Room mode calculator

How to use it

Measure the inside dimensions of the room, wall to wall and floor to ceiling, and enter them in metres or feet. The main table lists axial modes, the strongest ones, with the nearest musical note so you can check them against notes that sound boomy or weak. The summary gives the Schroeder frequency, above which individual modes stop mattering, and whether the room's proportions fall inside the range recommended for listening rooms in ITU-R BS.1116.

The method

The calculator uses the standard equation for the modes of a rectangular room with rigid walls:

f = (c / 2) × √((nL / L)² + (nW / W)² + (nH / H)²)

where c is the speed of sound, 343 m/s at 20 °C, and each n is a whole number. A mode with one non-zero n is axial, with two tangential, with three oblique. For axial modes the equation reduces to f = n × c / (2 × dimension). The Schroeder frequency is estimated as 2000 × √(RT60 / V). Proportions are also compared with the BS.1116 criterion, 1.1 w/h ≤ l/h ≤ 4.5 w/h − 4 with l/h < 3 and w/h < 3.

Worked example. The default room is 5 × 4 × 2.5 m. Its length gives axial modes at 34.3, 68.6, 102.9 and 137.2 Hz; its width at 42.9, 85.8 and 128.6 Hz; its height at 68.6 and 137.2 Hz. Because the length is exactly twice the height, their modes land on top of each other at 68.6 and 137.2 Hz, a doubled resonance near C#2 that will tend to boom. With RT60 = 0.4 s and a volume of 50 m³, the Schroeder frequency is 2000 × √(0.4 / 50) ≈ 179 Hz.

Room ratios people aim for

Several published ratios spread the axial modes evenly. None is magic, and all assume rigid walls, but they make a useful comparison with your room's ratio of 1.00 : 1.60 : 2.00:

• Sepmeyer A: 1 : 1.14 : 1.39
• Sepmeyer B: 1 : 1.28 : 1.54
• Sepmeyer C: 1 : 1.6 : 2.33
• Louden: 1 : 1.4 : 1.9
• Golden ratio: 1 : 1.618 : 2.618

The worst proportions are those where one dimension is a whole multiple of another, or two are equal: a cube is the extreme case, with all three sets of modes stacked on the same frequencies.

Where it stops being reliable

The equation describes an empty rectangular box with perfectly rigid, reflective surfaces. Real rooms differ in ways that move and soften the modes: plasterboard walls flex and absorb bass, windows and doors leak it, furniture and alcoves break up the geometry, and sloped or vaulted ceilings are not rectangular at all. Expect real modes a few hertz away from the predictions and much less extreme than the arithmetic suggests. The flags and the BS.1116 check are screening aids, not a verdict on whether a room will sound good.

To hear the predicted frequencies in your own room, play them one at a time on the tone generator at a moderate level and walk around; the difference between a peak and a null is often obvious. For firm numbers, measure with a calibrated microphone.