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Why printed drawings lose their scale

A drawing marked 1:50 is only at 1:50 if nothing between the file and the paper changed its size. Several things routinely do, none of them announce it, and only one of the two outcomes can be repaired with a reprint.

The usual causes

Almost all of it comes from one place: a dialog decided the drawing should fill the paper rather than keep its size. “Fit to page” and “shrink oversized pages” scale the content to the printable area, which is smaller than the sheet by the hardware margins, so the output typically lands somewhere around 94–98% of the intended size — close enough to look correct and far enough to be useless for measuring. Printing on the wrong sheet does the same thing with cruder numbers: A3 content on A4 is 70.7%, A1 on A3 is 50%, and swapping between US Letter and A4 gives awkward factors in the mid-90s.

The remaining causes are physical rather than digital. Every photocopy or scan generation can add its own factor, and scanner glass and feed rollers can stretch one direction more than the other. Paper itself takes up and gives off moisture and changes size with it — small, but real across a large sheet at fine tolerances. What these have in common with the dialog settings is that the drawing keeps its printed “1:50” label while no longer being at 1:50.

Two different failures that look the same

Measure one dimension and you learn that something changed. Measure two, at right angles, and you learn what changed — which decides whether the sheet is recoverable at all.

A uniformly reduced print versus a distorted oneThree states of a border that should measure 200 by 200 mm, drawn to scale. As intended it is 200 by 200 mm and the aspect ratio is 1.000. Uniformly reduced it measures 193.6 by 193.6 mm: both axes are at 96.8 percent, the aspect ratio is still 1.000, and a single reprint at 103.306 percent restores it. Distorted it measures 193.6 mm across and 197.0 mm down: the axes are at 96.8 and 98.5 percent, the aspect ratio is 0.9827, and restoring the axes would need 103.306 percent horizontally and 101.523 percent vertically, which one reprint percentage cannot deliver.AS INTENDED200.0 × 200.0UNIFORM193.6 × 193.6NON-UNIFORM193.6 × 197.0X 100.0%Y 100.0%aspect 1.0000referenceX 96.8%Y 96.8%aspect 1.0000one reprint:103.306%X 96.8%Y 98.5%aspect 0.9827needs two:103.306% X101.523% Y
Drawn to scale. The distorted case differs from the uniform one by 3.4 mm on one axis only — small enough to pass a single-axis check, and large enough that no single reprint percentage can undo it.

The uniform case is the friendly one. A 200 mm border reading 193.6 mm across and 193.6 mm down means one factor was applied to everything:

k_applied = 193.6 ÷ 200 = 0.968 = 96.8% → correction = 1 ÷ 0.968 = 103.305785…%

One reprint at that percentage restores the sheet, because the shape was never altered — the aspect ratio is still exactly 1.000, and every dimension is short by the same proportion.

The non-uniform case is a different animal. The same border reading 193.6 mm across and 197.0 mm down has been through two different factors at once:

across: 193.6 ÷ 200 = 96.8% → needs 103.305785…%
down:   197.0 ÷ 200 = 98.5% → needs 101.522842…%
aspect ratio: 193.6 ÷ 197.0 = 0.98274… — no longer 1.000

A reprint applies one number to both axes, so it cannot deliver two. The 3.4 mm discrepancy between the axes is what makes this failure mode dangerous: it is far too small to notice by eye, and it will pass a single-axis check without complaint.

Why averaging the two corrections fails

The instinct is to split the difference. Averaging the two required corrections gives 102.414313…%, and applying that to the distorted print produces:

across: 193.6 × 1.024143… = 198.274111… mm (target 200 — still short)
down:   197.0 × 1.024143… = 201.756198… mm (target 200 — now over)

Both axes are now wrong, in opposite directions, and the aspect ratio is exactly as distorted as before — because a uniform factor multiplies both axes and therefore cannot change their ratio. That is the structural point: distortion is not an error in size, it is an error in shape, and no amount of resizing addresses shape. The sheet has to be reprinted from the source file.

Why A-series reductions are 70.7% and not 75%

The ISO A series is built so that halving the area preserves the proportions, which fixes the aspect ratio at √2 and makes each step down a length factor of 1/√2:

(1/√2)² = 1/2 → A3 → A4 is 1/√2 ≈ 0.7071 = 70.7% of the length, 50% of the area

So A3 to A4 is 70.7% and A1 to A3 is two steps, (1/√2)² = exactly 50%. This is the one figure on this page that is irrational rather than a fraction: 1/√2 cannot be written exactly as a ratio of integers, and 70.7% is a rounded stand-in for it. Its square, however, is exactly 1/2 — which is the entire point of the system, and the reason two-step reductions land on clean numbers while single steps never do.

How to check a sheet in front of you

Measure something whose intended size is known — the title-block scale bar, the sheet border, or a written dimension — and take it on both axes:

k_applied = measured ÷ intended

Equal on both axes means uniform scaling and a single recoverable factor. Unequal means distortion, and the right response is to go back to the source rather than to correct the copy. Prevention is the same short list every time: print at 100% or “actual size”, on the paper the drawing was set up for, from the source file rather than from a copy, with a printed scale bar so the next person can verify it — and check one known dimension before working from the sheet.

Why drawings say “do not scale”

Because written dimensions survive printing and measured ones do not. The note is not about distrusting your ruler; it is about the fact that the paper in your hands may no longer be the drawing that was issued. Where a written dimension exists, it governs — and where it does not, confirm the print scale before you measure. The general habit behind that, and the reason a second measurement on a different axis counts as an independent check while a repeated calculation does not, is set out in how to verify a scaled result.