How do I calculate centrifugal force from unbalance?

Centrifugal force F = U × ω², where U is the unbalance in kg·m and ω is the angular velocity in rad/s. If unbalance is in g·mm, convert to kg·m by dividing by 10⁶. The angular velocity ω = 2π × n / 60, where n is speed in RPM.

What is the unit of unbalance?

Unbalance is measured in mass × distance units: g·mm (gram-millimeters) is most common in industry, oz·in (ounce-inches) is used in North America, and kg·m is the SI unit. 1 oz·in ≈ 720 g·mm.

Why does centrifugal force increase with the square of speed?

Centrifugal force F = m × r × ω². Since ω is proportional to RPM, doubling the speed quadruples the force. This is why high-speed rotors require much tighter balance tolerances than slow-speed rotors.

How does unbalance force affect bearings?

Unbalance creates a rotating force vector at 1× RPM frequency. This force is transmitted through the bearings, increasing dynamic bearing load, causing accelerated wear, fatigue, and vibration. The unbalance force adds directly to the bearing load.

What is the relationship between unbalance force and vibration?

Unbalance force is the primary excitation at 1× RPM in rotating machinery. The resulting vibration amplitude depends on the force magnitude, the machine's dynamic stiffness (mass, stiffness, damping), and the proximity to resonance frequencies.

Free Engineering Tool · #007

Centrifugal Force from Unbalance

Calculate the centrifugal force generated by residual unbalance in a rotating part. Enter unbalance and speed to instantly see force results.

F = U·ω² g·mm → N Bearing Load

Results

Centrifugal Force

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Force (kN)

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Force (lbf)

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Angular Velocity ω

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Frequency

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Unbalance (kg·m)

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Equivalent Static Mass

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Centrifugal Force from Unbalance

When a rotor has residual unbalance U (mass × eccentricity), rotation generates a centrifugal force:

F — centrifugal force (N)
U — unbalance in kg·m (= g·mm × 10⁻⁶)
ω — angular velocity = 2πn/60 (rad/s)
n — rotational speed (RPM)

Speed Dependence

Since force depends on ω², the relationship with RPM is quadratic:

Doubling the speed quadruples the centrifugal force. This is why high-speed machinery (turbines, turbochargers) requires much tighter balance tolerances.

Equivalent Static Load

The equivalent static mass is the mass that, placed at rest on a bearing, would produce the same load as the rotating unbalance force:

Practical Example

Example — Electric Motor

Given: Unbalance U = 1000 g·mm, Speed n = 3000 RPM

ω = 2π × 3000 / 60 = 314.16 rad/s

U (SI) = 1000 × 10⁻⁶ = 0.001 kg·m

F = 0.001 × 314.16² = 98.7 N

Equivalent static load: 98.7 / 9.81 = 10.06 kg

Typical Unbalance Forces

Unbalance (g·mm)	Speed (RPM)	Force (N)	Application
100	10 000	109.7	Turbocharger
1 000	3 000	98.7	Electric motor
5 000	1 500	123.4	Centrifugal pump
10 000	750	61.7	Large fan
50 000	300	49.3	Crusher

⚠️ Note: This calculation assumes a rigid rotor below the first critical speed. Above the first critical speed, the dynamic response is more complex and requires a rotor-dynamics analysis.

Centrifugal Force from Unbalance Calculator | Free Online Tool

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026

Results

Centrifugal Force from Unbalance

Speed Dependence

Equivalent Static Load

Practical Example

Typical Unbalance Forces