Percent Overshoot Calculator (Formula & Damping Ratio)

Calculate percent overshoot from measured peak response or damping ratio, reverse-solve a target damping ratio, and review second-order timing estimates.

Percent Overshoot Formula

PO = (MV - SV) / SV \times 100

Variables:

PO is the Percent Overshoot (%)
MV is the maximum value
SV is the positive final steady-state response, not automatically the commanded setpoint

For the measured mode, assume a positive response starting at zero. Subtract its actual final steady-state response from the maximum response, divide by the positive final response, and multiply by 100. Use matching units. A nonzero initial response or a negative step direction needs a different excursion normalization, which this measured mode does not implement. The standard second-order modes assume a zero-state step response of Kωn²/(s² +2ζωns +ωn²), with positive K and ωn, no finite zeros and 0<ζ<1. Under those assumptions, PO = 100 exp(−πζ/√(1−ζ²)), ωd =ωn√(1−ζ²), and first peak time tp =π/ωd. Inverting a target 0<PO<100 gives ζ =−ln(PO/100)/√(π² +ln²(PO/100)). Convert Hz using ωn =2πf. The common 2% settling estimate 4/(ζωn) is approximate, not an exact or guaranteed band-entry time, especially near model boundaries. At ζ=0 the ideal response does not settle; zero overshoot does not distinguish critical from overdamped behavior. Damping scenarios outside 0<ζ<1 are identified as outside the model instead of being clamped to invented values.

How to Calculate Percent Overshoot?

The following steps outline how to calculate the Percent Overshoot.

First, determine the maximum value.
Next, determine the positive final steady-state response.
Next, gather the formula from above = PO = (MV – SV) / SV *100.
Finally, calculate the Percent Overshoot.
After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

maximum value = 40

final steady-state response = 20

PO = (40 − 20) ÷ 20 × 100 = 100%. This measured response exceeds its final value by 100% under the zero-initial-baseline assumption; it is outside the positive underdamped model’s inverse target range.

Frequently Asked Questions

What is Percent Overshoot in control systems?

Percent overshoot describes the peak excursion beyond the final steady-state response under a stated normalization. It is one transient-performance measure. A measured peak or overshoot percentage alone does not establish stability, which depends on the system dynamics and poles.

Why is calculating Percent Overshoot important?

Overshoot helps compare transient excursions with application-specific limits. Large excursions can violate operating or safety limits, but a large overshoot does not by itself prove instability. Higher-order poles, zeros, delays, saturation and nonlinearities can invalidate the standard second-order prediction.

Can Percent Overshoot be negative?

Under this positive-final, zero-initial-baseline definition, a complete-response maximum at or above the final value gives nonnegative overshoot. A supplied value below the final value is not such a maximum and is rejected. A negative signed peak deviation over a limited observation interval is not proof that the response never reaches its final value. Measured 0% is allowed; inverse design targets must be strictly between 0% and 100% for the selected underdamped model. Very small positive model overshoot is displayed scientifically rather than rounded to an exact zero.

How can we reduce Percent Overshoot in a system?

Reducing Percent Overshoot in a system can be achieved through various methods, including tuning the system’s parameters (like gain, damping ratio), adding compensators, or adjusting the controller settings. The goal is to improve the system’s stability and response to meet the desired performance criteria.