Free Damping Ratio Calculator

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

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Damping Ratio (zeta)

0.4559

Damping Type0.4559

Damping Ratio (zeta) vs Measured Percent Overshoot

View formula & how it works →

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)

    • Example Calculation

    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

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