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.

Enter:

- Tolerance
**T**(this is the level to which a signal is considered as settled)_{%} - Damping Ratio
**ζ** - Natural frequency
**f**(Hz)_{n}

**Formula**

**T _{S} = -Log_{e}(0.01*T_{%}* √(1-ζ^{2}))/( ζ*2*π*f_{n})**

## 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**.