What is percent overshoot?

Percent overshoot is how much the step response exceeds its final steady-state value, expressed as a percentage. For a second-order underdamped system, it depends only on the damping ratio zeta: %OS = exp(-pi*zeta / sqrt(1 - zeta^2)) * 100.

What damping ratio gives zero overshoot?

A damping ratio of 1.0 (critically damped) or above produces no overshoot. Values between 0 and 1 produce underdamped responses with overshoot; values above 1 produce overdamped responses.

What is natural frequency in a control system?

Natural frequency (omega_n, in rad/s) is the oscillation frequency of an undamped second-order system. It scales the speed of the response — higher natural frequency means faster rise and settling times.

How is settling time defined here?

Settling time uses the 2% criterion: the time for the step response to remain within 2% of the final value. The approximation is Ts ≈ 4 / (zeta * omega_n) for underdamped systems.

Can this calculator handle overdamped systems?

Yes. When the damping ratio is greater than or equal to 1, the system is critically damped or overdamped. Percent overshoot is 0%, and peak time is not applicable. Settling time and rise time are still estimated.

Overshoot Calculator

Enter damping ratio and natural frequency to instantly compute percent overshoot, peak time, rise time, and settling time for a second-order control system.

System Parameters

Damping Ratio ζ (zeta)

0 < ζ < 1 = underdamped | ζ = 1 = critical | ζ > 1 = overdamped

Natural Frequency ω_n (rad/s)

Undamped natural frequency in radians per second

Unit Step Response

Click Calculate to plot the response.

Summary

This overshoot calculator computes the key step-response characteristics of a standard second-order control system. Enter the damping ratio (zeta) and natural frequency (omega_n) to get percent overshoot, peak time, rise time, and settling time instantly. A live plot of the unit step response helps you visualize how the system behaves over time.

How it works

Enter the damping ratio (zeta) between 0 and 1 for an underdamped system.
Enter the natural frequency (omega_n) in rad/s.
Click Calculate to compute the step response characteristics.
Review percent overshoot, peak time, settling time, and rise time.
Adjust the damping ratio or natural frequency to explore different system responses.
Use the step response plot to visualize the system behavior over time.

Use cases

Design PID controllers and tune damping for desired overshoot.
Evaluate servo motor and actuator response characteristics.
Verify second-order approximations of higher-order control systems.
Teach and learn control systems theory in engineering courses.
Compare underdamped, critically damped, and overdamped system behavior.
Estimate settling time for process control loops.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu