Room mode calculator

Enter the length, width and height of a room in metres or feet. The calculator lists every resonant mode up to the frequency you set, so you can spot clusters and gaps in the bass before treating a studio or listening room.

Unit

Length

Width

Height

Up to frequency, Hz20 to 500 Hz; room modes matter most in the bass

Lowest mode34.3 Hz

Axial modes, Hz (p-q-r): 34.3 (1-0-0), 42.9 (0-1-0), 63.5 (0-0-1), 68.6 (2-0-0), 85.8 (0-2-0), 102.9 (3-0-0), 127 (0-0-2), 128.6 (0-3-0), 137.2 (4-0-0), 171.5 (0-4-0), 171.5 (5-0-0), 190.6 (0-0-3)
Tangential modes, Hz: 54.9 (1-1-0), 72.2 (1-0-1), 76.6 (0-1-1), 80.9 (2-1-0), 92.4 (1-2-0), 93.5 (2-0-1), 106.7 (0-2-1), 109.8 (2-2-0), 111.5 (3-1-0), 120.9 (3-0-1), 131.6 (1-0-2), 133.1 (1-3-0), 133.9 (3-2-0), 134.1 (0-1-2), 143.5 (0-3-1), 143.7 (4-1-0), 144.4 (2-0-2), 145.8 (2-3-0), 151.2 (4-0-1), 153.3 (0-2-2), 161.8 (4-2-0), 163.5 (3-0-2), 164.7 (3-3-0), 174.9 (1-4-0), 176.8 (5-1-0), 180.8 (0-3-2), 182.9 (0-4-1), 182.9 (5-0-1), 184.7 (2-4-0), 187 (4-0-2), 188.1 (4-3-0), 191.7 (5-2-0), 193.6 (1-0-3), 195.3 (0-1-3)
Oblique modes, Hz: 84 (1-1-1), 102.9 (2-1-1), 112.1 (1-2-1), 126.9 (2-2-1), 128.3 (3-1-1), 138.4 (1-1-2), 147.5 (1-3-1), 148.2 (3-2-1), 150.6 (2-1-2), 157.1 (1-2-2), 157.2 (4-1-1), 159 (2-3-1), 167.9 (2-2-2), 169 (3-1-2), 173.8 (4-2-1), 176.5 (3-3-1), 184 (1-3-2), 184.6 (3-2-2), 186.1 (1-4-1), 187.8 (5-1-1), 191.8 (4-1-2), 193.4 (2-3-2), 195.3 (2-4-1), 198.3 (1-1-3), 198.5 (4-3-1)
Axial + tangential + oblique: 12 + 34 + 25 = 71
Room ratio (smallest = 1): 1 : 1.48 : 1.85

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How to use it

Choose metres or feet and enter the inside length, width and height of the room.
Set how high to list modes; 200 to 300 Hz covers the range where single modes are heard.
Read the axial modes first: they are the loudest. Each value is followed by its indices p-q-r.
Look for modes that land on the same frequency and for wide gaps between them.

How it works

Rayleigh’s equation for a rectangular room:

f = c ÷ 2 × √((p ÷ L)² + (q ÷ W)² + (r ÷ H)²)

c = 343 m/s (air at about 20 °C); feet are turned into metres first. Every combination of whole numbers p, q, r that gives a frequency up to your limit is listed. One non-zero index makes an axial mode, two a tangential one and three an oblique one. Each list shows up to 40 values.

Worked example

A room 5 × 4 × 2.7 m, modes up to 200 Hz:

axial along the length: 343 ÷ (2 × 5) = 34.3 Hz (1-0-0), then 68.6, 102.9 Hz …;
along the width: 343 ÷ 8 = 42.9 Hz (0-1-0); floor to ceiling: 343 ÷ 5.4 = 63.5 Hz (0-0-1);
the first tangential mode (1-1-0): 171.5 × √(1/25 + 1/16) = 54.9 Hz; the first oblique (1-1-1) is 84 Hz;
12 + 34 + 25 = 71 modes in all, and the ratio is 1 : 1.48 : 1.85.

The 4th width mode and the 5th length mode both fall on 171.5 Hz, because 4 × 5 = 5 × 4: a coincidence worth treating.

Tips

Bass traps work best in corners, where every mode has a pressure maximum.
Moving the listening position away from the middle of the room avoids sitting in the null of the first axial modes.
Room modes and reverberation are related: check the decay time with the RT60 reverberation calculator.

Frequently asked questions

What are axial, tangential and oblique modes?

Axial modes bounce between one pair of opposite surfaces (front and back walls, side walls, or floor and ceiling) and are the strongest. Tangential modes involve two pairs, four surfaces, and oblique modes all six. Each step down involves more reflections and usually less energy.

How is a room mode frequency calculated?

For a rectangular room, f = c ÷ 2 × √((p ÷ L)² + (q ÷ W)² + (r ÷ H)²), where c = 343 m/s, L, W and H are the dimensions and p, q, r are whole numbers. The first axial mode along a 5 m length is 343 ÷ 10 = 34.3 Hz.

What makes a good room ratio?

Dimensions that are not multiples of one another spread the modes evenly. A cube or a room with equal length and width stacks modes at the same frequencies, which makes some bass notes boom and others vanish. Look in the lists for modes that fall on the same or nearly the same frequency.

Does this work for irregular rooms?

The formula is for rectangular rooms with hard walls. Sloped ceilings, L-shaped rooms and open doorways shift the modes, so treat the results as a guide and confirm with a measurement.

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