Very precise speaker placement can open up a whole new dimension in listening, so I will outline the system that is becoming the standard of the industry. This standardized listening room is a Golden Cuboid and is the model for the math used in this system. This method will work with any box speaker, in any reasonably sized rectangular room. You may find that you have already positioned your speakers this way by ear.
Active nodes are the main concern when placing speakers in a rectangular room. A node, or the frequency where speakers and parallel walls interact, is proportional to the speaker to the wall distance.
The three most importance nodes, in order of importance, are proportional to the distance between the speaker and:
1. The side wall nearest the speaker
2. The rear wall
3. The side wall across from the speaker
A secondary factor is the speaker-to-speaker time constant.
When you use this Golden Ratio method to set your room up, the speakers are placed so the three nodes progress or differ from one another in Golden Ratio. This eliminates any unison or near unison resonance in the nodes.
Panel or dipole speakers such as Apogees and Magnepans cancel their side waves, so a formula of .618 x the ceiling height can be used for determining placement from the rear wall. Most box speakers radiate low frequencies in all directions thus a formula that places the speaker to rear wall distance at 1.618 the side wall distance should be used.
Speaker placement, simply stated:
The distance from the center of the woofer face to the side walls is:
Room Width * .276 (RW x .276)
The distance from the center of the woofer face to the wall behind the speaker is:
Room Width * .447 (RW x .447)
This is all you need to know to place speakers in a symmetrical, rectangular room!