# Best room shape for 2,895 ft³–5,000 ft³

One shape serves every room between 2,895 ft³ and 5,000 ft³: length 3.200 and width 1.231 times the ceiling height. It is the exact optimum at every volume in the band.

Canonical page: https://makerportal.ai/lab/room-shape/2895-5000
Page title: Best Room Shape for 2895–5000 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):** 3.200 : 1.231 : 1 — scale-free — multiply by the ceiling height you have
- **Covers:** 2,895 ft³–5,000 ft³ — 2,106 cubic-foot values
- **Worst case in band:** optimal — zero to machine precision across the whole range
- **At 3,948 ft³:** 12.32 × 32.03 × 10.01 ft — widest axial gap 17.57 Hz, 18 axial modes below 200 Hz

## Dimensions across the band

| Volume | Width × Length × Height | Widest axial gap | vs optimal |
|---|---|---|---|
| 2,895 ft³ | 11.11 × 28.88 × 9.02 ft | 19.48 Hz | optimal |
| 3,196 ft³ | 11.48 × 29.85 × 9.33 ft | 18.85 Hz | optimal |
| 3,496 ft³ | 11.83 × 30.75 × 9.61 ft | 18.30 Hz | optimal |
| 3,797 ft³ | 12.16 × 31.61 × 9.88 ft | 17.80 Hz | optimal |
| 4,098 ft³ | 12.47 × 32.43 × 10.13 ft | 17.35 Hz | optimal |
| 4,399 ft³ | 12.77 × 33.20 × 10.38 ft | 16.95 Hz | optimal |
| 4,699 ft³ | 13.05 × 33.94 × 10.61 ft | 16.58 Hz | optimal |
| 5,000 ft³ | 13.33 × 34.65 × 10.83 ft | 16.24 Hz | optimal |

## Questions this page answers

### What is the best room shape for 2,895 ft³–5,000 ft³?

A ratio of 3.200 : 1.231 : 1 — length : width : height. At the middle of the band, 3,948 ft³, that is 12.32 × 32.03 × 10.01 ft, and the widest gap between adjacent axial modes below 200 Hz is 17.57 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?

Not at all. Across the whole 2,895 ft³–5,000 ft³ range this shape is the best shape known at every volume in it — the worst case measured over the band is zero to machine precision. The reason is that the objective is a maximum over axial modes inside a fixed 200 Hz window: under pure scaling every axial frequency moves as the cube root of volume, so the optimal ratio does not change until a mode crosses the window edge. This band sits inside one such regime.

### 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 ON the Bolt boundary (L/H<=3.2). Above roughly 3,000 ft³ the elongation pull reasserts itself and the criterion is what stops it, so this is a reported state rather than a failure. 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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