Settling Time Calculator

Work out settling time instantly with clear inputs, formula shown and shareable results.

About Settling Time Calculator

For a second-order system settling time to a given band is -ln(tolerance)/(zeta x omega_n), so the 2% settling time is about 4/(zeta omega_n). Overshoot depends only on damping ratio: 0.7 gives about 4.6%, and 0.5 gives 16%.

Formula

Second-order response

ts = -ln(tolerance) / (zeta x wn); overshoot = 100 x exp(-pi zeta / sqrt(1 - zeta^2))

Worked example

With the default values below, Settling Time Calculator returns Settling time of 1.40. Change any input above and every figure here is recalculated in your browser.

Inputs used

Natural frequency: 4 rad/s
Damping ratio: 0.7
Settling band: 2 %

Results

Settling time: 1.40 s
Rise time: 0.56 s
Time to peak: 1.10 s
Overshoot: 4.599% %

Step by step

1Values used
2Second-order response
3Settling time= 1.40 s
4Rise time= 0.56 s
5Time to peak= 1.10 s
6Overshoot= 4.599 %

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 or fees or charges into account.
Figures are rounded for display to 3 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 is zeta = 0.707 the usual target?

It gives about 4-5% overshoot with the fastest settling for a given natural frequency, and corresponds to a maximally flat frequency response.

How do I speed up settling?

Increase omega_n (higher loop gain or stiffer mechanics) rather than reducing damping, which trades settling time for overshoot.