Overshoot Percentage Calculator

Work out overshoot percentage instantly with clear inputs, formula shown and shareable results.

About Overshoot Percentage Calculator

Overshoot is the peak excess over the setpoint divided by the step size, not by the setpoint. Inverting the standard second-order relation recovers the damping ratio, so a measured overshoot alone tells you how much damping the closed loop actually has.

Formula

Overshoot

overshoot % = (peak - setpoint) / (setpoint - start) x 100; zeta = -ln(OS) / sqrt(pi^2 + ln(OS)^2)

Worked example

With the default values below, Overshoot Percentage Calculator returns Overshoot of 22.500%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Setpoint: 100 units
Peak value reached: 118 units
Starting value: 20 units

Results

Overshoot: 22.500% %
Implied damping ratio: 0.4289
Absolute overshoot: 18.00 units
Response assessment: Acceptable for most loops

Step by step

1Values used
2Overshoot
3Overshoot= 22.500 %
4Implied damping ratio= 0.4289
5Absolute overshoot= 18.00 units
6Response assessment= Acceptable for most loops

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why divide by the step, not the setpoint?

Because the response is to the change. A move from 20 to 100 is an 80 unit step, so an 18 unit excess is 22.5% overshoot, not 18%.

Is some overshoot desirable?

Often yes. Zero overshoot means an over-damped loop that responds slowly. Aim for 5-15% unless the process cannot tolerate exceeding setpoint.