Room Mode Calculator

Predict rectangular-room resonances, not measured response

The calculation lists ideal pressure modes for a rectangular room. Construction, openings, furnishings, damping and source or listener position change what a microphone will measure.

Step 1 / 4 Room dimensions

Enter the inside room dimensions

Use finished inside length, width and height for one rectangular room. Do not substitute floor area or external building dimensions.

Formula and environmental references

The rectangular-enclosure equation classifies axial, tangential and oblique modes. Air temperature changes sound speed. The optional Schroeder estimate marks a statistical crossover, not a guaranteed treatment boundary.

Sources reviewed:

Calculate the ideal standing-wave frequencies of a rectangular room from its length, width and height. The results separate axial, tangential and oblique modes, preserve different mode tuples that share a frequency, and show where modes crowd together in the selected range. Use the estimate to choose frequencies for careful measurement in a studio, listening room, rehearsal space or home theatre. Dimensions alone cannot predict how loud or long-lived a resonance will be at a particular seat.

How to calculate room modes

  1. 1

    Enter the finished room dimensions

    Use the clear inside length, width and height of a rectangular room, then choose the matching measurement unit.

  2. 2

    Set the analysis range

    Choose the highest frequency to inspect. If you know the room RT60, add it for an optional Schroeder-frequency estimate.

  3. 3

    Read the spectrum and mode table

    Compare mode classes, integer tuples, spacing and clusters, then confirm suspected resonances with measurements in the real room.

Rectangular-room eigenfrequency formula

For an ideal rectangular room, each mode is identified by a non-negative integer tuple (nₓ, nᵧ, n_z):

f(nₓ,nᵧ,n_z) = (c / 2) × √[(nₓ/L)² + (nᵧ/W)² + (n_z/H)²]

Where f is frequency in hertz, c is sound speed, and L, W and H are the inside length, width and height in the same unit. The tuple (0,0,0) is excluded because it has no acoustic resonance. This is the analytical rigid-boundary solution illustrated by COMSOL’s room eigenmode model.

Non-zero tuple indices Class Surfaces involved
Exactly one Axial One pair of opposite surfaces
Exactly two Tangential Two pairs of opposite surfaces
All three Oblique All three pairs of opposite surfaces

The calculator keeps every tuple, including degenerate modes whose different shapes produce the same frequency. A close-frequency group is a prompt to investigate, not proof that the bass response is poor.

Worked room vector

For L = 5.0 m, W = 4.0 m, H = 2.5 m and c = 343 m/s, the first length mode (1,0,0) is 34.3 Hz, the first width mode (0,1,0) is 42.9 Hz, and the first height mode (0,0,1) is 68.6 Hz. The tangential mode (1,1,0) is 54.9 Hz. Room EQ Wizard also uses 343.0 m/s as its default, approximately the speed of sound in dry air at 20°C. Temperature and atmospheric conditions change the real value slightly.

If RT60 is supplied, the optional transition estimate is:

f_s ≈ 2000 × √(T60 / V)

Here T60 is seconds and V is cubic metres. COMSOL’s room-acoustics overview explains this Schroeder estimate. It is not calculated honestly without an RT60 value.

What the prediction cannot tell you

The formula assumes a rigid rectangular enclosure. Doors, openings, flexible walls, furnishings, absorption and non-parallel surfaces can shift or damp resonances. Source and listener position determine which modes are excited or observed; the REW Room Simulator documentation models those extra variables. Use measurements for treatment or equalisation decisions, and use numerical modelling or an acoustics professional for irregular rooms or critical builds.

When playing test tones, start quietly, avoid sustained high levels and stop if listening becomes uncomfortable. The WHO safe-listening guidance notes that risk depends on level, duration and repeated exposure.

Frequently Asked Questions

A room mode is a standing-wave resonance supported by the room boundaries. In a rectangular room, its ideal frequency is determined by the room dimensions, sound speed and an integer mode tuple.

Axial modes use one dimension, tangential modes use two and oblique modes use all three. The calculator classifies them by how many indices in the mode tuple are non-zero.

Different mode tuples can be degenerate: they have distinct pressure patterns but the same calculated frequency. The rows remain separate so that information is not lost.

No. The formula predicts possible resonance frequencies, not amplitude. Wall construction, damping, openings, loudspeaker position and listening position affect whether a mode appears as a peak, dip or long decay.

Not reliably. The calculation assumes three pairs of parallel surfaces. Irregular rooms need in-room measurement or numerical methods such as finite-element modelling.

A range up to roughly 200 or 300 Hz is practical for many small rooms. A higher limit produces more modes, but the ideal model becomes less descriptive as modes grow dense and furnishings affect shorter wavelengths.

No. It identifies frequencies worth measuring. Treatment and equalisation should be based on measured response and decay across relevant listening positions, preferably with qualified advice for critical rooms.

The normal calculator sends field values to the site server through Livewire to update the result. The step-by-step view may also place calculator values in the page URL and browser history. Do not enter sensitive information.

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