Room Mode & Standing Wave Calculator
Enter the inside dimensions of a rectangular room to list its calculated resonances through a chosen frequency. The results also show close mode clusters, idealized axial pressure locations, and a Schroeder-frequency estimate.
Schroeder transition frequency (Hz)198.09
- Speed of sound
- 343.21 m/s
- Room dimensions and volume
- 1,440 ft³ (40.78 m³)
- Height : width : length ratio
- 1 : 1.5 : 1.88
- Length axial modes
- 1: 37.53 Hz; 2: 75.07 Hz; 3: 112.6 Hz; 4: 150.14 Hz; 5: 187.67 Hz; 6: 225.21 Hz; 7: 262.74 Hz
- Width axial modes
- 1: 46.92 Hz; 2: 93.84 Hz; 3: 140.75 Hz; 4: 187.67 Hz; 5: 234.59 Hz; 6: 281.51 Hz
- Height axial modes
- 1: 70.38 Hz; 2: 140.75 Hz; 3: 211.13 Hz; 4: 281.51 Hz
- Near-coincident resonance clusters
- C1: 92.54–93.84 Hz (2 modes); C2: 101.06–102.9 Hz (2 modes); C3: 112.6–113.09 Hz (2 modes); C4: 120.17–121.99 Hz (2 modes); C5: 139.26–140.83 Hz (4 modes); C6: 145.67–146.58 Hz (3 modes); C7: 148.37–150.14 Hz (2 modes); C8: 157.3–157.37 Hz (2 modes); C9: 159.52–159.52 Hz (2 modes); C10: 161.78–162.6 Hz (2 modes); C11: 165.81–166.28 Hz (2 modes); C12: 172.32–173.28 Hz (2 modes); C13: 180.25–180.25 Hz (2 modes); C14: 185.07–186.26 Hz (2 modes); C15: 187.67–187.67 Hz (2 modes); C16: 190.52–191.39 Hz (2 modes); C17: 193.45–193.5 Hz (2 modes); C18: 199.06–200.43 Hz (3 modes); C19: 202.13–203.92 Hz (4 modes); C20: 205.8–205.85 Hz (3 modes); C21: 209.82–211.13 Hz (3 modes); C22: 212.74–214.44 Hz (3 modes); C23: 216.28–217.5 Hz (2 modes); C24: 218.86–219.51 Hz (2 modes); C25: 224.08–225.21 Hz (2 modes); C26: 228.7–230.04 Hz (4 modes); C27: 234.07–235.95 Hz (6 modes); C28: 237.57–239.28 Hz (4 modes); C29: 240.34–240.57 Hz (2 modes); C30: 242.93–244.92 Hz (5 modes); C31: 246.31–247.78 Hz (3 modes); C32: 249.33–250.43 Hz (2 modes); C33: 252.66–253.92 Hz (3 modes); C34: 256.17–257.02 Hz (3 modes); C35: 259.07–260.22 Hz (3 modes); C36: 262.74–264.62 Hz (3 modes); C37: 265.41–266.9 Hz (4 modes); C38: 269.56–269.69 Hz (2 modes); C39: 272–273.58 Hz (3 modes); C40: 274.58–276.14 Hz (5 modes); C41: 277.61–278.99 Hz (4 modes); C42: 281.51–282.48 Hz (5 modes); C43: 283.69–285.39 Hz (5 modes); C44: 286.35–287.85 Hz (4 modes); C45: 290.17–291.35 Hz (3 modes); C46: 292.29–293.15 Hz (3 modes); C47: 294.84–296.74 Hz (4 modes); C48: 297.66–299.1 Hz (4 modes)
- Length nodes and antinodes (ft from front wall)
- 1: nodes 7.5; antinodes 0, 15 | 2: nodes 3.75, 11.25; antinodes 0, 7.5, 15 | 3: nodes 2.5, 7.5, 12.5; antinodes 0, 5, 10, 15 | 4: nodes 1.87, 5.63, 9.37, 13.12; antinodes 0, 3.75, 7.5, 11.25, 15 | 5: nodes 1.5, 4.5, 7.5, 10.5, 13.5; antinodes 0, 3, 6, 9, 12, 15 | 6: nodes 1.25, 3.75, 6.25, 8.75, 11.25, 13.75; antinodes 0, 2.5, 5, 7.5, 10, 12.5, 15 | 7: nodes 1.07, 3.21, 5.36, 7.5, 9.64, 11.79, 13.93; antinodes 0, 2.14, 4.29, 6.43, 8.57, 10.71, 12.86, 15
