Room mode calculator

How it is worked out

A room mode is a frequency at which sound bouncing between the walls reinforces itself. For a rectangular room with rigid walls each mode is f = (343 ÷ 2) × √((n ÷ length)² + (m ÷ width)² + (k ÷ height)²), where n, m and k are whole numbers and 343 m/s is the speed of sound in air at about 20 °C (it rises about 0.6 m/s per degree). Axial modes run between one pair of walls (one number is not zero), tangential modes between four surfaces (two numbers) and oblique modes between all six (three numbers). Axial modes are usually the strongest, which is why the table lists them first. The design studio and the REW Analyzer use the same formula.

At your seat

A mode is loudest at the walls and, for the first axial mode along a dimension, silent halfway between them; the second has two silent points, at a quarter and three quarters, and so on. Its level at your seat is 20 × log₁₀ |cos(n × π × seat ÷ length)| against its loudest point. The seat column marks a mode within 1 dB of its peak or more than 10 dB below it (our rule of thumb). On the centre line between the side walls every odd width mode cancels, which is one reason seats on the centre line hear less of them.

The checks

• Proportions: when two dimensions are equal or simple multiples (within 5% of 1×, 2× or 3×, the design studio's rule of thumb), their modes fall on the same notes and those notes ring.
• Bonello criterion (O. J. Bonello, Journal of the Audio Engineering Society, 1981): counted in third-octave bands, the number of modes should not fall from one band to the next. It is a guide to proportions, not a guarantee of good bass: a 2017 study (Calderón, De Palma and Masson, ICSV24) found it misleading for choosing room dimensions, and where the seat and subwoofer go matters more.
• Schroeder frequency, 2000 × √(RT60 ÷ volume): below it individual modes shape the bass; above it they overlap and the room behaves more evenly.

What the numbers cannot tell you

Real walls flex, doors and openings leak, and furniture absorbs, so measured modes are usually shallower and a little lower than the rigid-room figures. Where the subwoofer sits also decides which modes it excites. Measure with Room EQ Wizard (our guide: how to measure your room) and open the file in the REW Analyzer: its Room tab matches the measured peaks and dips to these modes. The usual order of fixes: move the seat off the nulls, place the subwoofer (or two) where they excite the modes evenly, add bass traps in the corners, then cut the remaining peaks with EQ.