Centrifugal Force Calculator
Compute the centrifugal force of a rotating mass from mass, radius and either rotational speed or circumferential velocity. The basis is uniform circular motion with ω = 2π·n/60, v = ω·r and F = m·ω²·r = m·v²/r. The calculator also returns the circumferential velocity and the centripetal acceleration, including as a multiple of the gravitational acceleration g – live with every input.
Centrifugal force calculator (F = m·ω²·r)
Model: uniform circular motion of a rigid point mass with F = m·ω²·r = m·v²/r and ω = 2π·n/60. Pure calculator without deformation, friction or strength verification (burst speed). For rotating shafts use the critical speed calculator.
Results
Calculating …
Formulas and fundamentals
In uniform circular motion a mass m moves at constant speed on a circle of radius r. To keep it on the path, a force directed toward the centre is required, the centripetal force. In the co-rotating frame it appears as an equal outward inertial force, the centrifugal force. The starting quantity is the angular frequency ω = 2π·n/60 in rad/s, obtained from the rotational speed n in rpm.
From the angular frequency follow the circumferential velocity v = ω·r and the centripetal acceleration a = ω²·r = v²/r. The centrifugal force is F = m·a = m·ω²·r = m·v²/r. It grows linearly with mass and radius but quadratically with speed: doubling the rotational speed quadruples the force. That is why fast-rotating parts produce very large forces even at small mass.
The acceleration a is also given as a multiple of the gravitational acceleration g = 9.81 m/s². In machine and plant engineering this g value is an intuitive measure of loading, for example on centrifuges, grinding wheels, fan impellers or balancing tasks. The calculation assumes the mass to be rigid and point-like at the radius; deformation, friction and strength limits (burst speed) are not considered.
Worked example
A mass of m = 2 kg rotates on a radius r = 0.5 m at n = 3000 rpm. The angular frequency is ω = 2π·3000/60 = 314.16 rad/s and the circumferential velocity v = ω·r = 157.08 m/s.
The centripetal acceleration is a = ω²·r = 49,348 m/s², about 5030·g. This gives the centrifugal force F = m·a = 98,696 N ≈ 98.70 kN.
The example shows the quadratic dependence: at half the speed (1500 rpm) the force would drop to a quarter, about 24.7 kN. For rotating parts the rotational speed is therefore by far the most sensitive parameter.
Frequently asked questions
What is the difference between centrifugal and centripetal force?
They are two views of the same magnitude. The centripetal force is the real, centre-directed force that keeps the mass on the circular path. The centrifugal force is the outward inertial force of equal magnitude F = m·ω²·r that appears in the co-rotating frame.
Why does the force grow quadratically with rotational speed?
Because in F = m·ω²·r the angular frequency ω is squared, and ω = 2π·n/60 is proportional to the rotational speed. Doubling the speed therefore quadruples the centrifugal force. Mass and radius enter only linearly.
Can I enter the circumferential velocity instead of the rotational speed?
Yes. Using the toggle you can provide either the rotational speed n in rpm or the circumferential velocity v in m/s. The calculator then uses F = m·v²/r and back-calculates the other quantity as well as the angular frequency.
What does the value as a multiple of g mean?
The centripetal acceleration a is divided by the gravitational acceleration g = 9.81 m/s². A value of 100·g means the mass experiences a centrifugal force of one hundred times its weight. It is an intuitive measure of the loading on rotating parts.
Does the calculator account for the strength of the part?
No. The calculator only provides the kinematic centrifugal force of a rigid point mass. Whether a real part withstands the resulting stresses (burst speed of grinding wheels or flywheels) is a separate strength verification and is not included here.
Related tools
Moment of Inertia
Mass moment of inertia of homogeneous bodies: solid cylinder, tube, cuboid, sphere, cone and ring.
Shaft critical speed
Estimate the bending critical speed of shafts using the Rayleigh and Dunkerley methods.
Torque, Speed & Power
Convert between torque, speed and power: P = M·ω for rotating drives.