- Width nodes and antinodes (ft from side wall)
- 1: nodes 6; antinodes 0, 12 | 2: nodes 3, 9; antinodes 0, 6, 12 | 3: nodes 2, 6, 10; antinodes 0, 4, 8, 12 | 4: nodes 1.5, 4.5, 7.5, 10.5; antinodes 0, 3, 6, 9, 12 | 5: nodes 1.2, 3.6, 6, 8.4, 10.8; antinodes 0, 2.4, 4.8, 7.2, 9.6, 12 | 6: nodes 1, 3, 5, 7, 9, 11; antinodes 0, 2, 4, 6, 8, 10, 12
- Height nodes and antinodes (ft from floor)
- 1: nodes 4; antinodes 0, 8 | 2: nodes 2, 6; antinodes 0, 4, 8 | 3: nodes 1.33, 4, 6.67; antinodes 0, 2.67, 5.33, 8 | 4: nodes 1, 3, 5, 7; antinodes 0, 2, 4, 6, 8
Room modes through 300 Hz
| Frequency (Hz) | p-q-r indices | Classification | Resonance cluster |
|---|---|---|---|
| 37.53 | (1,0,0) | Axial | — |
| 46.92 | (0,1,0) | Axial | — |
| 60.08 | (1,1,0) | Tangential | — |
| 70.38 | (0,0,1) | Axial | — |
| 75.07 | (2,0,0) | Axial | — |
| 79.76 | (1,0,1) | Tangential | — |
| 84.58 | (0,1,1) | Tangential | — |
| 88.52 | (2,1,0) | Tangential | — |
| 92.54 | (1,1,1) | Oblique | C1 |
| 93.84 | (0,2,0) | Axial | C1 |
| 101.06 | (1,2,0) | Tangential | C2 |
| 102.9 | (2,0,1) | Tangential | C2 |
| 112.6 | (3,0,0) | Axial | C3 |
| 113.09 | (2,1,1) | Oblique | C3 |
| 117.3 | (0,2,1) | Tangential | — |
| 120.17 | (2,2,0) | Tangential | C4 |
| 121.99 | (3,1,0) | Tangential | C4 |
| 123.15 | (1,2,1) | Oblique | — |
| 132.79 | (3,0,1) | Tangential | — |
| 139.26 | (2,2,1) | Oblique | C5 |
| 140.75 | (0,0,2), (0,3,0) | Axial | C5 |
| 140.83 | (3,1,1) | Oblique | C5 |
| 145.67 | (1,0,2), (1,3,0) | Tangential | C6 |
| 146.58 | (3,2,0) | Tangential | C6 |
| 148.37 | (0,1,2) | Tangential | C7 |
| 150.14 | (4,0,0) | Axial | C7 |
| 153.04 | (1,1,2) | Oblique | — |
| 157.3 | (4,1,0) | Tangential | C8 |
| 157.37 | (0,3,1) | Tangential | C8 |
| 159.52 | (2,0,2), (2,3,0) | Tangential | C9 |
| 161.78 | (1,3,1) | Oblique | C10 |
| 162.6 | (3,2,1) | Oblique | C10 |
| 165.81 | (4,0,1) | Tangential | C11 |
| 166.28 | (2,1,2) | Oblique | C11 |
| 169.17 | (0,2,2) | Tangential | — |
| 172.32 | (4,1,1) | Oblique | C12 |
| 173.28 | (1,2,2) | Oblique | C12 |
| 174.36 | (2,3,1) | Oblique | — |
| 177.05 | (4,2,0) | Tangential | — |
| 180.25 | (3,0,2), (3,3,0) | Tangential | C13 |
| 185.07 | (2,2,2) | Oblique | C14 |
| 186.26 | (3,1,2) | Oblique | C14 |
| 187.67 | (0,4,0), (5,0,0) | Axial | C15 |
| 190.52 | (4,2,1) | Oblique | C16 |
| 191.39 | (1,4,0) | Tangential | C16 |
| 193.45 | (5,1,0) | Tangential | C17 |
| 193.5 | (3,3,1) | Oblique | C17 |
