How this instrument works
Centrifugal force is the outward push felt by anything carried around with a rotating body, measured from inside that rotation. A sample spinning in a laboratory centrifuge, laundry pressed against a washing machine drum during the spin cycle, and grinding media flung to the rim of a ball mill are all being accelerated toward the axis by some real structure — the rotor arm, the drum wall, the mill shell — and each is felt, from the rotating vantage point, as an equal outward load pressing back against whatever is holding it in. F = m·ω²·r is the size of that load: mass times angular velocity squared times the distance out to the axis.
The formula is shaped the way it is because holding something at a steady angular velocity ω on a circular path forces its centripetal acceleration to equal ω²r, a result that drops out of differentiating circular position twice with respect to time. Multiply that acceleration by mass and Newton's second law hands back the size of force the rotation demands — the same size the rotating occupant feels pressing outward against whatever is holding them in, just aimed the other way. Using ω rather than tangential speed is deliberate: a motor nameplate, a centrifuge dial, or a drum's spin-cycle rating is given as a rotation rate, not a linear speed, so this instrument takes the number the machinery actually reports.
Two conditions have to hold for the plain formula to apply. Angular velocity has to be steady — a rotor still spinning up needs an extra term for angular acceleration, and a mass sliding inward or outward within the rotating frame needs a Coriolis term besides. And radius has to be measured from the true rotation axis, never from some other reference point; get that wrong and every downstream figure, from bearing load to drum-wall stress, is wrong by whatever factor the radius error introduces.
- Enter the object's Mass — the rotating sample, drum load, or rotor mass — in grams, kilograms, or pounds.
- Enter Angular velocity, the rotation rate. Type it directly in rad/s, or switch the unit menu to rpm or deg/s if that's what your spec sheet gives.
- Enter Radius, the distance from the true rotation axis out to the mass — never the diameter, and never a distance measured from some other point.
- Read Centrifugal force in newtons, or switch to kN or lbf to match the rating on whatever bearing, bolt, or drum wall must resist it.
- Double the Angular velocity and watch the force quadruple rather than double — confirming the ω² relationship before you trust the number against a real design load.
Worked example — 1 kg at 10 rad/s on a 0.5 m arm
A 1 kg calibration mass sits 0.5 m out on a rotating test arm spinning at 10 rad/s — about 95.5 rpm, the kind of rig used to check accelerometers against a known load. Square the angular velocity first: 10² = 100. Multiply by the radius: 100 × 0.5 = 50. Multiply by the mass: 50 × 1 = 50. The rig's arm, and whatever bolts hold the mass to it, must resist exactly 50 N pulling outward.
Because ω is squared, running the same arm at 20 rad/s instead of 10 would not double that reading but quadruple it, to 200 N; widening the arm to 1 m at the original 10 rad/s only doubles it, to 100 N. Divided by standard gravity, 9.80665 m/s², the original 50 N acting on a 1 kg mass works out to about 5.1 g — a controlled, repeatable load, which is exactly why calibration rigs like this one spin a known mass at a known rate rather than chasing g-forces some other way.
Questions
Is centrifugal force a real force or a fictitious one?
Neither answer alone is right without naming a frame. Watch a spinning centrifuge rotor from outside, in the lab's stationary frame, and there is no outward force anywhere in the diagram — only the rotor arm pulling the sample inward, centripetally, to keep it on its circular path. Ride along with the sample, rotating with it, and that inward pull is balanced in your frame by an outward term, m·ω²·r, which Newton's second law needs added before the books balance for a non-inertial observer. It is called fictitious because it exists only due to the observer's own acceleration, yet it stresses real hardware — rotor arms, drum welds, bearing races — exactly as if it were real.
Why does this calculator use angular velocity instead of speed?
Because most rotating machinery reports a rotation rate, not a tangential speed. A centrifuge dial, a motor nameplate, or a washing machine's spin-cycle rating gives rpm or rad/s directly, and converting that to a linear speed at some particular radius before calculating just adds a step and a rounding error. F = m·ω²·r skips that conversion — feed in the shaft speed and the radius together and the force falls out directly. The two forms agree exactly, since substituting v = ω·r into F = mv²⁄r reduces algebraically to m·ω²·r.
Why does doubling the angular velocity quadruple the force?
Because ω appears squared in the formula, so doubling it multiplies the force by 2² = 4, not 2. A washing machine drum accelerating from a 400 rpm wash cycle to an 800 rpm spin cycle is not putting twice the load on its bearings and suspension mounts — it is putting four times the load, which is exactly why spin cycles shake and roar so much harder than the wash itself.
How do I convert rpm to rad/s for this formula?
Multiply the rpm figure by 2π and divide by 60, since one revolution is 2π radians and one minute is 60 seconds: ω = 2π·N ⁄ 60. A drum spinning at 1,200 rpm works out to about 125.7 rad/s. This calculator's Angular velocity field accepts rpm directly and performs that conversion internally, so entering 1200 with the rpm unit selected gives the same result as entering 125.7 with rad/s selected.
What happens to the force if the radius changes but the spin rate stays fixed?
It scales directly with radius, not with its square. Doubling the radius at a constant ω doubles the force; doubling ω at a constant radius quadruples it. That asymmetry is why engineers spinning up a rotor watch shaft speed far more closely than how far the mass sits from the axis, and why the outer rim of a flywheel or grinding wheel — sitting at the largest radius — always carries the highest hoop stress for a given rotation rate.
Where does this outward force actually get resisted in real machinery?
Whatever structure holds the rotating mass on its circular path — a centrifuge rotor arm, a washing-machine drum wall, a flywheel rim, a bearing race — must supply an equal inward force to stop that mass flying off in a straight line. Engineers size that structure using this same m·ω²·r figure as a design load, checking it against the material's tensile strength and the bearing's rated capacity, and building in a safety margin well beyond the calculated force.