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How Print Enlargement and Reduction Percentages Are Calculated

The percentage a copier or printer asks for is a linear scale factor, not an area factor β€” a distinction that trips up nearly everyone the first time they enlarge a document.

Scale % = (target dimension Γ· original dimension) Γ— 100

To enlarge a document from one width to a target width, divide the target by the original and multiply by 100. The same ratio should be applied consistently to both dimensions to avoid stretching the content.

ISO paper sizes (A4, A3, A5...) scale by √2, about 141%

The international ISO 216 series is designed so each size is exactly half the area of the next size up, while keeping the same aspect ratio. That fixed relationship is why enlarging A4 to A3 is always 141% (√2 Γ— 100), not 200%.

200% quadruples the area, it does not double it

Doubling both width and height (a 200% scale) actually multiplies the area by four, since area scales with the square of the linear dimension. This is the single most common mistake people make when guessing an enlargement percentage.

US Letter and Legal do not share the ISO ratio

Unlike the ISO series, US Letter (8.5Γ—11 in) and Legal (8.5Γ—14 in) do not maintain a consistent aspect ratio across sizes, so scaling between them (or to Tabloid/Ledger, 11Γ—17 in) at a single percentage usually leaves either empty margin or content cropped on one dimension.

"Fit to page" resolves aspect-ratio mismatches automatically

When source and target paper do not share an aspect ratio, most printers offer a "fit to page" or "shrink to fit" option that scales by the more restrictive dimension, leaving margin on the other side rather than cropping content.

Why ISO paper sizes scale so cleanly

The ISO 216 standard was deliberately designed around a 1:√2 aspect ratio, a mathematical property where cutting the long side in half produces a new rectangle with exactly the same aspect ratio, just at half the area. That single design choice is why every ISO-to-ISO enlargement or reduction (A4 to A3, A5 to A4, and so on) always converts at 141% or 71%, regardless of which pair of adjacent sizes is involved.

Why the percentage on a copier is not an area setting

It is easy to assume "200%" means "twice as big" in the everyday sense of covering twice the paper, but a copier's scale percentage is applied to both width and height independently, so doubling it quadruples the area. Anyone printing a poster from tiled pages, or enlarging a document to fill a specific paper size, needs to calculate the target-to-original ratio directly rather than guessing a round percentage.

Frequently Asked Questions

Why is enlarging A4 to A3 141% and not 200%?

Because A3 has exactly double the area of A4 while keeping the same aspect ratio, and doubling area only requires multiplying each linear dimension by the square root of 2, which is about 1.41, or 141%.

Can I scale US Letter to Tabloid the same clean way as A4 to A3?

Not perfectly. Letter and Tabloid do not share the same aspect ratio the way ISO sizes do, so a single scale percentage will either leave a margin on one side or crop content slightly, unless the printer's "fit to page" option handles the mismatch automatically.