Centrifugal Force Calculator

centrifugal force = mass × ω² × radius ω = 2π × rpm ÷ 60 tangential speed = ω × radius

m

Mass of the rotating object in kilograms — the field also takes grams, tonnes and pounds, so 4.4 lb is 2 kg

ω

Angular velocity in radians per second. The field takes rpm directly and converts internally: ω = 2π × rpm ÷ 60, so 1400 rpm is 146.61 rad/s. This is the term that gets squared

r

Radius from the axis of rotation to the centre of mass, in metres. The distance that matters is the distance to the mass, not the size of the drum — a load sitting against the wall of a 0.5 m drum is at 0.25 m

v

Tangential speed, ω × r, reported in m/s and mph. It is the speed the object would fly off at if the restraint disappeared, and it is the input the centripetal force page asks for

Use this page when you are the one spinning something and want to know what the structure has to hold: a washing machine drum at the end of a cycle, a fan or blower impeller, a grinding wheel, a turbine blade, a centrifuge rotor, a hard drive platter, a wheel that has thrown a balance weight. The question in all of those is the same — can the bearings and the housing take the pull — and the answer is this force. Two things make the answers more useful. First, remember that the radius here is the distance from the axis to the mass, not the diameter of the machine: halving the radius halves the force, and a load that is not centred sits at some radius between zero and the wall. Second, do not read the output as a design margin by itself — the interesting quantity is usually the force compared with the weight of the object, which is why the same load at the same radius is about 2,200 times heavier at 2800 rpm than it is sitting still. That ratio, measured in g, is how centrifuge rotors are rated, and unlike the force it comes out the same for every sample mass. If instead you are watching something go round from the outside — a car cornering, a ball on a string, a satellite in orbit — the centripetal force page is the one whose question matches yours.

1. A 4.4 lb load in a 10 inch drum at 1400 rpm

   1. 1400 rpm = 1400 × 2π ÷ 60 = 146.61 rad/s
   2. Radius: 10 inches = 0.254 m (the field takes metres)
   3. Force: 2 × 146.61² × 0.254 = 10918.9 N
   4. In the other units: 10.919 kN, which is 2454.7 lbf — about 1.1 tonnes
   5. Tangential speed: 146.61 × 0.254 = 37.24 m/s, or 83.3 mph

   Ten kilonewtons is the number to keep hold of: a load you can carry with one hand becomes a tonne of force on the drum once the machine is up to speed. Nothing about the load changed — it is the same 4.4 lb of wet clothes — and the force came entirely from the rotation. This is also the force the spin bearing has to hold, and it is why a machine with a brick in it thumps: the load is not centred, so the radius of its centre of mass swings round once per revolution and the whole machine reacts.

2. The same load, spin speed doubled to 2800 rpm

   1. 2800 rpm = 293.22 rad/s — exactly twice the angular velocity of the previous example
   2. Force: 2 × 293.22² × 0.254 = 43675.4 N
   3. Compare with the previous example: 10918.9 N, so the force went up by 4.0 times
   4. In the other units: 43.675 kN, or 9818.6 lbf — about 4.5 tonnes
   5. Tangential speed: 74.48 m/s, or 166.6 mph — that one only doubled

   This pair of examples is the entire page. Doubling the speed multiplies the force by four, because the ω in the formula is squared, while the tangential speed merely doubles because it is linear in ω. Machine designers lean on that hard: raising the spin speed is the cheapest way to get water out of clothes, and the price lands on the bearings: twice the rpm is four times the load. It also explains why the last few hundred rpm of a spin cycle are the ones that make the machine shake, and why an unbalanced load that is tolerable at 1400 rpm is a service call at 2800.

3. An ultracentrifuge: 50 g at 3.15 inches, 100 000 rpm

   1. 100000 rpm = 10471.98 rad/s
   2. Radius: 3.15 inches = 0.08 m
   3. Force: 0.05 × 10471.98² × 0.08 = 438649.1 N
   4. In the other units: 438.649 kN, or 98612.2 lbf
   5. Tangential speed: 10471.98 × 0.08 = 837.76 m/s — Mach 2.4, and 1874 mph

   Fifty grams is a sample tube; the force on it is nearly 45 tonnes, which is a little under a million times its own weight. That ratio is what a centrifuge is actually sold on, and it is why the rotor has to be machined from titanium or carbon fibre rather than aluminium: the material has to hold this force at every point of its own mass, and the rim of the rotor is moving at more than twice the speed of sound. Nothing in this number is exotic arithmetic — it is the same formula as the washing machine, with a speed 70 times higher and a mass 40 times smaller, and the speed squared wins by a wide margin.

