The equilateral triangle — where your speakers actually need to go
The equilateral stereo triangle — equal distance between each speaker and the listener — is the foundation of accurate imaging. In a 14-foot room with an 8-foot listening distance, the speakers want to sit 8 feet apart, 30 degrees of toe-in, and at least 2 feet off the front wall if they're rear-ported.
This calculator gives you the speaker coordinates, toe-in angle, sweet-spot width, and a live diagram from just your room width and listening distance. It also warns when rear-ported speakers land too close to the wall and computes the SBIR (Speaker-Boundary Interference Response) null frequency so you know what bass cancellation to expect.
Use this when laying out a stereo or 2.1 system, especially in a multi-purpose room where the speakers don't get free rein over placement.
How the Stereo Triangle Geometry Works
The Formula
For an equilateral triangle, speaker-to-speaker distance equals speaker-to-listener distance. Speakers sit at (room_width / 2) +/- (distance / 2) on the X axis and at a fixed Y from the listener. Toe-in angle (each speaker rotated to point at the listener) is atan((distance / 2) / listening_distance) from the speaker's straight-ahead axis — typically about 30 degrees in a true equilateral. Sweet-spot width (zone where stereo imaging stays stable) is approximated as 0.35 x listening_distance based on Toole's measurements of perceived image shift at off-axis positions.
Worked Example
Room width: 14 feet. Listening distance: 8 feet. Speaker spacing: 8 feet. Speaker X: 14/2 +/- 4 = 3 ft and 11 ft from the left wall. Side-wall clearance: 3 feet (above the 2-foot SBIR threshold). Toe-in: atan(4/8) = 26.6 degrees. Sweet spot: 0.35 x 8 = 2.8 feet wide — one-and-a-half seats centered. If the speaker is rear-ported and only 18 inches from the front wall, SBIR null frequency: 1130 ft/s / (4 x 1.5 ft) = 188 Hz — a midbass suckout the calculator flags.
Standards
The equilateral triangle convention is documented in Floyd Toole's "Sound Reproduction" and matches the AES recommendations for stereo monitoring. The 30-degree toe-in starting point comes from the ITU-R BS.1116 reference listening configuration. Sweet-spot width using 0.35x distance is an empirical fit to perceived image-shift data; the actual width depends on speaker directivity (wide-dispersion speakers give wider sweet spots). SBIR null math: cancellation occurs at the quarter-wavelength of the speaker-to-boundary distance.
Limitations
The calculator assumes the listener is centered between the speakers; off-center positions need a different layout (e.g., near-field with one wall). Room width is the only room dimension considered — front-back wall distance and ceiling height shape low-frequency response separately (see the room-modes calculator). Toe-in is a starting point: adjust by ear if the center image is vague (toe in more) or the soundstage feels narrow (toe out). Rear-ported warning fires below 2 feet of clearance — in practice 3 feet is the safer cutoff if you can afford the room depth.
