Big box, 20 x 16 x 10 in
- Input
- 50 x 40 x 25 cm | 20 x 16 x 10 in
- Expected output
- 110 cm | 43 7/8 in
The standard method asks for 55 x 44 in: the diagonal saves 21% of the paper.
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diagonal gift wrapping method
In the diagonal method the box sits at 45 degrees in the center of a square sheet and the four corners fold to the middle of the lid. The side of the square is the square root of 2 times the sum of the longest and shortest edge. For a 20 x 16 x 10 in box that is 43 7/8 in, against a 55 x 44 in sheet in the standard method.
The standard method asks for 55 x 44 in: the diagonal saves 21% of the paper.
The standard method asks for 35 x 28 in: the diagonal saves 41%.
The standard method asks for 63 x 52 in: the saving is 16%.
The standard method asks for 25 x 20 in: the diagonal saves 10%, and a tight seam reverses that.
The standard method needs 34 in on the short side and does not fit; the diagonal does.
For a 14 x 8 x 5 in shoe box, a 29 x 28 in sheet with the standard method. The width is 2 x width + 2 x height + 3 in (16 + 10 + 3) and the length is length + 2 x height + 4 in (14 + 10 + 4). With the diagonal method a square 28 3/8 in on a side is enough, and it also covers the whole box.
It depends. With the calculator allowances it saves from 3% to 41%, and more on cubic boxes. If the standard method allowances are trimmed tight, the gain disappears on flat boxes and the standard sheet becomes smaller. What the diagonal guarantees is the square, useful when the paper is short.
In the center, with the longest edge pointing to a corner and the shortest as the height. Fold two opposite corners to the middle of the lid, then the other two, and tape. The calculator diagram shows the base of the gift at 45 degrees.
You can, as long as both sides are at least the side of the square. The extra at the ends is not needed. For a 20 x 16 x 10 in box, a 44 x 56 in sheet works, and a 30 in roll does not work even for the diagonal.
It works, but the gain is small and can reverse. On a 12 x 9 x 2 in shirt box the diagonal saves 10% with the default allowances, and the standard method comes out smaller if the seam is tight. For flat boxes the standard method usually does, and the diagonal comes in when the sheet is not wide enough.
The source formula uses 3 in (7.6 cm) and the quick method says 2 to 3 in.
28 3/8 in x 28 3/8 in
Diagonal method, 5.56 sq ft of paper.
Rule: side = square root of 2 x (longest edge + shortest edge + 1 in allowance), with the box turned 45 degrees (How to Wrap a Present, NRICH, University of Cambridge).
29 in x 28 in
Needs a roll at least 28 in wide.
28 3/8 in x 28 3/8 in
Needs a roll at least 28 3/8 in wide.
Uses 1% less paper than the standard method.
78 7/8 in
From 75 7/8 in to 81 3/4 in, depending on the bow size.
Rule: 2 x length + 2 x width + 4 x height + a 12 to 18 in bow.
The gift sits at 45 degrees in the center of the square sheet and the four corners fold to the middle of the lid.