Centrifugal Force Calculator — F = mω²r
Enter the mass, orbit radius, and rotation speed (RPM or rad/s) to calculate the centrifugal/centripetal force, linear velocity, centripetal acceleration, and equivalent g-force for a rotating object.
kg
m
Speed unit
F = m × ω² × r (centripetal: inward; centrifugal: apparent outward)
- 1
Angular velocity (ω = RPM × 2π ÷ 60)
60 × 2π ÷ 60 = 6.2832 - 2
Centripetal acceleration (a = ω² × r)
6.2832² × 0.5 = 19.7392 - 3
Force (F = m × a)
1 × 19.7392 = 19.7392
How does this calculator work?
Centrifugal/centripetal force: F = m × ω² × r. Convert RPM to rad/s with ω = RPM × 2π/60. Linear velocity v = ωr; centripetal acceleration a = ω²r; g-force = a / 9.80665. Doubling radius doubles force; doubling ω quadruples it (force scales with ω²).
Formula
How this is calculated
When an object moves in a circle it continuously accelerates toward the center — centripetal acceleration — because velocity direction changes even when speed is constant. For a mass m rotating at angular velocity ω (rad/s) at radius r from the center, the centripetal force is F = m × ω² × r, directed inward. The equal and opposite reaction — the outward push the object 'feels' in the rotating frame — is the centrifugal force (a fictitious force in the non-inertial rotating reference frame), equal in magnitude: F = mω²r.
Angular velocity in rad/s relates to rotational speed in RPM by ω = RPM × 2π / 60, since one full revolution is 2π radians and there are 60 seconds per minute. Linear (tangential) speed at the radius is v = ω × r. Centripetal acceleration a = ω² × r can also be expressed as v² / r.
G-force is a / g = ω² × r / 9.806 65. An object at 1 g experiences the same acceleration as Earth's surface gravity; at 100 g it would weigh 100 times more than at rest. This is used in centrifuge design, roller-coaster engineering, and aerospace physiology. Real bodies experience both this radial acceleration and tangential acceleration if ω is changing — this calculator assumes constant angular velocity.
Frequently asked questions
Centripetal force is the real inward force keeping the object on a circular path (provided by a string, track, gravity, etc.). Centrifugal force is the apparent outward force felt in the rotating reference frame — a fictitious pseudo-force arising from the frame's own acceleration. Both have the same magnitude F = mω²r.
Multiply RPM by 2π and divide by 60: ω = RPM × 2π / 60. For example, 60 RPM = 60 × 2π / 60 = 2π ≈ 6.283 rad/s. This calculator does the conversion automatically when you select the RPM unit.
G-force is the centripetal acceleration expressed as a multiple of standard gravity (9.80665 m/s²). A g-force of 1 g equals normal gravitational weight; 5 g means the object experiences five times its resting weight. Human consciousness is typically lost above about 5–9 g without a pressure suit.
Also known as
TG we-Calculate Editorial Team. (2026). Centrifugal Force Calculator — F = mω²r [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/centrifugal-force-calculator
TG we-Calculate Editorial Team. "Centrifugal Force Calculator — F = mω²r." TG we-Calculate. 2026. https://we-calculate.com/calculator/centrifugal-force-calculator.
TG we-Calculate Editorial Team, "Centrifugal Force Calculator — F = mω²r," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/centrifugal-force-calculator
@misc{wecalculate_centrifugal_force_calculator, title = {Centrifugal Force Calculator — F = mω²r}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/centrifugal-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
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