# 14 × 20 × 9 ft room

Every standing wave this room supports below 300 Hz, solved from its geometry alone. Lowest mode 28.1 Hz on the length; 21 axial, 108 tangential and 141 oblique modes in total.

Canonical page: https://makerportal.ai/lab/room-modes/14x20x9
Page title: 14 × 20 × 9 ft Room Modes — lowest mode 28 Hz

This markdown document and the HTML page above are rendered from the same solved values at build time, by the same functions. Nothing here is written by a language model and nothing is fetched at request time.

## Key figures

- **Dimensions:** 14 × 20 × 9 ft — width × length × ceiling height
- **Volume:** 71.4 m³ — 2520 ft³, 108.9 m² of surface
- **Lowest mode:** 28.1 Hz — the length axis, 20 ft
- **Modes below 300 Hz:** 270 — 21 axial, 108 tangential, 141 oblique
- **Worst axial gap:** 28.1 Hz — widest hole between adjacent axial modes under 200 Hz
- **Densest cluster:** 8 modes at 172 Hz — modes within 5 Hz of each other, below 200 Hz
- **Bolt criterion:** inside — ratio 1 : 1.56 : 2.22 (height : width : length)
- **Schroeder frequency:** 130 Hz at RT60 0.3 s, 183 Hz at RT60 0.6 s — an assumption about materials, not a property of the shape

## Axial modes in full

The 21 modes that run between one pair of parallel surfaces. They carry the most energy and are the ones worth treating first.

| Frequency | Axis | Order | Indices (nx, ny, nz) |
|---|---|---|---|
| 28.1 Hz | length | 1 | 1, 0, 0 |
| 40.2 Hz | width | 1 | 0, 1, 0 |
| 56.3 Hz | length | 2 | 2, 0, 0 |
| 62.5 Hz | height | 1 | 0, 0, 1 |
| 80.4 Hz | width | 2 | 0, 2, 0 |
| 84.4 Hz | length | 3 | 3, 0, 0 |
| 112.5 Hz | length | 4 | 4, 0, 0 |
| 120.6 Hz | width | 3 | 0, 3, 0 |
| 125.0 Hz | height | 2 | 0, 0, 2 |
| 140.7 Hz | length | 5 | 5, 0, 0 |
| 160.8 Hz | width | 4 | 0, 4, 0 |
| 168.8 Hz | length | 6 | 6, 0, 0 |
| 187.6 Hz | height | 3 | 0, 0, 3 |
| 196.9 Hz | length | 7 | 7, 0, 0 |
| 201.0 Hz | width | 5 | 0, 5, 0 |
| 225.1 Hz | length | 8 | 8, 0, 0 |
| 241.1 Hz | width | 6 | 0, 6, 0 |
| 250.1 Hz | height | 4 | 0, 0, 4 |
| 253.2 Hz | length | 9 | 9, 0, 0 |
| 281.3 Hz | width | 7 | 0, 7, 0 |
| 281.3 Hz | length | 10 | 10, 0, 0 |

## Questions this page answers

### What is the lowest room mode in a 14 × 20 × 9 ft room?

28.1 Hz, set by the length (20 ft) dimension. A half-wavelength has to fit between the two parallel surfaces, so the first mode is c/2L — with c = 343 m/s at 20 °C. Below this frequency the room cannot support a resonance at all, and bass output falls off regardless of the loudspeaker.

### Where will a 14 × 20 × 9 ft room sound uneven?

The densest clustering below 200 Hz is 8 modes within 5 Hz of each other around 172 Hz — expect that region to sound louder and to ring longer. The largest gap between adjacent axial modes below 200 Hz is 28.1 Hz, and wide gaps are heard as a hole, not as neutrality.

### Are 14 × 20 × 9 ft proportions good for a listening or control room?

The ratio (1 : 1.56 : 2.22, height : width : length) falls inside the Bolt area — the region Bolt published in 1946 within which low-frequency modes distribute comparatively evenly. That is one criterion about proportions only; it says nothing about absorption, symmetry or speaker placement.

### Above what frequency do modes stop mattering here?

The Schroeder frequency for this 71.4 m³ volume is 130 Hz if RT60 is 0.3 s, and 183 Hz if RT60 is 0.6 s. Above it the modes overlap densely enough to behave statistically rather than individually. RT60 is a property of the materials in the room, not of its shape, so this page can only bracket it — measure your own to place the crossover exactly.

## Method and limits

Frequencies solve f = (c/2)·√((nx/Lx)² + (ny/Ly)² + (nz/Lz)²) for a rectangular room with rigid boundaries, at c = 343 m/s (20 °C). Real rooms have windows, doors, soffits and non-rigid walls, all of which shift and damp these frequencies — treat this as where to look, not as a measurement. The Schroeder crossover additionally depends on RT60, which is a property of the room's materials and not of its shape, so it is quoted here against two assumed values rather than as a fact about this room. Nothing on this page is fetched or estimated; it is solved from the three dimensions in the URL.

## Related tool

[Room Mode Analyzer](https://makerportal.ai/lab/acoustics-room-modes) — Interactive rectangular-room eigenmode solver — enter any width, length and ceiling height and read the axial, tangential and oblique modes, the Bolt ratio and the Schroeder crossover.

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Source: MakerPortal — https://makerportal.ai/lab/room-modes/14x20x9. Free to quote and cite with attribution and a link to the canonical page.