A0 has 16.0325 times the area of A4 — sixteen sheets, plus a third of a per cent from millimetre rounding. A0 is the base of the whole ISO 216 series and is defined as exactly one square metre.
About the units
A0 is 841 × 1189 mm, chosen so that the area is as close to one square metre as whole millimetres allow while keeping the 1 to √2 ratio. The exact geometric dimensions would be 840.896 × 1189.207 mm. Every smaller size is derived by successive halving: A1, A2, A3, A4 and so on. Because A4 is four halvings down from A0, it is one sixteenth of a square metre, and the useful consequence is that paper weight in grams per square metre translates directly — a sheet of 80 gsm A4 weighs 80 ÷ 16 = 5 grams.
The exact factor
The nominal ratio is 16, and the actual is 999,949 ÷ 62,370 = 16.0325, with the small excess accumulated from rounding at each halving. The gsm relationship is the practical payoff: 80 gsm A4 is 5.0 g per sheet, which is why a 500-sheet ream weighs 2.5 kg, and why postal weight brackets for letters are set where they are. A sheet of A0 at the same weight is 80 grams, since it is a square metre by definition.
Where you meet this conversion
Architectural and engineering drawing, where A0 and A1 are the standard sheet sizes for plans and A4 is the size they are reduced to for filing and distribution. Posters for academic conferences are almost universally A0. The square-metre definition makes material estimating straightforward: a roll of plotter paper quoted in grams per square metre gives sheet weights directly. Large-format printing, signage and technical documentation all rely on the relationship between the base sheet and the working size.