What is eccentricity in this context?

Eccentricity (e) is the radial distance from the shaft rotation axis to the center of mass of the unbalanced portion. For a rotor that is 5 g·mm out of balance, if the correction mass is 2 g, the eccentricity is 2.5 mm.

Why does the force grow so fast with speed?

Force is proportional to ω² (speed squared). A rotor at 3,000 RPM sees four times the force it sees at 1,500 RPM for the same imbalance, which is why high-speed rotors require tighter balancing grades.

What balancing grade standard should I use?

ISO 1940-1 defines balancing quality grades (G0.4 through G4000). Most industrial rotating machinery falls between G1 and G6.3. The tool gives the raw unbalance force; compliance to an ISO grade requires knowing total rotor mass.

Is this the same as centrifugal force?

Yes. The rotating unbalanced mass generates a centrifugal (centripetal reaction) force directed radially outward. That force rotates with the shaft and is felt as a synchronous (1×) vibration.

Can I use grams and millimeters?

Yes. The calculator accepts g + mm or kg + m. Internally it converts everything to SI (kg, m, N) before computing.

Rotating Imbalance Force Calculator

Calculate the centrifugal force from a rotating unbalanced mass using F = m·e·ω², with unit conversion and an operating-speed sweep chart.

Inputs

Unbalanced mass

Eccentricity (e)

Distance from rotation axis to mass center

Rotational speed

F = m · e · ω² · ω = 2π·N/60 (RPM→rad/s)

Unbalance Force

Force (N)

—

Force (lbf)

—

Force (kN)

—

ω (rad/s)

—

m·e (g·mm)

—

Force vs. Speed Sweep

Force at 25%, 50%, 75%, 100%, 125%, 150%, 200% of entered speed (same mass & eccentricity).

Speed	RPM	ω (rad/s)	Force (N)
Enter values to see sweep

Summary

Computes the unbalance force F = m·e·ω² generated when an eccentric mass rotates on a shaft. Enter the unbalanced mass, eccentricity (distance from shaft center to mass center), and rotational speed to get the peak centrifugal force. Results update instantly. Useful in rotor balancing, vibration analysis, machine design, and selecting bearing loads.

How it works

The unbalance force is F = m · e · ω², where m is the unbalanced mass, e is the eccentricity (offset from rotation axis), and ω is the angular velocity in rad/s.
Angular velocity converts from RPM via ω = 2π·N/60.
The result is the peak centrifugal force acting on the rotor at that speed — it rotates with the shaft and excites the structure at 1× running speed.
Force scales with the square of speed: doubling RPM quadruples the force.

Use cases

Determine bearing load contribution from rotor imbalance during machine design.
Set vibration acceptance criteria for assembled rotors after balancing.
Compare unbalance force before and after a balancing correction to verify improvement.
Estimate structural excitation force for foundation or mount sizing.
Check if residual imbalance after ISO 1940 balancing is within limits for the operating speed.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu