Uniform Circular Motion Calculator (Centripetal Force, Angular Velocity, Period)

Enter mass, radius, and speed (or angular velocity) to calculate the centripetal force, angular velocity, period, and frequency of uniform circular motion (F = mv²/r = mω²r).

Last updated: 2026-09-17

What Is Uniform Circular Motion?

Uniform circular motion describes an object traveling along a circular path while keeping its speed constant. Although the magnitude of the speed never changes, the direction of travel is constantly changing. Because a change in direction is itself a form of acceleration, the object experiences an acceleration that always points toward the center of the circle — called centripetal acceleration. Newton's equation of motion then tells us that a corresponding force, the centripetal force, must be acting toward the center as well.

With this calculator, you only need to enter the mass, radius, and speed (or angular velocity) to get the centripetal force, angular velocity, period, and frequency all at once. Speed and angular velocity are linked by the simple relationship ω = v/r, so knowing just one of them — from a lab measurement or a design spec — is enough to work out every other quantity. Many everyday rotating systems, from roller coaster loops to satellites orbiting the Earth, can be approximated with this same model.

How to Use the Uniform Circular Motion Calculator

Enter the mass (m) Enter the mass of the object in kilograms. This value is used to calculate the centripetal force.
Enter the radius (r) Enter the radius of the circular path in meters. A larger radius reduces the centripetal force for the same speed.
Choose whether to enter speed or angular velocity In "Value to Enter," pick whichever quantity you already know — speed (v) or angular velocity (ω). There's no need to enter both separately.
Enter the value for your chosen quantity Use meters per second (m/s) for speed, or radians per second (rad/s) for angular velocity.
Check the results The centripetal force, period, frequency, and the other velocity quantity are calculated automatically and update instantly whenever you change a value.

Tips for getting more out of it

Speed (v) and angular velocity (ω) are related by ω = v/r, so you only need to know one of them to calculate everything else. If your source value is in RPM, convert it to rad/s first with rpm × 2π ÷ 60.
Centripetal force keeps changing the direction of motion — it does not speed the object up along its path. In uniform circular motion, the speed itself stays constant while only the direction keeps changing.
Increasing the radius (r) while keeping speed (v) fixed reduces the centripetal force in inverse proportion (F = mv²/r). Conversely, doubling the speed at a fixed radius quadruples the centripetal force — a common mistake is assuming it only doubles.
Frequency (f) is the number of full revolutions per second and is the reciprocal of the period (T). To compare with a motor's RPM rating, multiply f by 60 to get revolutions per minute.

Where This Calculator Comes in Handy

Checking physics homework and exam prep

After solving a circular motion problem by hand, plug the same numbers into this calculator to verify your answer — it's a quick way to catch sign errors or unit mistakes.

Understanding centrifugal-feeling amusement park rides

On spinning teacups or roller coaster loops, try changing the radius and speed to get a concrete feel for how much centripetal force — the force your body actually perceives as pressure — is really involved.

A first look at satellite orbital motion

A satellite orbiting the Earth can be modeled as circular motion in which Earth's gravity supplies the centripetal force. This calculator offers a simple entry point for exploring the relationship between orbital radius and orbital speed.

Rough estimates for rotating machinery

For fast-spinning parts such as centrifuges or washing machine drums, this tool gives you a ballpark figure for the forces involved (rigorous engineering design still requires dedicated verification).

Circular Motion Glossary

Centripetal force: The force that always acts toward the center of the circle on an object in circular motion. It's what keeps the object moving along a curved path instead of a straight line.
Centripetal acceleration: The acceleration directed toward the center that arises from the continuous change in direction of motion. It always occurs whenever the direction keeps changing, even if the speed itself stays constant.
Angular velocity: The angle swept out per unit time, measured in radians per second (rad/s). It relates to speed (v) through v = ωr.
Period: The time it takes for the object to complete one full revolution, measured in seconds. A larger angular velocity means a shorter period.
Frequency: The number of full revolutions completed per second — the reciprocal of the period. Measured in hertz (Hz).
Centrifugal force (a fictitious force): An apparent force that only appears to an observer rotating along with the object. From the point of view of a stationary observer, it doesn't actually exist — it's an inertial effect.

Frequently Asked Questions

Uniform circular motion is motion in which an object travels along a circular path at a constant speed. Although the speed never changes, the direction of travel is constantly changing, which requires a continuous acceleration (centripetal acceleration) — and a corresponding force (centripetal force) — directed toward the center of the circle at all times.

Even though the speed stays constant in uniform circular motion, the direction of the velocity vector changes over time, which produces an acceleration. Analyzing the geometric change of the velocity vector over a small time interval shows that this acceleration (the centripetal acceleration) has magnitude v²/r. Substituting this into Newton's second law, F = ma, gives F = mv²/r.

Centripetal force is a real force — such as tension in a string, gravity, or friction — exerted on an object moving in a circle, always directed toward the center. Centrifugal force, on the other hand, is a fictitious (inertial) force that only appears to an observer rotating along with the object; it does not actually exist from the perspective of a stationary observer.

Angular velocity (ω) is the angle swept per unit time (rad/s), while speed (v) is the actual distance traveled along the circle per unit time (m/s). They are related by v = ωr, so for the same angular velocity, a larger radius produces a greater speed.

Side Note — The Newton–Hooke Dispute Over Universal Gravitation

The concept of centripetal force in uniform circular motion also played a key role in understanding the motion of celestial bodies. Isaac Newton reasoned that the Moon keeps orbiting the Earth in a roughly circular path because Earth's gravity acts as the centripetal force, and he extended this insight to planetary motion in general to derive the law of universal gravitation.

Interestingly, the idea that the strength of gravitational attraction falls off with the square of the distance was independently conceived not only by Newton but also by his contemporary Robert Hooke, leading to a famous priority dispute between the two. Hooke had hinted at the idea in a letter to Newton, but it was Newton who ultimately worked out the full mathematical treatment — using the centripetal force equation to derive the elliptical planetary orbits described by Kepler's laws.

Today, the concept of centripetal force extends far beyond orbital mechanics: it is routinely applied in engineering fields ranging from designing roller coasters at amusement parks, to setting the spin speed of a washing machine's drum, to calculating the tire friction needed for a car to safely take a curve.

Browse all trivia