Room Acoustics Calculator
Room Dimensions
Room Modes
Axial modes (single dimension) and tangential modes (two dimensions), sorted by frequency. Modes below the Schroeder frequency (37.9 Hz) are most problematic.
| #↕ | Frequency (Hz)↑ | Dimension↕ | Mode (nx,ny,nz)↕ | Type↕ |
|---|---|---|---|---|
| 1 | 28.1 | Length | 1,0,0 | axial |
| 2 | 37.5 | Width | 0,1,0 | axial |
| 3 | 46.9 | Length x Width | 1,1,0 | tangential |
| 4 | 56.3 | Length | 2,0,0 | axial |
| 5 | 62.5 | Height | 0,0,1 | axial |
| 6 | 67.6 | Length x Width | 2,1,0 | tangential |
| 7 | 68.5 | Length x Height | 1,0,1 | tangential |
| 8 | 72.9 | Width x Height | 0,1,1 | tangential |
| 9 | 75.0 | Width | 0,2,0 | axial |
| 10 | 80.1 | Length x Width | 1,2,0 | tangential |
| 11 | 84.4 | Length | 3,0,0 | axial |
| 12 | 112.5 | Width | 0,3,0 | axial |
| 13 | 112.5 | Length | 4,0,0 | axial |
| 14 | 125.0 | Height | 0,0,2 | axial |
| 15 | 140.6 | Length | 5,0,0 | axial |
Speaker Placement
| Speaker↕ | From Front Wall (ft)↕ | From Side Wall (ft)↕ | Angle↕ |
|---|---|---|---|
| Left Speaker | 7.6 | 4.4 | +30° |
| Right Speaker | 7.6 | 4.4 | -30° |
First Reflection Points
This room acoustics calculator analyzes how a rectangular room will sound by computing its resonant room modes, Sabine RT60 reverberation time, and Schroeder frequency, then recommends speaker placement for stereo or surround setups. Modes are found from the room dimensions and the speed of sound; reverberation comes from the absorption of your chosen wall, floor, and ceiling materials.
Formula
RT60 = 0.049 × V ÷ A; f_mode = (c/2) × √((nx/L)² + (ny/W)² + (nz/H)²)
- V
- Room volume in cubic feet (L × W × H)
- A
- Total absorption in sabins = Σ (surface area × absorption coefficient)
- c
- Speed of sound, about 1125 ft/s at room temperature
- nx, ny, nz
- Mode integers for the length, width, and height dimensions
How it works
- Enter the room length, width, and height in feet, and choose the wall, floor, and ceiling materials, each of which carries a published mid-band absorption coefficient.
- The calculator computes axial and tangential room modes, total absorption in sabins, and the Sabine RT60. It also derives the Schroeder frequency that separates the modal region from the diffuse-field region.
- Pick a 2.0, 5.1, or 7.1 speaker layout and the tool returns recommended distances from the front and side walls (using rule-of-thirds geometry) plus the first-reflection points to treat.
Worked example
A 20 ft × 15 ft × 9 ft room with drywall walls, carpet floor, and a drywall ceiling, set up for a stereo pair.
- Volume = 20 × 15 × 9 = 2,700 ft³.
- Absorption: walls 2×(20×9 + 15×9)=630 ft² × 0.05 = 31.5; floor 300 ft² × 0.30 = 90; ceiling 300 ft² × 0.05 = 15 → A = 136.5 sabins.
- RT60 = 0.049 × 2,700 ÷ 136.5 ≈ 0.97 s.
- First length-axial mode = (1125/2) × (1/20) ≈ 28.1 Hz; Schroeder ≈ 2000 × √(0.97/2700) ≈ 37.9 Hz.
RT60 ≈ 0.97 s, Schroeder frequency ≈ 37.9 Hz, and the first room mode sits at about 28.1 Hz — useful targets for bass trapping and absorption.
Frequently asked questions
- What is RT60 and what value should I aim for?
- RT60 is the time for sound to decay by 60 dB after the source stops. For home listening and home theaters a range of roughly 0.3 to 0.5 seconds is generally desirable; the example room's 0.97 s is fairly live and would benefit from added absorption.
- Why do room modes matter?
- Room modes are resonant frequencies where reflections reinforce or cancel, causing peaks and nulls in bass response. Knowing the modal frequencies (especially the low axial modes) tells you where to place bass traps and where a listener might hear boomy or thin bass.
- What is the Schroeder frequency?
- It marks the transition between the modal region (below it, where individual resonances dominate) and the diffuse region (above it, where statistical reverberation applies). Below the Schroeder frequency you treat the room with bass trapping and placement; above it, broadband absorption and diffusion are more effective.
- How accurate is the Sabine RT60 estimate?
- The Sabine equation is a good first approximation but assumes a fairly diffuse, evenly absorbent room. It loses accuracy in very dead rooms or rooms with highly uneven absorption, where the Eyring equation is preferred. Furniture and contents, which add absorption, are not modeled here.