Centrifugal Force Calculator
Use this calculator to find centrifugal (centripetal) force, mass, radius, tangential velocity, or angular velocity for any rotating object. Enter values in metric or imperial units, choose what you want to solve for, and the result updates instantly alongside a step-by-step breakdown and G-force readout.
What is centrifugal force?
Centrifugal force is the apparent outward force that acts on an object moving in a circular path when observed from the rotating reference frame. In an inertial (non-rotating) frame, the corresponding real force is centripetal force, which acts inward toward the center of rotation to keep the object on its curved path. Both have the same magnitude, given by F = mv^2/r or equivalently F = m*omega^2*r, where m is mass, v is tangential speed, omega is angular velocity, and r is the radius of the circular path. In everyday language, centrifugal and centripetal force are used interchangeably in magnitude, and this calculator solves for whichever quantity is unknown.
The centrifugal force formula and how to use it
The fundamental relationship is F = m * v^2 / r. When rotation is specified as angular velocity (omega in rad/s), you can substitute v = omega * r to get F = m * omega^2 * r. If you know rotational speed in RPM instead, convert with omega = 2*pi*RPM/60. This calculator accepts all three velocity forms. Use the "Solve for" menu to pick any one unknown: force, mass, radius, tangential velocity, or angular velocity. Enter the three remaining values and the result appears instantly. For example, a 5 kg object at 0.5 m radius travelling at 10 m/s experiences a centrifugal force of 5 * 100 / 0.5 = 1,000 N, which is about 20.4 g.
G-force and why it matters
G-force expresses centripetal acceleration as a multiple of standard gravity (g_0 = 9.80665 m/s^2). A G-force of 1 g is what you feel standing still. Roller coasters typically peak at 3-5 g, fighter aircraft maneuvers can reach 9 g, and industrial centrifuges routinely exceed thousands of g. For human physiology, sustained forces above about 5 g cause blood to pool away from the brain, leading to grey-out and eventually blackout. Laboratory ultracentrifuges run at hundreds of thousands of g to separate macromolecules by density. Engineering systems from washing machines (about 100 g) to gas centrifuges (thousands of g) all rely on precise control of centrifugal acceleration, which is why this calculator also outputs G-force alongside the force in Newtons or pound-force.
Unit system and reverse-solve modes
Switch between metric (kg, m, m/s, N) and imperial (lb, ft, ft/s, lbf) with the unit system selector. The radius can also be entered in centimetres or inches via the unit-number field. The five solve-for modes let you find any unknown: use "Centrifugal Force" for standard forward calculation, "Mass" to find what mass would produce a given force, "Radius" to find the required orbital radius, "Tangential Velocity" or "Angular Velocity" to find the speed needed for a target force. All modes display the G-force and centripetal acceleration alongside the primary answer.
Typical G-force ranges by application
| Application | Typical G-Force | Notes |
|---|---|---|
| Car cornering (road) | 0.3-0.8 g | Normal driving |
| Roller coaster | 1-5 g | Peaks at bottom of loops |
| Fighter jet maneuver | 5-9 g | Pilot wears a G-suit |
| Sports car racing | 3-6 g | Sustained through corners |
| Industrial centrifuge | 500-3,000 g | Separation of materials |
| Medical ultracentrifuge | 100,000-500,000 g | Protein/cell separation |
| Centrifuge training | 3-8 g | Astronaut/pilot training |
Centrifugal G-force levels encountered in real-world systems and activities.
Frequently asked questions
What is the formula for centrifugal force?
Centrifugal force equals mass times the square of tangential velocity divided by radius: F = m * v^2 / r. An equivalent form using angular velocity is F = m * omega^2 * r, where omega (rad/s) = 2*pi*RPM/60. Both give the same answer; choose whichever velocity form you know.
What is the difference between centrifugal and centripetal force?
Centripetal force is the real, inward-directed force that pulls an object toward the center of a circular path - for example, the tension in a string or the friction of a banked curve. Centrifugal force is the equal-and-opposite outward force felt by an observer in the rotating frame. They have the same magnitude (F = mv^2/r) but opposite directions. Physicists prefer centripetal; engineers and everyday language often say centrifugal.
How do I convert RPM to centrifugal force?
First convert RPM to angular velocity: omega (rad/s) = 2 * pi * RPM / 60. Then calculate F = m * omega^2 * r. For example, a 2 kg mass at 0.3 m radius spinning at 500 RPM gives omega = 52.36 rad/s and F = 2 * (52.36)^2 * 0.3 = 1,644 N. This calculator does both steps automatically when you set "Velocity type" to RPM.
What is G-force and how does it relate to centrifugal force?
G-force is the centripetal acceleration (a = v^2/r or omega^2*r) expressed as a multiple of standard gravity (9.80665 m/s^2). A centrifuge producing 1,000 m/s^2 centripetal acceleration exerts about 102 g. G-force lets you compare very different systems on a common scale, from a car corner (0.5 g) to a lab centrifuge (500,000 g).
Can I solve for mass, radius, or velocity instead of force?
Yes. Use the "Solve for" dropdown to pick which quantity you want. If you select "Mass", enter the desired force, radius, and velocity, and the calculator rearranges F = mv^2/r to m = F*r/v^2. Similarly for radius (r = mv^2/F) or velocity (v = sqrt(F*r/m)) or angular velocity (omega = sqrt(F/(m*r))).
Does the calculator work in imperial units?
Yes. Switch the unit system selector to "Imperial" and the inputs change to pounds (lb), feet (ft), and feet per second (ft/s), while the force output switches to pound-force (lbf). All conversions are handled internally so the physics is the same in both systems.
What is the difference between tangential velocity and angular velocity?
Tangential velocity (v, in m/s or ft/s) is the linear speed of the object along its circular path at any instant. Angular velocity (omega, in rad/s) describes how fast the angle is changing. They are related by v = omega * r. RPM (revolutions per minute) is a third form: omega = 2*pi*RPM/60. This calculator accepts any of the three - pick whichever you know.