A correspondent on a newsgroup wrote on the subject of the US going metric:
"When the SI explains A4 paper sizes we can move on to criticize US
measures."
Here's the explanation: A4 is very much a regular metric size - but it refers to the AREA of the paper rather than its linear dimensions. A4 is just one of a series of sizes, with each being half the area of the next size up.
A0 = 1 square metre
A1 = 1/2 square metre
A2 = 1/4 square metre
A3 = 1/8 square metre
A4 = 1/16 square metre
...
An = 1/(2^n) square metres
The aspect ratio of the various sizes is fixed, so to move up or down to the next size, you multiply or divide by the square root of 2. On copiers, that's 141% to magnify up from A4 to A3, or 71% to reduce from A4 to A5 - most modern copiers have these sizes built in. Magnifying again by the same factor (overall 200% or 50%), will take you two sizes up or down (from A4 to either A2 or A6).
The other feature of the range is that the length of A4 is the same as the width of A3, and the width of A4 is half the length of A3. I.e., if you cut a sheet of A3 exactly in half, you will get two sheets of A4. Fold a sheet of A4 (printed two-up duplex) in half, and you get an A5 pamphlet. Fold an A7 mini index card in half and you get an A8 table place card.
For all this to work, the aspect ratio can only be one specific value, the square root of 2, or roughly 1.41:1, or 1:0.71.
From the rules on area and aspect ratio, the length of A4 can be worked out as:
The convenience of halving and doubling, and cutting and folding, is such that the actual linear dimensions of A4 paper simply don't matter. If you're using a computer, you let it do the calculations. If working by hand, your brain doesn't worry about the exact size of the paper - only that what you're writing or drawing will into the available space - and since the fixed aspect ratio is what you're always used to, it's very easy to adapt to larger or smaller paper.
By European standards, the normal US paper sizes are very odd. The aspect ratio is different for every size - no more obviously than between US Letter and US Legal (same width, but different lengths). If you change from one paper size to another, the whole document needs redesigned.
Another point is that with most paper weights now measured in gsm (grams per square metre), you can now easily work out the actual weight of a standard 2500-sheet box of 80gsm A4 paper: It works out at 12.5kg. A tonne of 80gsm A4 paper will neatly fill 80 such boxes or 200,000 sheets (ignoring packaging). Metric is real easy!
The other standard feature of metric paper is the punched holes for use in ring binders. European paper has either 2 or 4 holes, with the hole centres 80mm apart. Four hole paper will fit a two ring binder without adjustment, and a two-hole punch can still be used to cut four holes in three easy steps (middle holes, upper pair, lower pair). Most four-hole punches are actually a pair of two- hole punches welded together at the correct separation!