Room mode calculator

Enter your room's length, width and height to list its theoretical room modes: the frequencies at which a rectangular room resonates. The calculator uses the standard rigid-wall formula with sound travelling at 343 m/s, sorts every axial, tangential and oblique mode up to the frequency you choose, and flags axial modes that pile up at the same frequency.

How the calculator works

A room mode is a standing-wave pattern that fits a whole number of half-wavelengths between the room's surfaces. For an ideal rectangular room, each mode is described by three whole numbers — how many half-wavelengths fit along the length (nx), the width (ny) and the height (nz) — and its frequency is:

f = (c / 2) · √( (nx / L)² + (ny / W)² + (nz / H)² )

Here c is the speed of sound, 343 m/s, and L, W and H are the room dimensions in metres (feet are converted at 0.3048 m per foot). The calculator tries every combination of indices that can stay below your highest frequency, skips (0, 0, 0), and sorts the results.

• Axial modes have one non-zero index: sound bouncing between one pair of opposite surfaces. They are usually the strongest.
• Tangential modes have two: sound travelling around four surfaces, parallel to the third pair.
• Oblique modes have three: sound involving all six surfaces. They are usually the weakest individually, but they become the most numerous as frequency rises.

Worked example

In a room 5.0 m long, the first length mode is f = 343 / (2 × 5.0) = 34.3 Hz, and the next ones fall at whole-number multiples: 68.6 Hz, 102.9 Hz and so on. In the example room above, the 2.5 m ceiling is exactly half the length, so the first height mode also lands at 68.6 Hz. Two strong modes at one frequency is the kind of coincidence the calculator flags. The same room measured in feet (16.4 × 13.1 × 8.2 ft) gives the same frequencies to within rounding.

What predicted modes cannot tell you

The table is a model of an empty, rigid, perfectly rectangular box. Real rooms differ in ways that move, weaken or blur these frequencies:

• Walls are not rigid. Drywall, doors and windows flex and leak bass, which damps modes and can shift them.
• Rooms are not boxes. Open plans, alcoves, sloped ceilings and adjoining spaces change the patterns completely.
• Furniture and absorption add damping. A heavily damped mode is broader and shallower than the model suggests.
• Positions decide what you hear. A mode only shows up as a peak or a dip if the subwoofer excites it and your seat is in a high- or low-pressure part of its pattern. The table cannot say which.
• Temperature changes the speed of sound by roughly 0.6 m/s per °C, which moves every mode by about 0.2% per °C.

What to do with the results

Read room modes explained for what each mode type means, and standing waves for where in the room each pattern is loud or quiet. When you are ready to move things, the subwoofer placement guide walks through measuring candidate positions across every seat.