Centrifugal Force Calculator
Calculate centrifugal (centripetal) force from mass, radius, and angular velocity or RPM. Shows g-force, linear velocity, and period. See also our Angular Velocity Calculator and Force Calculator.
How to Calculate Centrifugal Force
Centrifugal force is the apparent outward force experienced by an object moving in a circular path, as observed from the rotating reference frame. In an inertial (non-rotating) frame, what actually exists is centripetal force — the inward force that keeps the object on its circular path. Both have the same magnitude: F = mω²r = mv²/r. Whether you call it centrifugal or centripetal depends on your reference frame, but the calculation is identical.
To calculate the force, you need the mass of the object, the radius of the circular path, and either the angular velocity (ω in rad/s), the rotational speed (RPM), or the linear (tangential) velocity. These are related: ω = 2π×RPM/60, and v = ωr. The force increases with the square of the speed — doubling the RPM quadruples the force. It also increases linearly with radius and mass.
The result is often expressed in g-forces (multiples of gravitational acceleration, 9.81 m/s²). A centrifuge at 3000 RPM with r = 0.1 m produces about 1000 g — meaning the effective weight of a sample is 1000 times its normal weight. This is used to separate blood components, purify chemicals, and test equipment for high-g environments. Fighter pilots experience up to 9 g in tight turns.
Centrifugal Force Formula
Centrifugal/Centripetal Force:
F = mω²r = mv²/r = m(2πf)²r
Angular Velocity from RPM:
ω = 2π × RPM / 60 (rad/s)
Linear Velocity:
v = ωr = 2πr × RPM / 60
Centripetal Acceleration:
a = ω²r = v²/r
G-Force (RCF):
g-force = ω²r / 9.81 = (2π×RPM/60)²×r / 9.81
Period and Frequency:
T = 2π/ω, f = ω/(2π) = RPM/60
Example Calculation
A 2 kg mass rotates at 1000 RPM on a 0.5 m radius arm:
Given: m = 2 kg, RPM = 1000, r = 0.5 m
ω = 2π × 1000/60 = 104.72 rad/s
v = ωr = 104.72 × 0.5 = 52.36 m/s
F = mω²r = 2 × 104.72² × 0.5
F = 2 × 10,966.2 × 0.5 = 10,966.2 N ≈ 11.0 kN
Centripetal acceleration: a = ω²r = 5483.1 m/s²
G-force: 5483.1/9.81 = 558.9 g
The mass experiences ~559 times its own weight!
Centrifugal Force Reference Table
| Application | RPM | Radius (m) | G-Force |
|---|---|---|---|
| Washing machine spin | 1200 | 0.25 | ~400 g |
| Car on curve (60 km/h, r=50m) | — | 50 | ~0.57 g |
| Centrifuge (lab) | 3000 | 0.1 | ~1000 g |
| Ultracentrifuge | 60000 | 0.05 | ~200,000 g |
| Fighter jet turn | — | ~500 | 9 g |
| Roller coaster loop | — | 10 | 3-5 g |
| Space station (artificial gravity) | 2 | 100 | ~0.45 g |
| Grinding wheel | 3000 | 0.15 | ~1500 g |
Frequently Asked Questions
What is the difference between centrifugal and centripetal force?
Centripetal force is the real inward force that keeps an object moving in a circle (tension in a string, gravity for orbits, friction for cars on curves). Centrifugal force is the apparent outward force felt in the rotating reference frame — it is a fictitious force (pseudo-force) that appears because the reference frame is accelerating. Both have magnitude F = mω²r. In engineering calculations, either perspective gives correct results when applied consistently.
What is RCF (Relative Centrifugal Force)?
RCF (also called g-force) is the centripetal acceleration expressed as a multiple of gravitational acceleration: RCF = ω²r/g = (2π×RPM/60)²×r/9.81. It is the standard way to specify centrifuge settings in biology and chemistry because it directly indicates the separation force on samples, independent of the centrifuge rotor size. A protocol specifying "10,000 g for 10 minutes" gives consistent results on any centrifuge.
How does a centrifuge work?
A centrifuge spins samples at high speed, creating large centripetal acceleration (hundreds to hundreds of thousands of g). Denser particles experience greater outward force and sediment faster than lighter particles, enabling separation. Blood centrifuges separate red cells (bottom), white cells (middle), and plasma (top). Ultracentrifuges can separate proteins, viruses, and even isotopes. The sedimentation rate depends on particle size, density difference, and the applied g-force.
Why does centrifugal force increase with the square of speed?
Centripetal acceleration is a = v²/r = ω²r. The v² (or ω²) dependence comes from the geometry of circular motion: the rate of change of velocity direction is proportional to both the speed and the angular rate of turning. Doubling the speed doubles both the velocity magnitude and the rate at which direction changes, giving 4× the acceleration. This is why high-speed rotating machinery requires extremely strong materials — forces grow rapidly with RPM.
What provides centripetal force in different situations?
The centripetal force is provided by different physical forces depending on the situation: tension (ball on a string), gravity (planets orbiting the sun, satellites), friction (car turning on a road), normal force (banked curves, roller coaster loops), electromagnetic force (charged particles in magnetic fields), and structural forces (spinning machinery). If the required centripetal force exceeds what the constraint can provide, the object flies off tangentially.
Can centrifugal force create artificial gravity?
Yes — a rotating space station can simulate gravity through centrifugal force. The floor is the outer wall, and occupants feel pushed outward just like gravity. For comfortable 1g simulation, the station needs ω²r = 9.81 m/s². A 100 m radius station needs ω = 0.313 rad/s (about 3 RPM). Smaller radii require faster rotation, which causes uncomfortable Coriolis effects and differences in g-force between head and feet. Most designs propose radii of 100-500 m.
Engineering Applications
Centrifugal force calculations are essential in designing rotating machinery (turbines, flywheels, grinding wheels), vehicle dynamics (cornering forces, banked roads), centrifuges (laboratory and industrial separation), amusement park rides (safety analysis), satellite orbits, and proposed space habitats. Engineers must ensure that structural components can withstand the centrifugal loads, which can be enormous at high speeds — a turbine blade tip at 10,000 RPM may experience forces equivalent to hanging a 10-ton weight from it.