]> ISO 216–style boxes

# 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.

SizeArea (m2)Dimension (m)
12
A020 = 12−1/4 ≈ 0.8409, 37/44, 5/621/4 ≈ 1.189, 44/37, 6/5
A12−1 = 1/22−3/4 ≈ 0.59462−1/4 ≈ 0.8409
A22−2 = 1/42−5/4 ≈ 0.42042−3/4 ≈ 0.5946
A32−3 = 1/82−7/4 ≈ 0.29732−5/4 ≈ 0.4204
A42−4 = 1/162−9/4 ≈ 0.21022−7/4 ≈ 0.2973

Larger sizes are denoted with prefixes: 2A0, 4A0, etc. Intermediate sizes are denoted with different letters: B0 starts at 21/2 m2, C0 at 21/4 m2, and D0 at 23/4 m2, sometimes going all the way to H0 at 27/8 m2.

What if there were an analogous series of boxes?

SizeExternal volume (m3)External dimension (m)
123
A020 = 12−1/3 ≈ 0.7937, 50/63, 4/520/3 = 121/3 ≈ 1.260, 63/50, 5/4
A12−1 = 1/22−2/3 ≈ 0.63002−1/3 ≈ 0.793720/3 = 1
A22−2 = 1/42−3/3 = 0.52−2/3 ≈ 0.63002−1/3 ≈ 0.7937
A32−3 = 1/82−4/3 ≈ 0.39692−3/3 = 0.52−2/3 ≈ 0.6300
A42−4 = 1/162−5/3 ≈ 0.31502−4/3 ≈ 0.39692−3/3 = 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.

If you&a;re willing to settle for a very rough approximation, cardboard boxes with the following dimensions are available:

Volume (in3)Internal dimension (in)
123
60 × 20 = 60345
60 × 21 = 120456
60 × 22 = 240568
60 × 23 = 4806810
60 × 24 = 96081012
60 × 25 = 1920101216
60 × 26 = 3840121620
60 × 27 = 7680162024