How big is A4?

Richard Suchenwirth 2002-12-29 - Letter and Legal paper formats are popular in the US and other places. In Europe and elsewhere, the most widely used paper format is called A4. To find out how big a paper format is, one can measure an instance with a ruler, or look up appropriate documentation. The A formats (DKF - I believe these are defined in a DIN document somewhere...) can also be deduced from the following axioms:

• A0 has an area of one square meter
• A(n) has half the area of A(n-1)
• The ratio between the longer and the shorter side of an A format is constant

How much this ratio is, can easily be computed if we consider that A(n) is produced from A(n-1) by halving it parallel to the shorter side, so

 2a : b = b : a, 2 a2 = b2, b=sqrt(2) a, hence b : a = sqrt(2) : 1

So here is my Tcl implementation, which returns a list of height and width in centimeters (10000 cm2 = 1 m2) with two fractional digits, which delivers a sufficient precision of 1/10 mm:

 proc paperA n {
    set w [expr {sqrt(10000/(pow(2,$n) * sqrt(2)))}]
    set h [expr {$w * sqrt(2)}]
    format "%.2f %.2f" $h $w
 }
 % paperA 4
 29.73 21.02

Detailed info on the format A, which is from ISO 216, can be found here [L1 ]. Michael Schlenker