Gyrators are synthetic inductors, which are often used to form bandpass filters. The active buffering device can be a transistor or opamp, as shown in the two examples here.
This type of bandpass filter is commonly used in graphic equalizers and other frequency control circuits such as tone controls.
To use the calculator, enter the values of R1, R2, C1 and C2 then hit the Calculate button. The center frequency of the bandpass filter will be displayed as well as the Q (bandwidth).
The higher the Q of the filter, the more narrow the passband will be. A typical 1/3 octave bandpass will have a Q of about 4.3 and a 2/3 octave filter Q value could be around 2.1. Use the second calculator to find the Q for a specific bandwidth.