Damping Ratio Calculator

Calculate the damping ratio of a second-order system from measured overshoot or from system parameters.

%

Damping Ratio (zeta)

0.4559

Damping Type0.4559

Damping Ratio (zeta) vs Measured Percent Overshoot

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Formula

## Damping Ratio from Overshoot The damping ratio determines the character of a second-order system response. It can be extracted from a measured step response by noting the percent overshoot. ### Formula **zeta = |ln(%OS/100)| / sqrt(pi² + ln²(%OS/100))** - zeta < 1: underdamped (oscillatory) - zeta = 1: critically damped (fastest non-oscillatory) - zeta > 1: overdamped (sluggish, no oscillations)

Esempio Risolto

A step response shows 20% overshoot.

  1. 01ln(0.20) = -1.6094
  2. 02zeta = 1.6094 / sqrt(9.8696 + 2.5902)
  3. 03zeta = 1.6094 / sqrt(12.4598) = 1.6094 / 3.5299
  4. 04zeta = 0.4559