Room Modes Calculator

Sound in a small room does not spread out evenly. At certain low frequencies the waves bounce between the walls, floor and ceiling and line up with themselves, producing standing waves, called room modes. The bass at these frequencies is much louder in some places and much quieter in others. Everyone who mixes in a bedroom or sets up a home cinema has met them. This calculator lists them for a rectangular room, so you can see where the problems are likely to be.

The formula

For a rectangular room of length L, width W and height H, the mode frequencies are f = (c ÷ 2) × √((p ÷ L)² + (q ÷ W)² + (r ÷ H)²), where c is the speed of sound and p, q and r are whole numbers, 0, 1, 2 and so on, not all zero. Axial modes have one non-zero number and involve two surfaces; they are the strongest. Tangential modes have two non-zero numbers and involve four surfaces. Oblique modes involve all six and are weaker still. The speed of sound depends on temperature: about 343.4 m/s at 20 °C.

A worked example

Press Sample: a room 5 m long, 4 m wide and 2.6 m high, at 20 °C, with an RT60 of 0.4 s. The volume is 52.0 m³ and the speed of sound 343.4 m/s. The lowest mode is 34.3 Hz, the first length mode (1,0,0), then 42.9 Hz for the width (0,1,0) and 55.0 Hz as the first tangential mode. The height gives an axial mode at 66.0 Hz, and the second length mode, (2,0,0), is at 68.7 Hz. With the limit at 200 Hz there are 68 modes, in 6 groups where modes lie within 5 Hz of each other, starting at 66 to 69 Hz. The largest gap between modes is 12.0 Hz, between 43 and 55 Hz. The Schroeder frequency is 175 Hz.

Reading the display

The lines on the frequency axis show each mode, tall for axial, middle for tangential and short for oblique, so groups and gaps are easy to see. The warning lists clusters, where bass will boom because several modes reinforce the same band. A large gap means a band where the room has no resonance and bass notes can be weak. The table gives each mode’s frequency, type and its order numbers for length, width and height.

The Schroeder frequency

Above the Schroeder frequency, roughly 2,000 times the square root of RT60 divided by volume, modes overlap so densely that the room behaves smoothly. Below it, individual modes dominate. That is the region where treatment such as bass traps matters and where the listening position makes the most difference. The figure here comes from the RT60 you enter, which is optional and which you can estimate from the room’s furnishings.

Using the results

Avoid dimensions that are equal or simple multiples of each other, such as a cube, which stacks modes on the same frequencies. If you have a choice, a room with uneven ratios spreads the modes more evenly. Avoid putting the listening seat exactly in the middle of a dimension or against a wall, where several strong modes peak or vanish together, and use the Speaker Placement Calculator as a start. Measure with a microphone if you can.

Edge cases

The model assumes rigid, parallel walls and an empty room, so furniture, doors, windows and non-parallel walls shift and damp the modes. Open-plan rooms and rooms with large openings do not have clean modes. The warm-air speed of sound raises frequencies a little: at 30 °C the lowest mode of the sample room moves up by about 0.6 Hz.

Limits

This calculates frequencies, not levels or positions. It does not model non-rectangular rooms or absorption. The list shows at most 60 modes, even if more fall below the limit. Everything is computed on your device.

Related tools

• Speaker Placement Calculator positions monitors in the room.
• Tone Generator plays the mode frequencies so you can hear the room.
• Sound Level Meter shows how loud each frequency is at your seat.
• Note Frequency Chart tells you which notes the modes fall on.