About

Centrifugal force is the apparent outward force experienced by an object moving along a curved path in a rotating reference frame. It is not a real force in Newtonian mechanics but a pseudo-force (inertial force) arising from the object's inertia. The magnitude equals F = m ⋅ ω² ⋅ r, where m is mass, ω is angular velocity in rad/s, and r is the radius of rotation. Miscalculating this value in engineering contexts - centrifuge design, road banking, flywheel stress analysis - leads to structural failure, bearing damage, or catastrophic rotor burst. This calculator accepts mass, radius, and rotational speed in multiple unit systems and computes force alongside derived quantities: centripetal acceleration, tangential velocity, period, and frequency.

The tool handles three input modes: direct angular velocity (ω), linear (tangential) velocity (v), or revolutions per minute (n). Conversion between modes follows ω = 2πn ÷ 60 and ω = v ÷ r. Note: results assume a rigid body in uniform circular motion. Elastic deformation, bearing friction, and aerodynamic drag are not modeled. For high-speed rotating machinery, consult ISO 1940-1 balancing standards.

Formulas

The centrifugal (centripetal) force for uniform circular motion is computed as:

F = m ⋅ ω² ⋅ r

When input is linear (tangential) velocity v, substitute ω = v ÷ r:

F = m ⋅ v²r

When input is revolutions per minute (n), convert to angular velocity:

ω = 2πn60

Derived quantities computed by this tool:

a_c = ω² ⋅ r

v = ω ⋅ r

T = 2πω

f = 1T

Relative Centrifugal Force (RCF) in multiples of gravitational acceleration:

RCF = ω² ⋅ rg

where F = centrifugal force N, m = mass kg, ω = angular velocity rad/s, r = radius m, v = tangential velocity m/s, n = revolutions per minute RPM, a_c = centripetal acceleration m/s², T = period s, f = frequency Hz, g = 9.80665 m/s² (standard gravitational acceleration).

Reference Data

Application	Typical Radius	Typical RPM	Approx. RCF (× g)	Notes
Laboratory Microcentrifuge	0.06 m	14,000	~16,000	Eppendorf tubes, DNA pelleting
Clinical Centrifuge	0.15 m	4,000	~2,700	Blood separation (PRP, PPP)
Ultracentrifuge	0.10 m	100,000	~800,000	Viral isolation, protein sedimentation
Washing Machine Spin	0.25 m	1,200	~400	Water extraction from fabric
Automotive Tire (120 km/h)	0.33 m	~960	~340	Tread stress, balancing critical
Gas Turbine Blade Root	0.30 m	15,000	~75,000	Nickel superalloy, creep limit
Flywheel Energy Storage	0.50 m	30,000	~500,000	Carbon fiber composite rim
Amusement Park Ride	5.0 m	24	~3.2	Rider comfort limit ~4g
Planetary Centrifugal Mixer	0.08 m	2,000	~360	Paste/epoxy degassing
Cream Separator	0.12 m	6,500	~5,700	Dairy fat separation
Uranium Enrichment (Zippe)	0.10 m	50,000	~280,000	UF₆ isotope separation
Spin Coater (Semiconductor)	0.075 m	5,000	~2,100	Photoresist thin film
Centrifugal Pump Impeller	0.15 m	3,600	~2,200	Water/fluid transport
Hammer Throw (Athletics)	1.22 m	~150	~30	Wire + ball, release at ~29 m/s
Space Station (Artificial g)	100 m	~3	~1.0	O'Neill cylinder concept

Frequently Asked Questions

Centripetal force is the real inward-directed force that constrains an object to circular motion (tension, friction, gravity). Centrifugal force is the pseudo-force perceived in the rotating reference frame, equal in magnitude but directed outward. This calculator computes the magnitude F = mω²r, which applies to both - the distinction is the reference frame and direction.

Use RCF = 1.118 × 10⁻⁵ ⋅ r ⋅ n², where r is in centimeters and n is in RPM. This tool outputs RCF automatically. Always verify the rotor radius from the manufacturer specs - using the wrong radius is the most common error in centrifuge protocols.

No. Centrifugal force depends only on mass, radius, and angular velocity. However, local g varies by latitude and altitude (from about 9.764 to 9.834 m/s²), which affects the RCF ratio. This calculator uses the standard value g = 9.80665 m/s². Temperature may indirectly matter through thermal expansion of the radius in precision machinery.

As r → 0, the force approaches zero when using angular velocity input (F = mω²r). However, with linear velocity input (F = mv²÷r), force diverges to infinity - physically impossible since maintaining constant tangential velocity at zero radius requires infinite angular velocity. The calculator flags r = 0 as invalid for the linear velocity mode.

No. The formula F = mω²r assumes constant angular velocity and a fixed radius (uniform circular motion). For elliptical orbits, the instantaneous centripetal acceleration varies with curvature. For variable-speed rotation, you would need instantaneous ω(t) and may also require accounting for Euler (tangential) and Coriolis forces.

For rotating discs/flywheels, the hoop stress is σ = ρω²r², where ρ is material density. The centrifugal force per unit volume equals ρω²r. Once stress exceeds the material's ultimate tensile strength, the rotor fragments. Carbon fiber composites tolerate tip speeds up to ~1,200 m/s; steel fails around ~450 m/s. This tool calculates force, not stress - but the tangential velocity output helps assess proximity to material limits.