Calculating the three room modes or eigenmodes
(eigenfrequencies) of rectangular rooms

axial                          tangential                          oblique

The axial, tangential, and oblique room modes of rectangular homogeneous rooms are computed. Axial room modes hit on two facing surfaces. Tangential room modes hit on four surfaces and oblique room modes include six surfaces crosswise. Thus one can find the optimal room dimensions for home cinemas, control rooms, sound studios, and exercise rooms. The distribution of the modal frequencies should be as homogeneous as possible.

Notice: Only low frequencies up to 300 cycles per second are to be regarded. Higher modal frequencies lose their meaning, because the interfering effect is  covered by other room acoustic effects.

Theory is good, but it shows up: The empty room can be computed marvelously, but afterwards the brought in mixer, the couch, the cabinets, the racks, and the shelves for the effect devices destroy the nice computations. Such is practice.

Eric Desart, a Belgique acoustican, tells us, that this calculator shows not all eigenfrequencies. Therefore this calculator is useless for scientific calculations. If you look for another program you can try the
Room Modes Calculator by Bob Golds.

The three graphics above: Courtesy of Brüel & Kjær - Technical Review.

To calculate the frequencies of the axial, oblique und tangential modes, use the following formula:


f = Frequency of the mode in Hz
c = Speed of sound 343 m/s at 20 °C (68 °F)
n_x = Order of the mode of the room length
n_y = Order of the mode of the room width
n_z = Order of the mode of the room height
L, B, H = Length, width, and height of the room in meters

The number of modes per frequency width Δ f and even more per frequency interval of Δ f / f increases with rising frequency. Problems with inhomogeneities through in the spectrum clearly separated natural oscillations arise thus particularly in small rooms and at low frequencies. Eigenoscillations arise not only in rectangular rooms, but also in skew rooms. They can be determined there however no longer as simply as here computed, but must be calculated by numeric procedures. An even mode distribution over the frequencies can be reached only by favorable room proportions, especially the eigenfrequencies of different room dimensions should not fall together. Favorable distributions result for proportions (standardized H = 1 on the height) like: (H/B/L).

There is no room correction by setting EQ.

The notion of using EQ to fix bad room response is mostly misguided. In some cases EQ can help only "a little bit" to tame modal peaks at the very lowest frequencies. But most low frequency response errors are highly position dependent, and include nulls as deep as 30 dB. So any EQ correction will help only one very specific place in the room, and will by definition make other places worse. Even a foot away the response can be very different. And EQ does nothing for other acoustic problems like first reflections, flutter echo, modal ringing, and so forth.

You are doing only loudspeaker frequency response correction.

EQ systems are not normally used to create a perfect inversion of the room's response because a perfect correction would only be valid at the location where it was measured. A few centimeters away the arrival times from various reflections will differ and the inversion will be imperfect. The imperfectly corrected signal may end up sounding worse than the uncorrected signal because the acausal filters used in digital room correction may cause pre-echo.