This is a calculation in the rotating frame, and the force it gives is an inertial effect rather than an interaction: nothing is pushing outward on the object, and if you cut the restraint the object does not accelerate outward at all, it flies off along the tangent. The page therefore tells you what the bearings, the rope or the housing has to supply — the equal and opposite reaction to the centripetal force — and not what is acting on the object in an inertial frame. It assumes the object is rigid, that its centre of mass sits at the radius you typed, and that it does not move relative to the drum; a load that slides outward as the speed rises is a different calculation, and so is a spinning object that deforms. It assumes steady rotation: during spin-up and spin-down there is also a tangential force from the angular acceleration, which this page does not compute. It ignores gravity and the weight of the object itself, so a vertical axis is assumed — for a horizontal axis the load on a bearing varies through the revolution, which is the mechanism behind the shaking of an unbalanced machine. Buoyancy and drag on a rotor inside a fluid are ignored, which matters for a centrifuge rotor inside a chamber of air at speed. Finally, the result is a single-body number: it says nothing about the stresses inside the object, the balancing of the assembly, or the fact that the maximum safe speed of a rotor is set by the material's strength rather than by this force.

What is the centrifugal force formula?

F = mω²r, where m is the mass, r is the radius from the axis, and ω is the angular velocity in radians per second. If your rotation rate is in rpm, convert first: ω = 2π × rpm ÷ 60, so 1400 rpm is 146.61 rad/s. A 2 kg load at 0.25 m and 1400 rpm gives 2 × 146.61² × 0.25 = 10746.9 N, which is a little over a tonne of force.

Is centrifugal force a real force?

Not in the sense that gravity or a rope is. In the ground frame the only real force on a spinning object points inward, toward the axis, and it is always supplied by something — a rope, a tyre, the wall of a drum. The centrifugal force is what that real force looks like when you do the arithmetic in the rotating frame: an apparent push outward that balances the real inward force so that, in that frame, nothing accelerates. The magnitude is right either way, which is why the formula is useful, but there is no agent pushing outward and nothing flies outward if the restraint is cut.

Why does doubling the rpm give four times the force?

Because the angular velocity is squared in F = mω²r. Going from 1400 to 2800 rpm doubles ω, and 2² = 4, so a load that pulled 10.9 kN pulls 43.7 kN. The tangential speed only doubles in the same step, because v = ωr is linear in ω. That difference is why spin dryers are rated by rpm rather than by the speed of the drum wall, and why the last part of a spin cycle is where machines shake hardest.

How do I turn rpm into radians per second?

Multiply by 2π and divide by 60, so ω = rpm × 0.10472. That gives 1400 rpm = 146.61 rad/s, 2800 rpm = 293.22 rad/s, and 100000 rpm = 10471.98 rad/s. The field on this page accepts rpm directly and does that conversion for you; the rad/s figure is worth knowing because it is the number that gets squared, and because radial acceleration and the other rotational formulas are written in it.

What is the difference between centrifugal and centripetal force?

They are the same magnitude seen from two different frames, and the centripetal force page computes exactly the same number from the tangential speed instead of from the rpm. Centripetal means the real inward force in the ground frame — the tension in the rope, the friction between tyre and road, the gravity that holds a satellite. Centrifugal means the outward apparent force in the rotating frame, and it is the useful one if you are the machine holding the load, because it is the load your bearings have to take.

Why does an unbalanced washing machine walk across the floor?

Because the load's centre of mass no longer sits on the axis. A 2 kg imbalance 0.25 m out pulls about 10.7 kN at 1400 rpm, and that force points in a fixed direction in the rotating frame — which means it rotates once per revolution as seen from the floor, so the machine is pushed one way, then the opposite way, 23 times a second. The floor and the suspension cannot absorb that as a steady load, so the machine translates. It also scales with the square of the spin speed, which is why the problem appears at the end of the cycle and not at the start.

• Centripetal Force (College Physics 2e, §6.3) — the real force in the inertial frame, and the apparent outward force that appears when you do the analysis in the rotating frame — OpenStax
• Centrifugal force — the rotating-frame treatment, the washing machine and centrifuge examples, and why the force vanishes in an inertial frame — Wikipedia
• NIST Guide to the SI — radians per second as the SI unit of angular velocity, the exact pound and inch factors used above, and standard gravity — National Institute of Standards and Technology