Centrifugal Force Calculator

How to use this calculator

Three inputs are always required: mass, radius, and rotational speed.

Mass (kg): The mass of the object or body experiencing the centrifugal effect.

Radius (m): The distance from the rotation axis to the object. For a ball on a string, this is the string length. For a washing machine drum, it is the drum radius.

Speed Input Type: Choose how you will specify rotational speed:

• Angular Velocity (rad/s): Enter ω directly.
• RPM: Enter revolutions per minute. The calculator converts to rad/s.
• Tangential Velocity (m/s): Enter the linear speed of the object along its circular path. The calculator derives ω = v / r.

Click Calculate to see centrifugal force in Newtons, centripetal acceleration, tangential speed, RPM, and angular velocity. The Force vs RPM chart shows the parabolic relationship (F grows with ω²), with your input point marked.

The rotating reference frame

To understand centrifugal force, you need to understand what a reference frame is and what makes a frame “non-inertial.”

An inertial frame is one that is not accelerating. Newton’s laws apply without modification in an inertial frame. If you observe a ball from a stationary train station platform, you see it follow its natural path under real forces.

A non-inertial frame is one that is accelerating (including rotating). A rotating carousel is a non-inertial frame. If you stand on the carousel, the world appears to rotate around you. Objects that are actually stationary appear to drift outward (away from the center).

To make Newton’s laws work mathematically in a rotating frame, you introduce pseudo-forces: fictitious forces that account for the frame’s acceleration. In a frame rotating at angular velocity ω, two pseudo-forces appear:

1. Centrifugal force: points outward, magnitude = mω²r
2. Coriolis force: acts perpendicular to motion, magnitude = 2mωv (causes weather patterns)

Neither of these exists in the inertial frame. They are mathematical corrections to make the equations work in the rotating frame.

Why centrifugal force is called “fictitious”

The word “fictitious” is technically accurate but often misunderstood. It does not mean you do not feel the effect. You absolutely feel it. What it means is:

In the inertial frame, the only real force acting on you in circular motion is the centripetal force pointing inward (provided by a rope, seat belt, friction, or gravity). Your body tends to move in a straight line (Newton’s first law). The seat or rope continuously redirects you inward. From your perspective inside the rotating car, this feels like something pushing you outward.

The pushing sensation is real. The outward force causing it is not: it is your own inertia being interpreted from a rotating reference frame.

Both have the same magnitude. One is real; one is a bookkeeping device. Physicists typically work in inertial frames and call it centripetal force. Engineers analyzing rotating machinery often work in rotating frames and find centrifugal force useful.

Deriving F = mω²r

Start from Newton’s second law in the inertial frame. A mass m moving in a circle of radius r must have centripetal acceleration directed inward:

The centripetal force required is:

Substituting v = ωr gives the two equivalent forms.

In terms of RPM:

Because ω appears squared, the force grows with the square of rotational speed. Doubling RPM quadruples the force. This quadratic growth is critical in high-speed machinery design.

The force is measured in Newtons (N = kg·m/s²).

Applications: centrifuges and laboratory separators

A laboratory centrifuge creates controlled acceleration many times greater than gravity, used to separate materials by density.

The centrifugal acceleration is often expressed as a multiple of gravity:

where RCF is Relative Centrifugal Force (also written as ”× g”), r is in meters, and g = 9.81 m/s².

Ultracentrifuges operating at 100,000 RPM achieve RCF values of 500,000 × g, allowing separation of protein molecules and viruses.

Washing machines, dryers, and laundry physics

A front-loading washing machine drum rotates clothes through water. During the spin cycle, the drum spins at 800-1600 RPM.

Higher spin speeds remove more water, shortening drying time and saving energy. However, very high speeds cause more vibration if the load is unbalanced, which is why washing machines have vibration sensors.

Car dynamics and cornering forces

When a car turns, centripetal force must be supplied by tire friction. If the required force exceeds the available friction, the car slides (understeer or oversteer).

The maximum friction force available is:

Setting them equal gives the maximum cornering speed for a flat road:

For μ = 0.8 (dry tarmac), g = 9.81, r = 50 m:

v_max = √(0.8 × 9.81 × 50) = √392.4 = 19.8 m/s ≈ 71 km/h

Banked curves increase v_max by providing a component of the normal force in the centripetal direction, reducing the friction requirement. Formula 1 circuits use banking; so do highway entrance ramps.

