Settling Time Calculator

The settling time is the time from the application of an ideal instantaneous step input to the time at which the system output has entered and remained within a specified tolerance (also known as the error band).

This tool calculates the settling time for a second order system with a damping ratio ζ less than 1.


  • Tolerance T% (this is the level to which a signal is considered as settled)
  • Damping Ratio ζ
  • Natural frequency fn (Hz)


TS = -Loge(0.01*T%* √(1-ζ2))/( ζ*2*π*fn)

Example Calculation

For a tolerance of 2%, damping ratio of 0.5 and natural frequency 100 Hz, the settling time is 13 ms. As the tolerance decreases to 1%, the settling time increases to 15 ms.

Related Calculators

ADC Settling Time