Area of a4 paper

Answer 1

It is 62,370 mm2.

====

The first respondent is correct. But here is a little more information...

Notice how the area of A4 paper is approximately 1/16 of a square meter (62,500 mm2), or just under that amount. This is no coincidence. Take the number 4 in "A4" paper and that is the power, or exponent to the fraction 1/2. So (1/2)4, or 1/16, as measured in square meters, is the "definition" of how much paper there should be there.

It was defined many years ago that A0 paper is to have exactly 1 m2 of area.

It was also defined that for each number after A0, the size, area and dimensions of the paper is exactly that of the preceding sheet, but cut in half across the longest side.

So A1 paper has 1/2 the area of A0 paper, and A2 paper has 1/2 the area of A1 paper, so on. Thus A4 paper has 1/2 of 1/2 of 1/2 of 1/2 (or 1/16) of the area of A0 paper.

But just as importantly are the dimensions of the sheet itself. The longest side of A2 paper has the same length as the shortest side of A1 paper. The shortest side of A2 paper is 1/2 the length of the longest side of A1 paper. It was defined this way so that scaling paper was easier. As it turns out, the longest side of any sheet is √2 times the shortest side of that same sheet.

These are the standards and definitions set for the A-Series paper.

So the question then is, "if A4 paper is supposed to have 62,500 mm2 of area, then why does it have 62,370 mm2 of area?" The answer to that question lies in rounding.

By definition A0 paper has 1 m2 of area and the ratio between longest and shortest sides is √2 to allow for this halving scaling process. It turns out this is not an exact scaling process for the actual manufactured papaer. If we kept with these definitions then A0 paper should have 840.8964... mm by 1,189.207... mm. But these values were rounded to the nearest millimeter. A0 paper actually has the dimensions of 841 mm by 1189 mm (and so an area of 0.999949 m2).

This error exists for each paper size (and more than likely gets compounded as you work your way up the numbers to A4 paper). Each paper size is measured, rounded and cut to whole millimeter dimensional lengths. Ultimately arriving at A4 paper at exactly 210 mm by 297 mm (and an exact area of 62,370 mm2).