| 199.06 | (0,3,2) | Tangential | C18 |
| 200.43 | (0,4,1), (5,0,1) | Tangential | C18 |
| 202.13 | (2,4,0) | Tangential | C19 |
| 202.56 | (1,3,2) | Oblique | C19 |
| 203.22 | (3,2,2) | Oblique | C19 |
| 203.92 | (1,4,1) | Oblique | C19 |
| 205.8 | (4,0,2), (4,3,0) | Tangential | C20 |
| 205.85 | (5,1,1) | Oblique | C20 |
| 209.82 | (5,2,0) | Tangential | C21 |
| 211.08 | (4,1,2) | Oblique | C21 |
| 211.13 | (0,0,3) | Axial | C21 |
| 212.74 | (2,3,2) | Oblique | C22 |
| 214.03 | (2,4,1) | Oblique | C22 |
| 214.44 | (1,0,3) | Tangential | C22 |
| 216.28 | (0,1,3) | Tangential | C23 |
| 217.5 | (4,3,1) | Oblique | C23 |
| 218.86 | (3,4,0) | Tangential | C24 |
| 219.51 | (1,1,3) | Oblique | C24 |
| 221.31 | (5,2,1) | Oblique | — |
| 224.08 | (2,0,3) | Tangential | C25 |
| 225.21 | (6,0,0) | Axial | C25 |
| 226.18 | (4,2,2) | Oblique | — |
| 228.7 | (3,3,2) | Oblique | C26 |
| 228.94 | (2,1,3) | Oblique | C26 |
| 229.9 | (3,4,1) | Oblique | C26 |
| 230.04 | (6,1,0) | Tangential | C26 |
| 231.04 | (0,2,3) | Tangential | — |
| 234.07 | (1,2,3) | Oblique | C27 |
| 234.59 | (0,4,2), (0,5,0), (5,0,2), (5,3,0) | Tangential, Axial | C27 |
| 235.95 | (6,0,1) | Tangential | C27 |
| 237.57 | (1,4,2), (1,5,0) | Oblique, Tangential | C28 |
| 239.24 | (5,1,2) | Oblique | C28 |
| 239.28 | (3,0,3) | Tangential | C28 |
| 240.34 | (4,4,0) | Tangential | C29 |
| 240.57 | (6,1,1) | Oblique | C29 |
| 242.93 | (2,2,3) | Oblique | C30 |
| 243.84 | (3,1,3) | Oblique | C30 |
| 243.97 | (6,2,0) | Tangential | C30 |
| 244.92 | (0,5,1), (5,3,1) | Tangential, Oblique | C30 |
| 246.31 | (2,4,2), (2,5,0) | Oblique, Tangential | C31 |
| 247.78 | (1,5,1) | Oblique | C31 |
| 249.33 | (4,3,2) | Oblique | C32 |
| 250.43 | (4,4,1) | Oblique | C32 |
| 252.66 | (5,2,2) | Oblique | C33 |
| 253.75 | (0,3,3) | Tangential | C33 |
| 253.92 | (6,2,1) | Oblique | C33 |
| 256.17 | (2,5,1) | Oblique | C34 |
| 256.51 | (1,3,3) | Oblique | C34 |
| 257.02 | (3,2,3) | Oblique | C34 |
| 259.07 | (4,0,3) | Tangential | C35 |
| 260.22 | (3,4,2), (3,5,0) | Oblique, Tangential | C35 |
| 262.74 | (7,0,0) | Axial | C36 |
| 263.28 | (4,1,3) | Oblique | C36 |
| 264.62 | (2,3,3) | Oblique | C36 |
| 265.41 | (5,4,0) | Tangential | C37 |
| 265.57 | (6,0,2), (6,3,0) | Tangential | C37 |
| 266.9 | (7,1,0) | Tangential | C37 |
| 269.56 | (3,5,1) | Oblique | C38 |
| 269.69 | (6,1,2) | Oblique | C38 |
| 272 | (7,0,1) | Tangential | C39 |
| 273.58 | (0,5,2), (5,3,2) | Tangential, Oblique | C39 |
| 274.58 | (5,4,1) | Oblique | C40 |
| 274.74 | (6,3,1) | Oblique | C40 |
| 275.54 | (4,2,3) | Oblique | C40 |
| 276.02 | (7,1,1) | Oblique | C40 |
| 276.14 | (1,5,2) | Oblique | C40 |
