Centrifugal Force Calculator: Formula & Examples

This calculator computes the magnitude of centrifugal force acting on an object moving in a circular path. You enter the object’s mass, the radius of the circle, and either the linear speed or the angular speed (rotations per minute), and you get the force in newtons (or pound-force). The result tells you the outward force you must counteract to keep the object moving in that circle.

Formula

The centrifugal force is calculated using the same formula as the centripetal force, but directed outward:

F = m × v² / r

Where:

• F = centrifugal force (newtons, N)
• m = mass of the object (kilograms, kg)
• v = linear speed of the object (meters per second, m/s)
• r = radius of the circular path (meters, m)

If you know the angular speed ω (in radians per second) instead of linear speed, use v = ω × r and substitute: F = m × ω² × r.

Worked Example

Using the default values: mass = 2 kg, radius = 1.5 m, linear speed = 4 m/s.

1. Square the speed: v² = 4² = 16 m²/s²
2. Multiply by mass: 2 × 16 = 32 kg·m²/s²
3. Divide by radius: 32 / 1.5 = 21.33 N

The calculator returns 21.33 N as the centrifugal force, and the acceleration is 16 / 1.5 = 10.67 m/s².

What Centrifugal Force Really Is

Centrifugal force is often called a “fictitious� or “pseudo� force because it appears only in a rotating reference frame. If you stand inside a turning car, you feel pushed outward – that is centrifugal force. But an observer on the ground sees your body trying to continue in a straight line (inertia) while the car turns. The “outward� push is your inertia resisting the change in direction.

In engineering and physics, the real, inward force that keeps an object moving in a circle is centripetal force (F = m·v²/r). Centrifugal force has the same magnitude but opposite direction. For design purposes – like a rotating shaft or a centrifuge – the outward force is what matters because it creates stress on the structure.

When to Use This Calculator

Use it whenever you need the outward force on a rotating object:

• Designing a centrifuge or spin dryer – to know the load on the drum wall.
• Calculating the force on a car tire or a passenger in a sharp turn.
• Checking the stress on a rotating arm or flywheel.
• Sizing bolts or clamps that hold a mass on a rotating table.

The result is a force, so you can then compare it to material strength or friction limits. For example, if a 2 kg mass spins at 4 m/s on a 1.5 m radius, you need a structure that can withstand at least 21.33 N pulling outward.

Common Mistakes and Unit Mix-Ups

The most frequent error is mixing units. The formula works only with SI units: kilograms, meters, seconds. If you enter mass in pounds or radius in feet, the result will be off by a factor of 4.45 (pound-force vs newtons). Convert first:

• 1 kg = 2.20462 lb (mass)
• 1 m = 3.28084 ft
• 1 N = 0.224809 lbf

Another mistake is using diameter instead of radius. The radius is half the diameter. Also, if you have rotations per minute (RPM), convert to radians per second: ω = RPM × 2π / 60. Then use F = m·ω²·r.

Finally, remember that centrifugal force is not a real force on the object itself – it is an apparent force. If you are doing a force balance from an inertial (non-rotating) frame, you should use centripetal force instead. The magnitude is identical, but the direction is opposite.

Limits of the Formula

The formula assumes a constant speed and a perfect circle. In real systems, speed may vary, or the path may be an ellipse. It also ignores air resistance and friction. For high speeds or very large masses, relativistic effects are negligible at everyday scales, so the classical formula is fine.

If the radius is very small and speed is high, the force can become enormous. For example, a 1 kg mass at 10 m/s on a 0.1 m radius gives F = 1 × 100 / 0.1 = 1000 N. This is why centrifuge rotors are built from high-strength materials and have speed limits.

Frequently Asked Questions

Is centrifugal force real?

In physics, it is a fictitious force that appears in rotating reference frames. It feels real to you inside a turning car, but an outside observer sees only inertia and centripetal force. For engineering calculations, you can treat it as a real outward load.

What is the difference between centripetal and centrifugal force?

Centripetal force acts inward, toward the center of the circle, and is what keeps the object moving in a circle. Centrifugal force acts outward, away from the center, and is the apparent reaction. They have the same magnitude, F = m·v²/r, but opposite directions.

How do I convert RPM to linear speed?

First convert RPM to radians per second: ω = RPM × 2π / 60. Then multiply by the radius: v = ω × r. For example, 120 RPM on a 0.5 m radius gives ω = 120 × 6.2832 / 60 = 12.566 rad/s, and v = 12.566 × 0.5 = 6.283 m/s.

Can I use this for a car turning a corner?

Yes. Enter the car’s mass, the turning radius, and the speed. The result is the outward force that the tires must counteract (via friction) to keep the car on the curve. If the required force exceeds the friction available, the car skids outward.

What if I only know the angular speed?

Use the alternative formula F = m·ω²·r. You can also convert to linear speed first, then use the main calculator. Just make sure ω is in radians per second, not degrees or RPM.

Why does the force increase so quickly with speed?

Because speed is squared in the formula. Doubling the speed quadruples the force. This is why high-speed rotation is dangerous – a small increase in RPM can cause a large increase in stress.

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in m | Mass | kg | 2 | 0
in r | Radius | m | 1.5 | 0
in v | Linear speed | m/s | 4 | 0
out F | Centrifugal force | N | m * v^2 / r | 2
out a | Centrifugal acceleration | m/s² | v^2 / r | 2