Proposal for Square Sizes.
Version of 5 July 2007.
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For some applications, a sheet of paper needs to be square. One example is the label for the end of a box containing a cylindrical item, while another case involves the paper-folding art of origami where the norm is the square sheet. Because we know of no standard for square sizes, we offer a scheme.

In the usual European sheet sizes (from which the well-known ISO sizes are derived), the ratio of the longer edge to the shorter is the square root of two, numerically about 1.41421. This is closely approximated by the ratio 7/5 = 1.4; the difference is just a shade over one percent. This error is small enough to present no major problem, because with paper sizes a certain amount of variation is inevitable anyway; one major reason for this follows.

When atmospheric humidity increases, paper will absorb moisture from the air and change dimensions, likely expanding. Later when the humidity falls, the paper will release moisture, probably shrinking. Adding to the complication, a square piece of paper may not remain square when the weather changes. This is because typical manufacturing equipment carries the liquid that will become paper on a conveyor belt. In this fluid environment, the cellulose fibers that will be the main ingredient of the finished product tend to align themselves parallel to the direction of travel -- this is called the machine direction. Perpendicular to that is the cross direction. After manufacturing is complete, there is a risk that under variations of humidity, the percent of expansion or contraction in the machine direction will differ from that in the cross direction. For this reason along with the usual errors of measurement that can occur in any industrial process, the attainment of absolute squareness is difficult if not impossible.

However, there are two approaches to generating sheets that are nearly enough square to be useful. Under either method, the first step is thus: in one large rectangular sheet, make four evenly-spaced cuts (yielding five strips) perpendicular to the shorter edge. For instance, a B0 sheet (1414 by 1000 mm) would be cut into five strips measuring 1414 by 200 mm. Then choose one of the following procedures:

The first method minimizes cutting and eliminates waste, while the second yields squares that are more precise. Either way, one large rectangular sheet yields 35 small square sheets.

In major production work, the squares alternatively might be cut from a roll of paper several meters wide and hundreds of meters long, not from standard sheets. In that case there is every reason to cut to the precise square size, as waste can assuredly be minimized .

These square sizes need names. In an arbitrary choice, we start with the letter "S" (for square) and use with it the three succeeding letters of the Latin alphabet. We might have used the letters starting with "E", but the are already used in sundry ways to indicate other paper sizes. The chart below gives some examples of square sizes, and the rectangular sheets from which they are efficiently cut.

Source SheetResultant Sheet
DesignationLonger EdgeShorter EdgeDesignationAny Edge
B01414.1000.T0200.0
C01297.917.0U0183.4
A01189.840.9S0168.2
D01091.771.1V0154.2
B11000.707.1T1141.4
C1917.0648.4U1129.7
A1840.9594.6S1118.9
D1771.1545.3V1109.1