Room Mode Calculator
Calculate the axial, tangential and oblique modes of a rectangular room, see where each is loud or null, and how your subwoofer placement drives them.
5.5 by 7.5 by 2.8 m room: the lowest modes are 22.9 Hz along the length, 31.2 Hz across the width and 61.3 Hz floor to ceiling. There are 15 modes below 80 Hz: 6 axial, 8 tangential and 1 oblique.
One seat in a rectangular room with floor subs. Sub models, gain, delay, polarity, more seats and other room shapes are in Cinema Designer. Damping is an assumption, not measured room decay.
Light: the mode is loud there. Dark: a null.
Room modes
| Frequency | Mode | Kind | At your seat | From the subs | Reaches your seat |
|---|---|---|---|---|---|
| Length 10,1,0 | axial | 0.06 weak | 0.99 strong | weak 0.06 | |
| Width 11,0,0 | axial | 0.00 weak | 0.99 strong | weak 0.00 | |
| Width 1, length 11,1,0 | tangential | 0.00 weak | 0.98 strong | weak 0.00 | |
| Length 20,2,0 | axial | 0.99 strong | 0.98 strong | strong 0.97 | |
| Width 1, length 21,2,0 | tangential | 0.00 weak | 0.97 strong | weak 0.00 | |
| Height 10,0,1 | axial | 0.33 partial | 1.00 strong | partial 0.33 | |
| Width 22,0,0 | axial | 1.00 strong | 0.96 strong | strong 0.96 | |
| Length 1, height 10,1,1 | tangential | 0.02 weak | 0.99 strong | weak 0.02 | |
| Width 2, length 12,1,0 | tangential | 0.06 weak | 0.95 strong | weak 0.06 | |
| Length 30,3,0 | axial | 0.19 weak | 0.95 strong | weak 0.18 | |
| Width 1, height 11,0,1 | tangential | 0.00 weak | 0.99 strong | weak 0.00 | |
| Width 1, length 1, height 11,1,1 | oblique | 0.00 weak | 0.98 strong | weak 0.00 | |
| Width 1, length 31,3,0 | tangential | 0.00 weak | 0.94 strong | weak 0.00 | |
| Length 2, height 10,2,1 | tangential | 0.33 partial | 0.98 strong | partial 0.32 | |
| Width 2, length 22,2,0 | tangential | 0.99 strong | 0.94 strong | strong 0.93 | |
| Width 1, length 2, height 11,2,1 | oblique | 0.00 weak | 0.97 strong | weak 0.00 | |
| Width 2, height 12,0,1 | tangential | 0.33 partial | 0.96 strong | partial 0.32 | |
| Width 2, length 1, height 12,1,1 | oblique | 0.02 weak | 0.95 strong | weak 0.02 | |
| Length 40,4,0 | axial | 0.97 strong | 0.91 strong | strong 0.88 | |
| Length 3, height 10,3,1 | tangential | 0.06 weak | 0.95 strong | weak 0.06 | |
| Width 2, length 32,3,0 | tangential | 0.19 weak | 0.91 strong | weak 0.17 | |
| Width 33,0,0 | axial | 0.00 weak | 0.91 strong | weak 0.00 | |
| Width 3, length 13,1,0 | tangential | 0.00 weak | 0.90 strong | weak 0.00 | |
| Width 1, length 41,4,0 | tangential | 0.00 weak | 0.90 strong | weak 0.00 | |
| Width 1, length 3, height 11,3,1 | oblique | 0.00 weak | 0.94 strong | weak 0.00 | |
| Width 2, length 2, height 12,2,1 | oblique | 0.33 partial | 0.94 strong | partial 0.31 | |
| Width 3, length 23,2,0 | tangential | 0.00 weak | 0.89 strong | weak 0.00 | |
| Length 4, height 10,4,1 | tangential | 0.32 partial | 0.91 strong | partial 0.29 | |
| Width 2, length 42,4,0 | tangential | 0.97 strong | 0.88 strong | strong 0.85 | |
| Width 2, length 3, height 12,3,1 | oblique | 0.06 weak | 0.91 strong | weak 0.06 | |
| Width 3, height 13,0,1 | tangential | 0.00 weak | 0.91 strong | weak 0.00 | |
| Width 3, length 1, height 13,1,1 | oblique | 0.00 weak | 0.90 strong | weak 0.00 | |
| Length 50,5,0 | axial | 0.31 partial | 0.87 strong | partial 0.27 | |
| Width 1, length 4, height 11,4,1 | oblique | 0.00 weak | 0.90 strong | weak 0.00 | |
| Width 3, length 33,3,0 | tangential | 0.00 weak | 0.87 strong | weak 0.00 | |
| Width 1, length 51,5,0 | tangential | 0.00 weak | 0.86 strong | weak 0.00 |
Showing 36 of 144 modes, 20 to 120 Hz.
Response at your seat
Calculating for your numbers…
Rigid rectangular room, uniform damping assumed, ideal subs, relative level, not calibrated SPL. Ticks along the top are the room's axial modes: W width, L length, H height.
Arrangements for one sub
Moving a sub changes which modes it drives: a mode cannot reach your seat from a sub sitting in its null. The layouts are not ranked; keep a curve and compare.
What room modes are
This room mode calculator takes the width, length and height of a rectangular room and lists every mode from 20 to 200 Hz, with the axial, tangential and oblique kind marked. A mode is a standing wave. At its frequency the sound between the walls lines up with itself, so the pressure is loud at some points in the room and almost silent at others. Those loud and silent places are why bass sounds different from seat to seat in a home theater or home cinema.
Each mode is a set of three whole numbers, one per axis. The frequency is 343 metres per second, the speed of sound the engine uses, divided by 2, times the square root of the sum of each number over its wall-to-wall distance, squared. A one on its own is an axial mode between one pair of surfaces: 1 along the length is the lowest note the room’s length supports. Two non-zero numbers make a tangential mode and three an oblique mode.
Reading the table
Each row is one mode with its frequency, which walls it involves, and two couplings between 0 and 1. At your seat says how loud the mode is where you sit: 1 is the loudest point of the mode and 0 a null. From the subs says how strongly your subwoofers excite it, taking each sub at its own position with equal drive. Reaches your seat is the product of the two, as strong, partial or weak, with the words “cancelled by the subs” when the subs sit in a null of a mode your seat would otherwise hear.
Press a frequency to map that mode on the plan: light is loud, dark is a null, at ear height. In the default room the first length mode is almost silent at the centre seat (0.06) while the second is at nearly full strength (0.99), which is why moving the seat changes the bass so much.
Room ratios and why the low modes matter most
Below roughly 80 Hz the modes are few, each is heard on its own and each can lift or hollow out one note. Above that the modes crowd together and blend into a smoother response. The room’s shape sets where the first few fall: a long room puts a low length mode near 20 Hz, and a room where two dimensions match stacks two modes on one frequency. Choose dimensions that are not simple multiples of each other if you have the choice, but expect to manage the modes whatever the ratio.
What you can do
The order that works is seat, subwoofers, then treatment. Move the seat off a null, or the subs to where they drive the modes that matter: two subs at the front quarter-points cancel the odd width modes together, and four subs cancel more. Then use bass traps for the ringing and equalisation for what remains. This calculator shows the first two; a REW sweep shows whether the room agrees.
What this calculator assumes
The room is a closed rectangle with rigid walls, so the mode frequencies are those of an ideal box. Real walls give a little and shift the modes. The subs are ideal point sources on the floor at equal drive, one seat is modelled, and the response curve uses an assumed damping rate rather than measured room decay. It does not model sub models, gain, delay or polarity, EQ, or other room shapes.
Subwoofer placement and the designer
The same inputs drive the subwoofer placement calculator, which adds the predicted response at your seat and the one to four-sub layouts to try. Continue in the Cinema Designer to add sub models, gain, delay and polarity, every seat and RP22 bass headroom, with this room and these subs already in place.