--- title: "Room Mode Calculator with Bonello Check | Sound Attic" description: "Room modes for a rectangular room in metres or feet: axial, tangential and oblique modes to 300 Hz, nearest notes, Schroeder frequency and Bonello check." url: https://soundattic.me/ --- Metres · feet · °C · °F # Room mode calculator Type your room’s length, width and height to see where it booms and where bass goes missing: every room mode up to 300 Hz, charted and checked. ## Why a room booms at some notes Sound bounces between the walls. At certain frequencies the reflections line up with the sound going the other way and build a **standing wave**, or room mode: loud in some places, almost silent in others. The calculator uses the standard formula for a rectangular room: f = (c / 2) · √((nx / L)² + (ny / W)² + (nz / H)²) where c is the speed of sound at your air temperature and nx, ny and nz are whole numbers. One non-zero number gives an **axial** mode between two opposite surfaces, usually the strongest; two give a **tangential** mode around four surfaces; three give an **oblique** mode involving all six. Low down, modes are few and far apart, so single notes boom and others thin out. Higher up they crowd together until the room behaves evenly; the **Schroeder frequency** estimates where that happens. The **Bonello check** counts modes in third-octave bands: the counts should never fall from one band to the next, and no two modes should coincide. Here “coincide” means the same frequency to 0.05 Hz, a tolerance this calculator chooses; pairs under 1 Hz apart are ringed on the chart as well. The formula assumes a closed box with rigid walls. Under a sloping attic roof, or with an open door, real modes shift, so treat the list as a guide and confirm by measuring. ## Sources - Mode formula, mode types and their relative strength: F. A. Everest and K. C. Pohlmann, *Master Handbook of Acoustics*, 6th edition (McGraw-Hill, 2015), the chapter on modal resonances. The same formula, free to read: R. Osman, [Designing small music practice rooms for sound quality](https://www.acoustics.asn.au/conference_proceedings/ICA2010/cdrom-ICA2010/papers/p754.pdf), Proceedings of the 20th International Congress on Acoustics (ICA 2010), Sydney. - Speed of sound in dry air, c = √(γRT/M) with γ = 1.4, R = 8.314 J/(mol·K) and M = 0.02895 kg/mol (331.39 m/s at 0 °C): R. Nave, [Speed of Sound](https://hyperphysics.gsu.edu/hbase/Sound/souspe3.html), HyperPhysics, Georgia State University. - Schroeder frequency f ≈ 2000·√(T/V), T in seconds and V in m³: M. R. Schroeder, [The “Schroeder frequency” revisited](https://doi.org/10.1121/1.414868), Journal of the Acoustical Society of America 99(5), 3240–3241 (1996). - Bonello criterion: O. J. Bonello, [A New Criterion for the Distribution of Normal Room Modes](https://aes2.org/publications/elibrary-page/?id=3889), Journal of the Audio Engineering Society 29(9), 597–606 (1981). Its two conditions as summarised by Osman (ICA 2010, above) and by C. Pop, R. Osman and J. Knight, [Music practice rooms: ambitions, limitations and practical acoustic design](https://pub.dega-akustik.de/ISMA2019/data/articles/000076.pdf), Proceedings of ISMA 2019, Detmold. The 0.05 Hz tolerance for “coincident” and the 200 Hz top band are this calculator’s choices. - Third-octave bands: IEC 61260-1:2014, base-ten band centres 1000·10^(x/10) Hz and edges a twentieth of a decade either side. - Room proportions for a reference listening room, 1.1·w/h ≤ l/h ≤ 4.5·w/h − 4 with l/h < 3 and w/h < 3: [Recommendation ITU-R BS.1116-3](https://www.itu.int/dms_pubrec/itu-r/rec/bs/R-REC-BS.1116-3-201502-I!!PDF-E.pdf) (02/2015), §8.2.2.3. - Published proportions, as tabulated by Osman (ICA 2010, above): L. W. Sepmeyer, Computed frequency and angular distribution of the normal modes of vibration in rectangular rooms, J. Acoust. Soc. Am. 37(3), 413–423 (1965); M. M. Louden, Dimension-ratios of rectangular rooms with good distribution of eigentones, Acustica 24, 101–104 (1971). They are guidance, not a guarantee. - Nearest note, MIDI number m = 12·log2(f / 440 Hz) + 69 with A4 = 440 Hz: J. Wolfe, [Note names, MIDI numbers and frequencies](https://newt.phys.unsw.edu.au/jw/notes.html), UNSW Sydney. - Foot = 0.3048 m exactly, and °F = °C × 9/5 + 32: [NIST Special Publication 811](https://www.nist.gov/pml/special-publication-811), Guide for the Use of the International System of Units. ## More for the attic studio Reverb, reflections, speakers, mics and files. - [Reverb time calculator](https://soundattic.me/reverb-time-calculator/): Sabine and Eyring RT60 per octave band, and the absorption a target needs. - [First reflection points](https://soundattic.me/first-reflection-points/): Where to put side-wall and ceiling panels, on a printable plan. - [Speaker placement calculator](https://soundattic.me/speaker-placement-calculator/): Wall-bounce dips from your speaker distances, and the stereo triangle. - [Comb filter calculator](https://soundattic.me/comb-filter-calculator/): Delay, samples and notch frequencies from two mic distances, with a 3:1 check. - [Audio file size calculator](https://soundattic.me/audio-file-size-calculator/): WAV and compressed file sizes, and how many hours fit on a card. ## Recommended Two free services for the online side of home recording. 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[Try WebTraceCheck](https://webtracecheck.com/) ## Questions **Which modes matter most?** The low axial modes, between the room’s opposite surfaces. They are usually the strongest and the most widely spaced, so each one makes its note boom or vanish depending on where you sit. Look for two modes landing close together, and for wide gaps with none. **What reverb time should I use for the Schroeder frequency?** Your room’s own, measured or estimated. The 0.4 s default is only a starting value. The estimate changes with the square root, so doubling the reverb time raises the Schroeder frequency by about 41%. **My room fails the Bonello check. Is it a bad room?** Not necessarily. Bonello’s criterion is one published way to judge how evenly modes are spread, and it says nothing about treatment, furniture or where you sit. Use it to compare possible layouts or to spot a problem frequency, then measure. **Does it work for an attic with a sloping ceiling?** Only roughly. The formula is for rectangular rooms, so a sloping roof shifts the modes in ways it cannot predict. Use the length and width of the floor and a typical ceiling height as a starting point, and confirm with a measurement.