Artificial gravity in space stations

A rotating space station can simulate gravity using centrifugal force. Occupants on the inner surface of the outer ring press against it with force mω²r, experienced as “gravity.”

To match Earth surface gravity (g = 9.81 m/s²):

A concern with small radii: the gravity gradient across a human body is noticeable. At r = 10 m and ω = 0.99 rad/s, the acceleration at someone’s head (r = 9.3 m) would be 9.1 m/s² while their feet (r = 11.3 m) feel 11.1 m/s². This difference causes discomfort. Larger radii spread the gradient out.

Proposed designs like the Stanford Torus (1800 m radius, 1 RPM) and O’Neill cylinder (3,200 m radius, 0.55 RPM) use large radii precisely to minimize this gradient.

Industrial applications

Centrifugal pumps

The most common pump type in industry. An impeller rotates at high speed, flinging fluid outward by centrifugal force. The kinetic energy converts to pressure as the fluid slows in the volute casing.

Flow rate and pressure depend on ω. Pump affinity laws state: flow rate scales with ω, pressure head scales with ω², and power scales with ω³. Doubling RPM doubles flow, quadruples pressure, and multiplies power by 8.

Centrifugal separators

Used in oil refineries and food processing to separate liquids of different densities or to remove solids from liquids. A cream separator spins whole milk at 6000-8000 RPM: the denser skim milk moves outward, the lighter cream stays near the center.

Flywheel energy storage

Flywheels store kinetic energy E = ½Iω². Modern composite flywheels (carbon fibre, kevlar) operate at 20,000-100,000 RPM in vacuum enclosures to minimise air drag. At such speeds, centrifugal stresses in the rotor material are extreme: hoop stress σ = ρω²r², where ρ is material density. The material’s tensile strength limits the maximum ω and r.

Safety

High-speed rotating equipment that fails can fragment with catastrophic results. A flywheel or turbine disc failure releases shrapnel with velocities determined by the stored rotational energy. Safety standards require containment rings, overspeed protection trips, and regular inspection of fatigue-prone components. The force required to hold a rotor rim together is exactly the centripetal force: materials must sustain mω²r without yielding.

Centrifugal force in industrial applications

Understanding centrifugal force is critical for designing rotating equipment that operates safely and efficiently.

Centrifuges: Laboratory and industrial centrifuges use centrifugal force to separate substances by density. The centrifuge rotor creates a centrifugal acceleration far exceeding gravity. A lab centrifuge at 10,000 RPM with a 10 cm rotor radius produces a centrifugal acceleration of:

Industrial ultracentrifuges can reach 100,000 RPM and create accelerations exceeding 600,000 g, used for separating viruses, proteins, and isotopes.

Washing machines: The spin cycle creates centrifugal force that pushes water outward through the drum holes. A typical front-loader spinning at 1400 RPM with a drum radius of 25 cm creates about 544 m/s² of centrifugal acceleration, approximately 55 g, which is sufficient to extract most water from laundry.

Centrifugal pumps: The most common pump type works by accelerating fluid outward using centrifugal force. The impeller rotates and imparts kinetic energy to the fluid, which converts to pressure energy as the fluid slows in the pump casing. Pump performance is described in terms of RPM, flow rate, and pressure head.

Road vehicle cornering: When a car turns, the occupants feel a centrifugal force pushing them outward. At highway entry ramps (typical radius 100 m, speed 50 km/h = 13.9 m/s): F_c = mv²/r = m × 1.93 m/s². This is about 0.2 g, noticeable to occupants. High-performance driving at race track limits may reach 3-4 g lateral acceleration.

Centrifugal force and artificial gravity

One of the most intriguing engineering applications of centrifugal force is creating artificial gravity in space. In microgravity, the human body loses bone density and muscle mass. Rotating a space habitat or spacecraft creates centrifugal force that mimics gravity for the inhabitants.

The required angular velocity for Earth-equivalent gravity (9.81 m/s²) depends on the rotation radius:

For a habitat radius of 50 meters: ω = √(9.81/50) = 0.443 rad/s = 4.23 RPM

For a smaller 10 meter radius: ω = √(9.81/10) = 0.99 rad/s = 9.45 RPM

Higher rotation rates at smaller radii create perceptible Coriolis effects (objects appear to deflect when moving) that cause nausea in humans. Engineering consensus suggests rotation rates above 3-4 RPM become uncomfortable for most people, requiring large habitats (50+ meter radius) for comfortable artificial gravity.