimate the sideways friction a 1200 kg car needs to stay on an 8 m roundabout.
• • Satellite and orbital motion: Enter the orbital period and radius of a low-Earth satellite to read the centripetal acceleration that gravity must supply.
• • Compact disc and hard-drive tracking: Plug in the rotation period and head tracking radius to read the surface speed and centripetal force on a tracking mass.
• • Amusement rides and lab centrifuges: Use the period and radius of a swing ride, carousel, or centrifuge to estimate the g-force at the rim.

Uniform circular motion describes any object that travels around a circle at constant angular speed. The linear speed is tangential, centripetal acceleration always points toward the centre, and the net force is the centripetal force supplied by tension, gravity, friction, or a combination.

This calculator covers the textbook UCM case with fixed radius and constant angular speed. Variable-radius or accelerated-rotation problems need extra physics.

For a deeper dive into the force side of the same problem, the Centripetal Force Calculator lets you set mass, velocity, and radius directly and read off the centripetal force.

The calculator evaluates the standard uniform circular motion formulas in sequence. It uses T to derive omega and f, multiplies by r to get v, then squares v over r to get a_c, and multiplies by m to get F_c.

• T (period): Time for one revolution in seconds. Smaller T means faster rotation and higher centripetal acceleration.
• r (radius): Distance from the centre of the circle to the moving object, in metres. Larger r at fixed period gives higher linear speed and centripetal acceleration.
• m (mass): Mass in kilograms. Only used for the centripetal force and g-force outputs.
• v (linear speed): Tangential speed around the circle, in metres per second, equal to omega * r.
• omega (angular velocity): Rate of change of angle, in radians per second, equal to 2*pi / T.
• f (frequency): Revolutions per second, in hertz, equal to 1 / T.
• a_c (centripetal acceleration): Inward acceleration toward the centre, in m/s^2, equal to v^2 / r.
• F_c (centripetal force): Net inward force needed to keep the object on its circular path, in newtons, equal to m * a_c.

The g-force readout divides centripetal acceleration by 9.80665 m/s^2 so the result is dimensionless and easy to compare with everyday accelerations. A g-force of 1 means the object feels its normal weight, while a g-force of 4 means it feels four times heavier than at rest.

According to OpenStax Physics, these formulas apply to any object in uniform circular motion, from a tetherball to a charged particle in a cyclotron, and describe planetary and satellite orbits when gravity supplies the centripetal force.

According to OpenStax Physics - 6.2 Uniform Circular Motion, an object in uniform circular motion has tangential speed v = 2*pi*r/T, centripetal acceleration a_c = v^2/r pointed toward the centre, and net centripetal force F_c = m*a_c.

When the motion leaves the circle and becomes a straight-line SUVAT problem, the Kinematics Motion Calculator covers the matching linear kinematics with the same SI units.

Four ideas from kinematics and dynamics that make the uniform circular motion formulas more than a list of equations.

These four ideas connect to classical mechanics, astronomy, and engineering. The same v = omega * r relation appears in satellite orbital speed, flywheel rim speed, and wind turbine tip speed.

When the centripetal force comes from gravity and the radius is set by the orbit, the Orbital Period Calculator ties the same T and r to satellite altitude and central-body mass.

Use the circular motion calculator in five steps to find every uniform circular motion quantity for a moving object.

1. 1 Enter the period T: Type the time for one full revolution in seconds. Use 60 for a 1 RPM rotation, 86400 for one Earth rotation, or your satellite's orbital period.
2. 2 Enter the radius r: Type the radius of the circular path in metres. Use the orbital radius for satellites, the chain length for a swing ride, or the tracking radius for a disc head.
3. 3 Enter the mass m: Type the mass of the moving object in kilograms. Mass only affects the centripetal force and g-force outputs.
4. 4 Read the kinematic outputs: The calculator returns linear speed v in metres per second, angular velocity omega in radians per second, and frequency f in hertz, all derived from T.
5. 5 Read the force and g-force outputs: The calculator returns centripetal acceleration a_c in metres per second squared, centripetal force F_c in newtons, and the g-force ratio to compare against everyday accelerations.

For a 1200 kg car on an 8 m roundabout that takes 15 seconds per loop, enter T = 15 s, r = 8 m, m = 1200 kg. The calculator returns v = 3.351 m/s, omega = 0.4189 rad/s, f = 0.0667 Hz, a_c = 1.404 m/s^2, F_c = 1684.4 N, g = 0.143.

If your circular motion is actually a swinging mass on a string of the same length, the Pendulum Period Calculator gives the small-angle period so you can compare constant rotation with oscillation.

Practical reasons to use this circular motion calculator instead of rearranging the uniform circular motion formulas by hand.

• • All six UCM quantities from one input set: Enter period, radius, and mass once and get linear speed, angular velocity, frequency, centripetal acceleration, centripetal force, and g-force.
• • No manual formula rearrangement: The calculator handles T, f, omega, and v conversions so you do not have to remember when to multiply or divide by 2*pi.
• • Auditable g-force readout: The g-force output divides centripetal acceleration by 9.80665 m/s^2, giving a dimensionless ratio that compares with everyday accelerations.
• • Useful for orbital and lab scales: The same formulas cover a 24 Hz disc head (about 16000 g) and a 90-minute low-Earth orbit.
• • Clear validation for impossible inputs: A zero or negative period or radius returns zero outputs and an error, so you do not silently divide by zero.
• • Pairs with adjacent physics calculators: Use the same period and radius in the orbital period or pendulum period calculator to compare gravity-driven and rotation-driven motion.

The calculator is intentionally narrow: it solves the textbook UCM equations for a single-radius circular path. Non-uniform motion, vertical circles, and banked-turn problems need extra physics beyond this period-and-radius form.

What changes the centripetal force, acceleration, and linear speed this calculator returns, and what it cannot capture.

• • The calculator assumes a single fixed radius and constant angular speed, so it does not capture vertical circles, non-uniform rotation, or spin-up and spin-down.
• • Air resistance and rolling resistance are not part of the model, so for real cars, bikes, and trains the actual tangential speed decays with time.
• • The g-force readout uses standard gravity 9.80665 m/s^2 in air; for deep-space or underwater settings, divide by the local g.

The same centripetal-force expression written in terms of period is F = 4*pi^2*m*r/T^2, which is exactly what the calculator evaluates when you enter T and r.

According to HyperPhysics - Centripetal Force, centripetal force for uniform circular motion is F = m*v^2/r, the radial pull required to keep the object on its circular path, with the period form F = 4*pi^2*m*r/T^2.

According to Wikipedia - Circular motion, the angular speed for an object completing one revolution every T seconds is omega = 2*pi/T radians per second, while the tangential speed is v = omega*r.

When the object leaves the circular path and becomes a launched projectile, the Projectile Motion Calculator carries the same initial speed into range, height, and flight time.