Pan pots and pan laws

A pan pot places a mono signal between the left and right channels. It looks trivial, but the choice of pan law decides whether a sound keeps the same loudness as it moves across the stereo image.

Two ways of dividing a signal

Let the pan position p run from 0 (left) to 1 (right).

Linear law. Left gain is 1 − p, right gain is p. At the centre each channel gets half of the amplitude, which is 6 dB down.

• In a mono sum (left plus right) the level stays constant as the sound pans.
• Heard on two loudspeakers, a sound in the centre is usually perceived as somewhat quieter than one at the sides, because at higher frequencies the two loudspeakers add by power rather than by amplitude.

Constant-power law. Left gain is cos(p · 90°), right gain is sin(p · 90°). At the centre each channel is 3 dB down.

• On two loudspeakers the loudness stays about the same across the image.
• In a mono sum, a centre signal is 3 dB louder than a hard-panned one.

Numbers

The compromise

Mixing consoles often use a pan law between the two: −4.5 dB at the centre. It limits the mono level difference to 1.5 dB and the loudspeaker level difference to 1.5 dB as well. Many digital audio workstations let you choose −3, −4.5 or −6 dB.

What this means for mixing

• If your mix will be heard mainly on loudspeakers, a constant-power law gives a stable level.
• If mono compatibility is paramount (broadcast, background music), a law closer to linear is safer.
• A level difference between channels is what places the image. Pan pots produce only level differences, so their images are precise but can sound less spacious than time-difference stereo.

A note on the difference between left and right

The level difference between the two channels determines the image position, not the individual gains. A constant-power pot at the quarter position gives a difference of about 7.6 dB, which places the image roughly 60 % of the way to the side; see stereo localisation for how level differences map to positions.

Try it

The adding levels tool shows why the centre signal is 3 dB louder in a mono sum: two equal coherent signals add by 6 dB, while two incoherent ones add by 3 dB.

Draft: written by an AI assistant, awaiting technical review.