# Best room shape for 1,333 ft³–2,894 ft³

One shape serves every room between 1,333 ft³ and 2,894 ft³: length 2.247 and width 1.281 times the ceiling height. Nothing in the band is more than 4.72% off its own optimum.

Canonical page: https://makerportal.ai/lab/room-shape/1333-2894
Page title: Best Room Shape for 1333–2894 cu ft | MakerPortal

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

- **Shape (L : W : H):** 2.247 : 1.281 : 1 — scale-free — multiply by the ceiling height you have
- **Covers:** 1,333 ft³–2,894 ft³ — 1,562 cubic-foot values
- **Worst case in band:** 4.72% — flat across 1,333 ft³–2,550 ft³
- **At 2,114 ft³:** 11.56 × 20.27 × 9.02 ft — widest axial gap 20.91 Hz, 14 axial modes below 200 Hz

## Dimensions across the band

| Volume | Width × Length × Height | Widest axial gap | vs optimal |
|---|---|---|---|
| 1,333 ft³ | 9.91 × 17.38 × 7.74 ft | 24.39 Hz | +4.72% |
| 1,556 ft³ | 10.44 × 18.30 × 8.15 ft | 23.16 Hz | +4.72% |
| 1,779 ft³ | 10.91 × 19.14 × 8.52 ft | 22.15 Hz | +4.72% |
| 2,002 ft³ | 11.35 × 19.90 × 8.86 ft | 21.30 Hz | +4.72% |
| 2,225 ft³ | 11.76 × 20.62 × 9.18 ft | 20.56 Hz | +4.72% |
| 2,448 ft³ | 12.14 × 21.28 × 9.47 ft | 19.91 Hz | +4.72% |
| 2,671 ft³ | 12.50 × 21.91 × 9.75 ft | 19.34 Hz | optimal |
| 2,894 ft³ | 12.84 × 22.51 × 10.02 ft | 18.83 Hz | optimal |

## Questions this page answers

### What is the best room shape for 1,333 ft³–2,894 ft³?

A ratio of 2.247 : 1.281 : 1 — length : width : height. At the middle of the band, 2,114 ft³, that is 11.56 × 20.27 × 9.02 ft, and the widest gap between adjacent axial modes below 200 Hz is 20.91 Hz. The same ratio applies at every volume in the band; only the absolute dimensions scale, as the cube root of the volume.

### How much worse than optimal is this shape for my exact volume?

At most 4.72%, and that figure holds flat across 1,333 ft³–2,550 ft³ rather than at one unlucky volume — above that range it is smaller. The optimal proportions are not constant across this band; they jump as the volume grows, and this shape is the single one that stays within the published tolerance of all of them.

### Why is this a range rather than a page per volume?

Because a recommended room gets built to a finite tolerance. A ±1 inch error in framing moves this objective by a median 6.86%, so splitting the range more finely than that publishes distinctions nobody can construct. Three shapes cover 800–5,000 ft³ at that tolerance, and the covering is provably minimal there rather than merely an upper bound, because each shape's coverage set is a single unbroken interval.

### Is this shape inside the Bolt area?

Yes — every shape published here is. The shape sits strictly inside the Bolt area, so the criterion is not what chose it — the objective is. Bolt (1946) is a citable constraint set rather than a sweep range someone typed: it caps length at 3.2 times the height, which puts the corridor outside the feasible set, and forces height ≤ width < length. Without it the answer to "what shape?" at a fixed volume is "build a longer corridor", which is a tautology rather than advice.

### What does the widest axial gap actually tell me?

It is the largest hole in the low-frequency response you cannot fix with absorption. Axial modes are the strongest room resonances, and a wide gap between two adjacent ones is a band where the room supports very little. Minimising the widest gap spreads the modes as evenly as the volume allows. It says nothing about tangential or oblique modes, absorption, speaker placement or anything above 200 Hz.

## Method and limits

Solved by minimising the widest gap between adjacent axial modes below 200 Hz, at fixed volume, over the Bolt (1946) ratio area. Axial modes are n·c/(2L) per axis with c = 343 m/s. The band is a covering: one shape is published for a range of volumes, with the range chosen so that no volume inside it pays more than 7% against the best shape known at that volume — the first tolerance above the 6.86% a ±1 inch framing error costs. "Best known" is the minimum over a live solve and every shape the solver returns anywhere on the range, which matters because the search is itself imperfect: it is beaten at 2.43% of volumes by a shape it finds elsewhere. Worst-case figures are measured across the band, not assumed. Tangential and oblique modes, absorption and placement are out of scope. Pure computation — nothing is fetched and nothing is recalled.

## Related tool

[Room Shape Optimizer](https://makerportal.ai/lab/room-shape-optimizer) — Enter the volume you have and solve for the room shape with the most evenly spread axial modes, inside the published Bolt area. Free, in your browser.

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