In addition to the linear panning functions, there are other mathematical functions to calculate the amplitude of each stereo channel based on the position of a panning potentiometer. Let’s now consider the Square-Law panning functions.

The motivation for using the Square-Law functions is based on the perceived strength of the signal across different panning positions. By using the square-law functions, equal combined power between the channels is achieved. Whereas, the linear panning functions achieve equal combined amplitude. In many ways, listeners perceive the strength of the signal based on the power, rather than the amplitude. In other words, listeners will perceive the same signal strength regardless of panning position when using the Square-Law functions.

Just as before, the relationship between an amplitude, $x$, and a pan knob value, $p$, is: $x = \frac{p}{200} + 0.5$.

For Square-Law panning, the amplitude of the right channel and left channel can be calculated:

rightAmp $= \sqrt{x}$

leftAmp $= \sqrt{(1-x)}$

There is a third type of panning function sometimes used by audio engineers. Next, let’s consider the Sine-Law panning functions.