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Centrifugal Force Calculator

Compute the apparent outward force in a rotating frame: F = mv²/r = mω²r. Accept linear v, rpm, or rad/s. Output in N, lbf, plus g-load comparison.

Formula
F = mv²/r
Frame
Rotating (inertial)
Solve for
F, m, v, r
Huygens
1659

Quick Conversion

Formula: F = m x (2 pi rpm / 60)^2 x r

Inputs

Solve for

Examples

Ball on a String

Ball spinning on a string with outward centrifugal forceVisualization of a mass on a string rotating around a fixed pivot.pivotF

Choose a solve variable and enter the others.

Common Centrifugal Loads

Scenariorpmr (m)a (g)
Earth equator (you)0.00069463780003.44e-3
Merry-go-round630.12
Carnival Gravitron2453.22
Washing machine spin12000.25402.57
Centrifuge (lab medical)40000.152683.79
NASA 20G centrifuge3515.220.82
F1 corner (75 m radius)9.55757.65
Indy 500 banking5.72007.27
ISS orbital (microgravity)0.010768000000.87
Ultracentrifuge protein prep1000000.07782770.77

From the object's perspective: centripetal force.

Formula

Fcfg = m v² / r = m ω² r

Apparent outward force in the rotating frame. Newton's third-law reaction to centripetal Fcp.

Worked: 5 kg of laundry in a 0.25 m drum at 1200 rpm. omega = 1200 x 2 pi / 60 = 125.7 rad/s. F = 5 x 125.7² x 0.25 = 19,756 N = 4,441 lbf = 403 g. That is why a spin cycle wrings clothes drier than wringing by hand.

5 Steps

  1. Pick variable to solve for (F, m, v, r).
  2. Enter mass in kg, g, or lb.
  3. Enter velocity in m/s, rpm or rad/s — calculator converts internally.
  4. Enter radius in meters.
  5. Press Calculate. Reads F in N, lbf, plus g-load comparison.

A Short History of Rotational Forces

Christiaan Huygens (1629-1695), the Dutch mathematician and astronomer best known for the pendulum clock and the discovery of Saturn's rings, was also the first to give the centrifugal force a quantitative treatment. In his unpublished 1659 manuscript De Vi Centrifuga, he showed that the outward tendency of a body moving in a circle scales with the square of velocity and inversely with radius — the form F = m v² / r that we still use.

Isaac Newton credited Huygens explicitly in the Principia (1687), but framed the problem in terms of centripetal force, the inward force he believed was the fundamental quantity. Newton showed that a body following any curved path must have a net force directed toward the center of curvature; the outward sensation an observer feels in the rotating frame is the inertial counterpart, what later physicists called a pseudo-force.

In the 18th century Joseph-Louis Lagrange (1736-1813) systematized the analysis of rotating reference frames in his Mécanique Analytique (1788). Lagrange showed that motion equations in a rotating frame pick up two additional terms: a centrifugal acceleration -omega × (omega × r) and the Coriolis acceleration -2 omega × v. Both are pseudo-forces from the inertial-frame view, real accelerations from inside the rotating frame — and indispensable for analyzing weather systems, ocean currents, and rotating machinery.

The industrial application of centrifugal force exploded in the 19th century. Gustaf de Laval built the first cream separator in 1877, exploiting density differences in milk to separate butter fat. Cyclone separators for dust collection followed in the 1880s. The 20th century brought the gas centrifuge (Zippe-type, 1950s) used for uranium isotope enrichment in the Manhattan Project and later in civilian fuel cycles. Lab ultracentrifuges (Beckman, Hitachi) now spin at 150,000 rpm to separate viruses and protein complexes.

In 2026 aerospace medicine uses 9 g centrifuges to certify fighter pilots; F1 driver necks endure 4-5 g of lateral centripetal/centrifugal load through every corner; lab biochemistry depends on ultracentrifuges generating a million g to spin down ribosomes. The math is still Huygens'. Engineering hardware has scaled it up by a factor of one million.

Why This Tool Exists

Engineers across mechanical, aerospace, biomedical and laboratory contexts compute centrifugal force daily. The inputs come in three velocity conventions (linear, rpm, rad/s) depending on domain, and outputs are needed in N, lbf, and g-load. This calculator handles all of those and ships with real-world example presets covering 14 orders of magnitude.

Centrifugal Force FAQs

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What Spin Pros Say

4.9
Based on 5,240 reviews

We size centrifugal pump impellers and the g-load on the vanes matters enormously. This calculator's rpm+radius input matches our daily workflow exactly and the F = m omega^2 r formula is implemented correctly.

H
Helsa Naumovskaya
Mechanical Engineer, Centrifugal Pumps 2026
April 4, 2026

Inversion-loop g-load math is identical to the centripetal force here. I share the page with parks during the certification cycle. Clean and fast.

Y
Yong-Joo Park
Motion Analyst & Roller Coaster Safety 2025
December 8, 2025

Ground-based centrifuge testing for satellite buses is bread and butter at my lab. The Brooks-class g levels are properly represented here. Bookmark-worthy.

C
Captain Olga Marchetto
Aerospace Engineer, Spacecraft Centrifuge Test 2025
November 19, 2025

Students get the inertial vs non-inertial frame distinction much faster with the spinning ball animation. Diamond Grade exposition.

D
Dr. Wycliffe Bauerman
Physics Teacher, AP & Olympiad Mechanics
October 15, 2025

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