kg
Enter a positive mass value.
m
Enter a positive radius value.
m/s
Enter a positive velocity / RPM / omega value.
Linear speed at radius r
Centrifugal Force
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📋 Calculation Breakdown
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Sources & Methodology
Centrifugal force formula verified against NIST physical constants and standard physics references including Halliday, Resnick & Walker "Fundamentals of Physics."
The Physics Classroom — Mathematics of Circular Motion
Full derivation of F = mv^2/r, unit analysis, worked examples, and the relationship between centripetal and centrifugal force
NIST SP 811 — Guide for the Use of SI Units
Standard SI unit definitions and conversion factors for mass (kg), length (m), velocity (m/s), and force (N)
Methodology: F = m x v^2 / r (Newtons). RPM mode: omega = 2pi x RPM / 60 (rad/s), v = omega x r. Angular velocity mode: v = omega x r. Mass conversions: g/1000, lb x 0.453592, oz x 0.0283495. Radius conversions: cm/100, mm/1000, in x 0.0254, ft x 0.3048. G-force = (v^2/r) / 9.80665. Period T = 2pi x r / v. Frequency f = 1/T.
⏱ Last reviewed: April 2026
How to Calculate Centrifugal Force — Physics & Engineering Guide
This centrifugal force calculator is an essential tools resource for physics students, mechanical engineers, and anyone working with rotating systems. Centrifugal force is the apparent outward force experienced by objects in circular motion, equal in magnitude to the centripetal force that keeps the object in its circular path. The formula F = mv²/r is one of the most important equations in classical mechanics.
The Centrifugal Force Formula
F = m × v² / r
F = force in Newtons | m = mass in kg | v = velocity in m/s | r = radius in meters
Example: m=2kg, v=10m/s, r=0.5m → F = 2 × 100 / 0.5 = 400 N
Example: m=2kg, v=10m/s, r=0.5m → F = 2 × 100 / 0.5 = 400 N
F = m × ω² × r (RPM form)
omega (rad/s) = 2 × pi × RPM / 60
Example: 1 kg at r=0.3m, 1000 RPM: omega=104.72 rad/s, F = 1 × 104.72² × 0.3 = 3,290 N
Example: 1 kg at r=0.3m, 1000 RPM: omega=104.72 rad/s, F = 1 × 104.72² × 0.3 = 3,290 N
Centrifugal Force Reference Table
| Mass | Velocity | Radius | Force | G-Force |
|---|---|---|---|---|
| 1 kg | 5 m/s | 1 m | 25 N | 2.5 g |
| 1 kg | 10 m/s | 1 m | 100 N | 10.2 g |
| 2 kg | 10 m/s | 0.5 m | 400 N | 40.8 g |
| 1 kg | 20 m/s | 1 m | 400 N | 40.8 g |
| 5 kg | 15 m/s | 2 m | 562.5 N | 11.5 g |
| 0.1 kg | 31.4 m/s (1000 RPM, r=0.3m) | 0.3 m | 3,290 N | 335 g |
Centrifugal vs Centripetal Force
Centripetal force is the real inward-directed force that keeps an object moving in a circle, provided by tension, gravity, friction, or normal force. Centrifugal force is the apparent outward force felt by an observer in the rotating frame of reference. In physics they have identical magnitudes (F = mv²/r) but opposite directions. Engineers commonly use "centrifugal force" when analyzing stresses in rotating machinery from the perspective of the rotating component.
Why Speed Matters Most
Centrifugal force scales with the square of velocity. Doubling speed quadruples force. This quadratic relationship is why high-speed turbines and centrifuges require extreme material strength — small RPM increases produce disproportionately large structural loads.
💡 Pro Tip: G-force is the most intuitive way to understand centrifugal intensity. A pilot pulling 9g feels 9 times their body weight outward. A lab centrifuge at 3,000 RPM with a 10cm rotor radius produces about 1,000g — 1,000 times gravity. The simplified centrifuge formula: RCF = 1.118 × 10² × r(cm) × RPM².
Frequently Asked Questions
F = mv^2/r where m=mass (kg), v=velocity (m/s), r=radius (m). RPM form: F = m x omega^2 x r, where omega = 2 x pi x RPM / 60 rad/s. Both give force in Newtons.
Convert RPM to omega = 2 x pi x RPM / 60. Then v = omega x r. Apply F = m x omega^2 x r. Example: 1 kg at 0.5m, 1000 RPM gives omega=104.72 rad/s and F=5,483 N.
G-force = (v^2/r) / 9.81. It measures centrifugal acceleration relative to gravity. G-force = 1 equals normal gravity. Lab centrifuges operate at hundreds to hundreds of thousands of g.
Centripetal force is the real inward force keeping an object in circular motion. Centrifugal force is the apparent outward force in the rotating reference frame. Both have the same magnitude F = mv^2/r but point in opposite directions.
Force increases with the square of velocity (F=mv^2/r). Doubling speed quadruples force. Tripling speed multiplies force by 9. Velocity is the most sensitive parameter in centrifugal force calculations.
At constant velocity: F inversely proportional to r (halving r doubles F). At constant RPM: F directly proportional to r (doubling r doubles F). The relationship depends on whether velocity or angular velocity is constant.
Newtons (N) in SI units. Mass in kg, velocity in m/s, radius in m gives Newtons directly. Divide by 1000 for kN. Multiply by 0.2248 for pounds-force (lbf).
Angular velocity omega (rad/s) = 2 x pi x RPM / 60. Centrifugal force F = m x omega^2 x r is the preferred form when RPM is known, as in motor and centrifuge applications.
RCF = 1.118 x 10^-5 x r(cm) x RPM^2. Used in laboratory centrifuge applications with radius in centimeters. RCF is dimensionless and represents g-force (centrifugal acceleration / gravity).
Centrifuge design, turbine blade stress analysis, vehicle cornering, washing machine spin cycles, amusement ride safety, and satellite orbital mechanics. Engineers calculate centrifugal forces to ensure structural integrity of rotating components.
Yes. F is directly proportional to mass. Doubling mass at constant velocity and radius doubles force. This contrasts with the quadratic relationship with velocity, making velocity the more sensitive variable.
Period T = 2 x pi x r / v = 60 / RPM seconds per revolution. Frequency f = 1/T Hz. Angular velocity omega = 2 x pi / T rad/s.
Centripetal acceleration a = v^2/r = omega^2 x r (m/s^2), directed toward the center. G-force = a/9.81. Centrifugal force F = m x a is the equal and opposite reaction felt in the rotating frame.
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