What is the damping ratio?

The damping ratio (zeta) is a dimensionless measure of how quickly oscillations decay in a system. It equals the actual damping coefficient divided by the critical damping coefficient (c_c = 2√(km)).

What do the three regimes mean?

Underdamped (zeta 1): slow return to equilibrium, no oscillation.

What units should I use?

Use SI units for consistent results: c in N·s/m (or kg/s), m in kg, and k in N/m. The resulting zeta is dimensionless regardless of consistent unit system used.

How is natural frequency related to damping?

The undamped natural frequency is ωn = √(k/m) rad/s. The damped natural frequency is ωd = ωn × √(1 − ζ²), which only applies when ζ < 1.

Can I calculate c from a target zeta?

Yes — rearrange: c = 2 × zeta × √(k × m). This calculator also shows c_c so you can derive c directly from a desired zeta.

Damping Ratio Calculator

Name: Damping Ratio Calculator
Availability: InStock
Author: Nham Vu

Enter damping coefficient, mass, and spring stiffness to compute the dimensionless damping ratio (zeta = c / (2 * sqrt(k * m))).

System Parameters

Damping Coefficient (c)

N·s/m

Mass (m)

Spring Stiffness (k)

N/m

Formulas used

ζ = c / (2√(k·m))

c_c = 2√(k·m)

ω_n = √(k/m) rad/s

ω_d = ω_n·√(1 − ζ²) (ζ < 1 only)

Enter c, m, and k then click Calculate

Summary

Enter damping coefficient, mass, and spring stiffness to compute the dimensionless damping ratio (zeta = c / (2 * sqrt(k * m))).

How it works

Enter the damping coefficient c (N·s/m) — the physical resistance of the damper.
Enter the mass m (kg) of the oscillating body.
Enter the spring stiffness k (N/m).
The tool computes the critical damping coefficient c_c = 2 * sqrt(k * m).
The damping ratio zeta = c / c_c is displayed with its regime (underdamped / critical / overdamped).
Natural frequency and damped natural frequency are also shown for reference.

Use cases

Verify suspension tuning in automotive engineering.
Assess vibration control in structural and civil engineering.
Design shock absorbers and dashpots for machinery.
Analyze MEMS and microelectromechanical resonators.
Validate damper specifications against ISO vibration standards.
Teaching and learning classical vibrations coursework.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu