Circular Motion Calculator
Find centripetal acceleration and force.
Results update as you type.
How it works
Any object moving in a circle is constantly accelerating, even at steady speed, because its direction keeps changing, and this calculator finds the centripetal acceleration and the inward force needed to sustain that motion. You enter the object's mass, its speed, and the radius of the circular path, and it returns the acceleration directed toward the centre and the corresponding centripetal force. The acceleration equals the speed squared divided by the radius, so it grows rapidly with speed and shrinks as the circle widens. The force, by Newton's second law, is simply mass times that acceleration. This inward force is not a new kind of force; it is provided by whatever physically pulls the object toward the centre, such as the tension in a string swinging a ball, friction between tyres and the road as a car corners, gravity holding a satellite in orbit, or the track pushing on a roller-coaster car in a loop. Understanding centripetal force explains why cars skid on tight or fast turns, how banked curves and centrifuges work, and what keeps planets in orbit. Physics students study it as a core topic in mechanics. Enter mass, speed, and radius to compute both the acceleration and the required force.
a = v² / r; F = m·v² / r
An object moving in a circle at constant speed still accelerates because its direction constantly changes, and this centripetal acceleration points toward the centre with magnitude equal to the speed squared divided by the radius. By Newton's second law, the inward force required to produce that acceleration is the mass times the acceleration, or mass times speed squared divided by the radius. A tighter circle or higher speed demands a larger force.
Source:Classical mechanics (centripetal force)
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Worked example
How to use this calculator
- 1
Enter your values
Enter mass (m), speed (v) and radius (r).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Centripetal acceleration updates instantly as you type — no button to press.
Frequently asked questions
What is centripetal force?
Centripetal force is the net inward force that keeps an object moving along a circular path, always directed toward the centre of the circle. It is not a separate type of force but the role played by whatever real force points inward, such as tension, friction, or gravity. Without it, the object would fly off in a straight line following its instantaneous velocity.
Why does an object in circular motion accelerate?
Acceleration is any change in velocity, and velocity includes direction as well as speed. An object going around a circle continuously changes direction, so even at constant speed its velocity is always changing, which means it is accelerating. This centripetal acceleration points toward the centre and is what the inward force produces, keeping the object on its curved path.
How does speed affect the required force?
The centripetal force grows with the square of the speed, so doubling the speed quadruples the force needed to maintain the same circular path. This is why taking a corner twice as fast demands four times the grip from your tyres, and why high-speed turns are so much more likely to cause skidding. A larger radius, by contrast, reduces the required force.
What is the difference between centripetal and centrifugal force?
Centripetal force is the real inward force that curves an object's path. Centrifugal force is the apparent outward push felt by someone in the rotating frame, such as a passenger pressed against a car door on a sharp turn. It is a fictitious force arising from being in an accelerating frame, not a real force acting on the object from outside.
Where does circular motion appear in real life?
Circular motion is everywhere: cars rounding bends, satellites and planets in orbit, spinning centrifuges separating substances, roller coasters looping, a ball on a string, and washing machines spinning clothes dry. In each case a centripetal force pulls the object toward the centre. Engineers use these equations to design safe roads, amusement rides, and rotating machinery.