Room Modes Calculator (axial)

Understanding the room modes calculator — concept and principle

In a small room, low-frequency sound bounces between opposite walls and forms standing waves called room modes. Some notes then boom while others vanish, depending on the seat. This calculator lists the first four axial modes along the length, width and height of a rectangular room and estimates the Schroeder frequency, below which individual modes dominate the sound.

Each pair of walls rings at its own ladder of frequencies; the 5 m length starts at 34.3 Hz.

How it is calculated

Axial mode frequencies: fₙ = n × c ÷ (2L), for n = 1, 2, 3, 4
c = 343 m/s, the speed of sound at about 20 °C
L is the room dimension in metres (length, width or height)
Schroeder frequency: f_s = 2000 × √(RT60 ÷ V), using an assumed reverberation time RT60 = 0.4 s and room volume V = length × width × height in m³

The principle

A standing wave forms when a whole number of half-wavelengths fits exactly between two parallel surfaces, because the reflected wave then reinforces the incoming one. The lowest mode has half a wavelength across the room, so λ = 2L and f = c/2L; higher modes are integer multiples. Axial modes, involving only two surfaces, are usually the strongest; tangential (four surfaces) and oblique (six surfaces) modes exist too but are weaker and are not listed here. At higher frequencies modes crowd together and overlap; Manfred Schroeder's formula marks that crossover.

Worked example

Inputs: length 5 m, width 4 m, height 2.6 m.
Length: 343 ÷ (2 × 5) = 34.3 Hz, so 34.3, 68.6, 102.9, 137.2 Hz.
Width: 343 ÷ 8 = 42.875 Hz, so 42.88, 85.75, 128.6, 171.5 Hz.
Height: 343 ÷ 5.2 = 65.96 Hz, so 65.96, 131.9, 197.9, 263.8 Hz.
Volume = 5 × 4 × 2.6 = 52 m³; f_s = 2000 × √(0.4 ÷ 52) = 175.4 Hz (175.4116039).

How to read the result

Look for modes that land close together or coincide, such as 65.96 and 68.6 Hz here, or 128.6, 131.9 and 137.2 Hz: clusters produce strong peaks, while large gaps leave holes in the bass. A cube is the worst case. Below the Schroeder frequency, treatment with bass traps, seat and speaker placement, and equalisation matter most; above it, ordinary absorption and diffusion control the sound.

Common mistakes

Measuring outside instead of inside dimensions.
Expecting the formula to apply to irregular, open-plan or L-shaped rooms.
Treating the Schroeder value as exact; it changes with the real reverberation time.

Keep in mind: The calculation assumes a rectangular room with rigid walls. Soft walls, openings and furniture shift and damp modes, so verify with measurements before investing in acoustic treatment.

Frequently asked questions

Where are the modes strongest?

Pressure peaks at the walls for every axial mode; the first mode has a null at the centre of the room, which is why sitting exactly in the middle often lacks bass.

Are there good room ratios?

Several recommended ratios have been published to spread modes evenly; the general idea is to avoid dimensions that are equal or multiples of each other.

Does a larger room have fewer bass problems?

Usually. Larger dimensions lower the first modes and pack them more densely, which evens out the bass.

Sources: F. A. Everest and K. C. Pohlmann, Master Handbook of Acoustics, McGraw-Hill · M. R. Schroeder (1996), "The 'Schroeder frequency' revisited", Journal of the Acoustical Society of America 99(5), 3240–3241

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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