Morvatek — ISO paper sizes | morvatek.com
Why the root-2 aspect ratio makes every folded half keep the same shape, and how area halves with each step.
Start with a sheet whose short side is 1 unit and whose long side is √2 units — the ratio ISO 216 fixes for every size. Fold the sheet across its long side and each half measures 1 × (√2 ÷ 2). Because √2 ÷ 2 equals 1 ÷ √2, the half again reads 1 : √2: same shape, half the area.
That is why folding an A3 sheet in half produces A4 rather than an odd strip: 420 mm becomes 210 mm, and 297 mm becomes the new long side. The proportion survives the cut.
On narrow screens, swipe or scroll the plate sideways.
Area and side length scale differently. Side length drops by a factor of about 0.707 each step (√2 ÷ 2), while area drops by exactly one half — which is why each size in a series is half the area of the size above it.
The rule applies to ISO 216, ISO 217 and ISO 269 sheets alike, with the exception of some envelope formats. Because the ratio holds across all three series, a design imposed on one size scales cleanly to any other.
The practical consequence: any sheet halved across its long side lands on a named size, so folds, trims and imposed layouts stay on the standard grid instead of producing unmatchable scraps.
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