Centrifugal Force Calculator
Find the outward force on a mass in a rotating frame from its radius and rotation rate, with RCF in g for centrifuges.
🌀 What is Centrifugal Force?
Centrifugal force is the outward push you seem to feel when you move in a circle. In a car taking a sharp turn you slide toward the door, on a spinning fairground ride you are pressed against the wall, and in a laboratory centrifuge a sample is driven toward the bottom of the tube. Its size is F = m w² r, where m is the mass, w the angular velocity and r the distance from the rotation axis. Written with the tangential speed v = w r, the same force is F = m v² / r. This calculator takes either description, converts the units for you, and returns the force, the acceleration, the relative centrifugal force in multiples of g, and the period of one turn.
The important subtlety is that centrifugal force is a fictitious force, also called an inertial force. It appears only when you describe the motion from a rotating frame of reference, such as the inside of the car or the rotor itself. Seen from the ground, which is an inertial frame, nothing pushes the passenger outward. The passenger simply tends to keep moving in a straight line while the car turns underneath. What does exist in the inertial frame is the inward centripetal force from the door, the seat belt, a string or friction, and it has exactly the same magnitude m v² / r. The two descriptions agree on every measurable result, which is why engineers happily use the rotating-frame force when it makes the algebra simpler. The sister page, the centripetal force calculator, works from the inertial viewpoint.
Practical uses are everywhere. Laboratories quote the relative centrifugal force (RCF), the acceleration w² r divided by standard gravity, to describe how hard a sample is spun, because the same rpm gives very different forces on rotors of different radius. Washing machines extract water at several hundred g, ultracentrifuges separate proteins at tens of thousands of g, and engineers size bearings, flywheels and turbine blades against the centrifugal load. Earth itself rotates, so every object on the equator feels a tiny centrifugal acceleration of about 0.034 m/s². For the underlying link between force and acceleration see the force calculator and the acceleration calculator.
Two misconceptions are worth clearing up. First, rpm alone does not tell you the force: the radius matters, and the force grows with the square of the rotation rate. Second, centrifugal force does not make objects fly off radially. When the inward force disappears, for example when a string breaks, the object leaves along the tangent to the circle, not along the radius.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — A Laboratory Centrifuge
A 15 g sample at a radius of 8 cm spun at 10,000 rpm
Example 2 — A Passenger in a Turning Car
A 70 kg passenger, a 50 m radius turn, at 15 m/s
Example 3 — A Washing Machine Drum
5 kg of wet laundry at a drum radius of 25 cm spinning at 1,200 rpm
Example 4 — A Child on a Merry-Go-Round
A 30 kg child sitting 2 m from the centre, turning at 1.5 rad/s
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for centrifugal force?
Centrifugal force is F = m w² r, where m is the mass, w the angular velocity in rad/s and r the distance from the axis. Using the tangential speed v = w r this is the same as F = m v² / r. A 1 kg mass at 0.2 m turning at 120 rpm feels 31.58 N.
Is centrifugal force real?
It is real in the sense that you feel it, but it is a fictitious force: it appears only when you describe motion from a rotating frame. In an inertial frame the object just tends to move in a straight line, and only the inward centripetal force acts.
How do you convert rpm to g force?
Convert rpm to rad/s with w = rpm x 2 pi / 60, then RCF = w² r / 9.80665 with r in metres. In centrifuge shorthand, RCF = 1.118e-5 x r(cm) x rpm². A rotor with an 8 cm radius at 10,000 rpm gives about 8,946 g.
What is the difference between centrifugal and centripetal force?
Centripetal force is the real inward force, from tension, a wall or gravity, that keeps an object on a circular path. Centrifugal force is the apparent outward force in the rotating frame. They have equal size, m v² / r, and opposite directions.
What is relative centrifugal force (RCF)?
RCF is the centrifugal acceleration expressed as a multiple of standard gravity, RCF = w² r / g. It tells you how many times heavier a sample effectively becomes in the rotor, which is why protocols quote it instead of rpm.
Does centrifugal force depend on mass?
The force is proportional to mass, but the acceleration w² r is not. Two objects at the same radius and rotation rate feel the same acceleration, and the heavier one feels a proportionally larger force.
Why does a washing machine spin so fast?
A high rotation rate gives a large w² r acceleration, hundreds of times gravity, which flings water outward through the drum holes while the clothes are held back by the wall. A 25 cm drum at 1200 rpm reaches about 403 g.
What happens to centrifugal force if the radius doubles?
At a fixed rotation rate the force doubles, because F = m w² r is linear in r. At a fixed tangential speed the force halves, because F = m v² / r. Always check which quantity is being held constant.
Does centrifugal force exist on Earth?
Yes, because Earth rotates. At the equator the centrifugal acceleration is about 0.034 m/s², roughly 0.35 percent of g, which slightly reduces the apparent weight. It is zero at the poles.
Can centrifugal force be larger than gravity?
Yes. Centrifuges, ultracentrifuges and fairground rides routinely produce RCF values from a few g to hundreds of thousands of g. Whenever RCF is above 1 g the rotating-frame force exceeds the weight of the object.