Centrifugal Force Calculator
This calculator works out the centrifugal (and equal and opposite centripetal) force acting on any object moving in a circle, using the standard physics formulas F = mv²/r and F = mω²r. It is useful for students checking homework, engineers sizing rotating machinery, and anyone curious about the forces at play in a centrifuge, a cornering car, a carousel or a spinning drum. You enter the object's mass in kilograms and the radius of its circular path in metres, then choose how you want to describe its speed: linear (tangential) speed in metres per second, angular velocity in radians per second, or rotational speed in RPM, which the calculator converts automatically. From these figures it instantly returns the centrifugal force in newtons and kilonewtons, the equivalent g-force compared with standard gravity, and the angular velocity in radians per second. A full breakdown also shows the period and frequency of rotation, the speed in km/h, the linear acceleration, and the force converted into kilograms-force and pounds-force. Adjust any field and the results update immediately, so you can compare scenarios such as different centrifuge speeds or cornering radii side by side. Because this uses classical Newtonian mechanics for uniform circular motion in a single plane, treat the results as indicative for engineering design work, and have a qualified engineer verify calculations for safety-critical rotating equipment or high-speed machinery.
1. Object Properties
2. Speed of Rotation
Calculation Breakdown
Additional Values
How Centrifugal Force is Calculated
When an object moves in a circle, it requires a force directed towards the centre to keep it on its circular path. This inward force is called the centripetal force. From the perspective of the rotating object itself, there is an apparent outward force of equal magnitude, known as the centrifugal force.
Where:
- F = centrifugal/centripetal force (newtons, N)
- m = mass of the object (kilograms, kg)
- v = linear (tangential) speed at the radius (metres per second, m/s)
- r = radius of circular motion (metres, m)
- ω = angular velocity (radians per second, rad/s)
The two formulas are equivalent because linear speed and angular velocity are related by v = ωr. Substituting into F = mv²/r gives F = m(ωr)²/r = mω²r.
Worked Example
A 2 kg object travels in a circle of radius 0.5 m at a linear speed of 10 m/s. What is the centrifugal force?
| Step | Calculation | Result |
|---|---|---|
| Mass | m = 2 kg | 2 kg |
| Radius | r = 0.5 m | 0.5 m |
| Speed | v = 10 m/s | 10 m/s |
| Force | F = mv²/r = 2 × 10² / 0.5 | 400 N |
| G-force | a = v²/r = 100/0.5 = 200 m/s² → 200/9.81 | 20.39 g |
This matches the calculator's default output: 400 N, 0.40 kN, and 20.39 g.
RPM to Angular Velocity Conversion
If you know the rotational speed in RPM (revolutions per minute), convert to angular velocity using:
For example, 300 RPM = 300 × 2π / 60 = 31.42 rad/s. The centrifugal force is then F = mω²r.
Practical Applications
Centrifugal force calculations appear in many engineering and everyday contexts:
- Centrifuges: Laboratories use high-speed centrifuges to separate materials. A sample 0.1 m from the axis at 10,000 RPM experiences roughly 11,000 g.
- Vehicle cornering: When a car turns, passengers feel an apparent outward push. Engineers size tyres and suspension based on the centripetal force needed to hold the car on the curve.
- Rotating machinery: Turbine blades, flywheels, and washing machine drums must be designed to withstand the centrifugal stresses at operating speeds.
- Amusement rides: The outward feeling on a carousel or loop-the-loop is centrifugal force. Ride engineers calculate maximum g-forces to ensure passenger safety.
- Satellites and orbits: A satellite in orbit is in free fall towards Earth; the centripetal acceleration of its orbit equals the local gravitational acceleration.
G-Force
G-force expresses acceleration as a multiple of standard gravity (g = 9.81 m/s²). The centripetal acceleration is a = v²/r (or a = ω²r), and the g-force is simply a/9.81. Fighter pilots can sustain around 9 g briefly; sustained exposure above 5 g causes blackout in most people without a pressure suit. Industrial centrifuges routinely operate at tens of thousands of g.
Related Calculators
- Science and Engineering Calculators
- Force Calculator (F = ma)
- Angular Velocity Calculator
- Angular Acceleration Calculator
- Acceleration Calculator
- Newton’s Second Law Calculator: f = ma, solve for any variable.
- Nm to ft-lbs Converter: Newton Metres to Foot-Pounds.
Sources and method: Newton's second law of motion and classical circular motion theory as given in Halliday, Resnick and Krane, Physics (5th ed.). Standard gravity g = 9.80665 m/s² (BIPM). Conversion 1 lbf = 4.44822 N.
This calculator applies to uniform circular motion in a single plane. It does not account for non-uniform rotation, relativistic effects, or three-dimensional orbital mechanics. For engineering applications involving high-speed rotating machinery, consult a qualified mechanical engineer.