The Room Mode Calculator lists the resonant frequencies (room modes or standing waves) of a rectangular room from its length, width and height. It shows the three axial modes, a sorted list of the lowest axial, tangential and oblique modes, and the Schroeder frequency.
Room modes cause peaks and dips in the bass at particular listening positions. Knowing where they fall helps you choose room dimensions, speaker and seat positions and bass treatment for a home studio, control room or home theater.
Room Mode Calculator
Resonant room modes (axial, tangential and oblique standing waves) for a rectangular listening room or studio, plus the Schroeder frequency.
Formula
f = (c ÷ 2) × √((p ÷ L)² + (q ÷ W)² + (r ÷ H)²)
Schroeder frequency fₛ ≈ 2000 × √(RT60 ÷ V)
Where:
- c = speed of sound, 343 m/s
- L, W, H = room length, width, height (m)
- p, q, r = whole numbers 0, 1, 2 … (the mode order along each dimension)
- RT60 = reverberation time (s); V = room volume (m³)
How the Calculation Works
Step 1: Axial modes use one non-zero index, e.g. the first length mode is c ÷ 2L.
Step 2: Tangential modes involve two dimensions (two non-zero indices); oblique modes involve all three.
Step 3: All combinations are calculated and sorted by frequency.
Step 4: The Schroeder frequency marks roughly where individual modes stop dominating.
Variables Explained
| Mode type | Indices | Reflects between |
|---|---|---|
| Axial | One non-zero, e.g. (1,0,0) | Two opposite surfaces |
| Tangential | Two non-zero, e.g. (1,1,0) | Four surfaces |
| Oblique | All non-zero, e.g. (1,1,1) | All six surfaces |
Axial modes are generally the strongest, followed by tangential, then oblique.
Example Calculation
Given: 6 × 4.2 × 2.7 m room, RT60 0.4 s
- Length axial: 343 ÷ 12 ≈ 28.6 Hz
- Width axial: 343 ÷ 8.4 ≈ 40.8 Hz
- Height axial: 343 ÷ 5.4 ≈ 63.5 Hz
- First tangential (1,1,0): ≈ 49.8 Hz
- First oblique (1,1,1): ≈ 80.7 Hz
- Volume = 68.04 m³; Schroeder ≈ 2000 × √(0.4 ÷ 68.04) ≈ 153 Hz
Notice the close pair at 85.5 and 85.8 Hz in the list — clusters like this can produce a noticeable peak.
Engineering Assumptions
- The room is a rectangular box with rigid walls; real rooms with openings, soft walls or irregular shapes behave differently.
- Sabine-style Schroeder estimate; it is an approximate boundary, not a hard cutoff.
Frequently Asked Questions
What are room modes?
Resonances where sound waves reflecting between surfaces reinforce each other at particular frequencies.
How do I calculate the first room mode?
Divide the speed of sound by twice the longest dimension: 343 ÷ (2 × L).
What is the Schroeder frequency?
The approximate frequency above which modes overlap densely and the room behaves statistically.
What are good room proportions?
Dimensions that spread modes evenly without clusters or large gaps; avoid dimensions that are equal or simple multiples of each other.
Can I use feet?
Yes — the calculator converts; results are always in hertz.