| 277.61 | (3,3,3) | Oblique | C41 |
| 278.52 | (4,4,2), (4,5,0) | Oblique, Tangential | C41 |
| 278.99 | (7,2,0) | Tangential | C41 |
| 281.51 | (0,0,4), (0,6,0) | Axial | C42 |
| 281.66 | (6,2,2) | Oblique | C42 |
| 282.48 | (0,4,3), (5,0,3) | Tangential | C42 |
| 283.69 | (2,5,2) | Oblique | C43 |
| 284 | (1,0,4), (1,6,0) | Tangential | C43 |
| 284.97 | (1,4,3) | Oblique | C43 |
| 285.39 | (0,1,4) | Tangential | C43 |
| 286.35 | (5,1,3) | Oblique | C44 |
| 287.27 | (4,5,1) | Oblique | C44 |
| 287.73 | (7,2,1) | Oblique | C44 |
| 287.85 | (1,1,4) | Oblique | C44 |
| 290.17 | (0,6,1) | Tangential | C45 |
| 291.35 | (2,0,4), (2,6,0) | Tangential | C45 |
| 292.29 | (2,4,3) | Oblique | C46 |
| 292.59 | (1,6,1) | Oblique | C46 |
| 293.15 | (6,4,0) | Tangential | C46 |
| 294.84 | (4,3,3) | Oblique | C47 |
| 295.1 | (2,1,4) | Oblique | C47 |
| 295.84 | (3,5,2) | Oblique | C47 |
| 296.74 | (0,2,4) | Tangential | C47 |
| 297.66 | (5,2,3) | Oblique | C48 |
| 298.07 | (7,0,2), (7,3,0) | Tangential | C48 |
| 299.1 | (1,2,4) | Oblique | C48 |
| 299.72 | (2,6,1) | Oblique | — |
Assumes a closed rectangular room with rigid, parallel boundaries; strongly angled, L-shaped, open-plan, or irregular rooms do not follow this model closely.
Node and antinode locations are idealized pressure locations for one axial mode at a time, not a speaker or listening-position prescription.
How to use this calculator
- Choose feet or meters, then enter the inside length, width, and average height of the room.
- Enter the air temperature and an estimated or measured RT60 reverberation time.
- Choose the highest frequency worth listing; lower limits keep the table focused on bass and low midrange.
- Set the near-coincidence tolerance, then inspect the mode table and the axial position summaries.
How room modes are calculated
A rectangular room supports standing waves between each pair of parallel boundaries. This calculator converts every room dimension to meters and calculates each nonzero index combination p, q, and r through the selected frequency limit:
f(p,q,r) = (c ÷ 2) × sqrt((p ÷ L)² + (q ÷ W)² + (r ÷ H)²)
L, W, and H are length, width, and height in meters. The speed of sound c changes slightly with temperature:
c = 331.3 × sqrt(1 + T ÷ 273.15)
One nonzero index is an axial mode, two are a tangential mode, and three are an oblique mode. Axial modes usually deserve attention first because they involve only one opposing boundary pair and are often the strongest low-frequency problem. Tangential and oblique modes include more surfaces and usually contribute less strongly, but their frequency crowding still affects the response.
Clusters, locations, and the transition to dense modes
Modes that are exactly equal are combined in one table row while retaining every p-q-r combination. Nearby rows are labelled as a cluster when their full frequency span is within your chosen tolerance. Clusters matter because multiple resonances in the same narrow band can produce an especially uneven peak or decay, although the calculation does not predict its level.
For axial order n along a dimension D, idealized pressure nodes occur at x = (2k + 1)D ÷ (2n) and antinodes at x = kD ÷ n. The reported distances start at the relevant wall, floor, or ceiling boundary. They are useful for avoiding obvious extremes when placing a seat or subwoofer, but they do not replace measurement.
The calculator estimates the Schroeder transition as fs = 2000 × sqrt(RT60 ÷ V), where V is room volume in cubic meters. Above this approximate region, individual modes overlap more densely and a statistical room-acoustics description becomes more useful.
What moves the result and what it leaves out
Changing a room dimension moves every mode involving that axis; low ceilings commonly make height modes particularly important. Equal dimensions and exact integer multiples cause repeated harmonics, which is why the calculator warns about them. A mildly sloped ceiling may be approximated with an average height, but it is no longer a true rectangular model.
The calculation assumes closed, rigid, parallel boundaries. Doors, windows, openings, furniture, wall flexibility, acoustic treatment, loudspeaker placement, and absorption change real frequencies, amplitudes, and decay. It predicts where ideal resonances occur, not the depth of a null, the width of a peak, or whether equalization will help.
Worked example
For a 15 ft by 12 ft by 8 ft room at 20 °C, the calculator first converts the dimensions to 4.572 m by 3.658 m by 2.438 m. The first length, width, and height axial modes are about 37.53 Hz, 46.92 Hz, and 70.38 Hz respectively.
With RT60 set to 0.4 seconds, the room volume is about 40.77 m³ and the Schroeder estimate is about 198 Hz. For the first length mode, pressure antinodes are at 0 and 15 ft from the front wall, while the pressure node is at 7.5 ft. A listening position exactly at that idealized node may be a poor place to judge bass near that mode, but other modes and the loudspeaker position still matter.
Common questions
What are axial, tangential, and oblique room modes?
A mode is axial when it varies along one room dimension, tangential when it involves two, and oblique when it involves all three. Axial modes generally have the most audible effect in small-room bass because fewer boundaries are involved. All three types contribute to the complete modal pattern.
Which room modes matter most for bass reproduction?
Begin with the lowest axial modes and with close clusters, especially below the Schroeder transition estimate. Those are practical places to measure decay, vary subwoofer placement, and test listening positions. The table is a planning guide, not a substitute for a frequency-response and decay measurement.
Why do several modes occur at almost the same frequency?
Dimensions that are equal or simple integer multiples create repeated mode frequencies and closely spaced harmonics. Different p-q-r combinations can also arrive near the same frequency by coincidence. A cluster can make a resonance more prominent or longer-lived, depending on damping and excitation.
What is the Schroeder frequency?
It is an approximate crossover region between sparse, individually identifiable modes and a denser field of overlapping modes. This calculator uses room volume and RT60 for the estimate, so it should be treated as a range rather than a sharp boundary. Below it, placement and modal behavior are usually more useful than a smooth-room assumption.
Can equalization fix a room-mode null?
Usually not reliably. A deep null often results from cancellation at the listening position, so boosting it can waste amplifier headroom while barely changing what reaches the listener. Move the listener, loudspeaker, or subwoofer first, then use measurement-guided equalization mainly on broad peaks.
Does this work for sloped ceilings, irregular rooms, or SBIR?
The equation models a closed rectangular room with parallel, rigid boundaries. An average height is only a rough estimate for a mildly sloped ceiling; open-plan, L-shaped, and strongly angled rooms need measurement or more detailed modelling. Speaker-boundary interference response (SBIR) is a separate path-length cancellation effect, although it can occur in the same frequency range as room modes.