ISO 216–style boxes

Originally posted on reddit.com/r/themotte

As you probably are aware, international paper sizes (defined by, inter alia, ISO 216) are configured so that the next size in the series can be obtained by cutting the current size in half across its longest dimension.

Size	Area (m²)	Dimension (m)
Size	Area (m²)	1	2
A0	2⁰ = 1	2^−1/4 ≈ 0.8409, 37/44	2^1/4 ≈ 1.189, 44/37
A1	2⁻¹ = 1/2	2^−3/4 ≈ 0.5946	2^−1/4 ≈ 0.8409
A2	2⁻² = 1/4	2^−5/4 ≈ 0.4204	2^−3/4 ≈ 0.5946
A3	2⁻³ = 1/8	2^−7/4 ≈ 0.2973	2^−5/4 ≈ 0.4204
A4	2⁻⁴ = 1/16	2^−9/4 ≈ 0.2102	2^−7/4 ≈ 0.2973

Larger sizes are denoted with prefixes: 2A0, 4A0, etc. Intermediate sizes are denoted with different letters: B0 starts at 2^1/2 m², C0 at 2^1/4 m², and D0 at 2^3/4 m², sometimes going all the way to H0 at 2^7/8 m².

What if there were an analogous series of boxes?

Size	Volume (m³)	External dimension (m)
Size	Volume (m³)	1	2	3
A0	2⁰ = 1	2^−1/3 ≈ 0.7937, 50/63	2^0/3 = 1	2^1/3 ≈ 1.260, 63/50
A1	2⁻¹ = 1/2	2^−2/3 ≈ 0.6300	2^−1/3 ≈ 0.7937	2^0/3 = 1
A2	2⁻² = 1/4	2^−3/3 = 0.5	2^−2/3 ≈ 0.6300	2^−1/3 ≈ 0.7937
A3	2⁻³ = 1/8	2^−4/3 ≈ 0.3969	2^−3/3 = 0.5	2^−2/3 ≈ 0.6300
A4	2⁻⁴ = 1/16	2^−5/3 ≈ 0.3150	2^−4/3 ≈ 0.3969	2^−3/3 = 0.5

These boxes would have inset corner castings, so that they could be fastened together (like intermodal containers) without having their combined dimensions messed up (unlike intermodal containers). For example, a standard high&h;cube intermodal container (8 ft × 9.5 ft × 40 ft, or approximately 2.438 m × 2.896 m × 12.19 m) could be replaced with a set of three 16B0 boxes (totaling approximately 2.245 m × 2.828 m × 10.69 m or 7.365 ft × 9.278 ft × 35.07 ft). With inset corner castings, the interior volume available in each of those 16B0 boxes could be around 1.885 m × 2.608 m × 3.204 m.