Last updated July 27, 2026
One number does most of the work: 70.7%. That is the reduction that takes any ISO A-size sheet down to the next one — A1 to A2, A2 to A3, A3 to A4. Enlarging the other way is 141.4%. Every other figure on this page falls out of those two.
Below are the ratios for ISO sheet sizes and for changing drawing scales — a useful list to keep near the plotter.
Why 70.7% and not 75%
The A series is built so that every size has the same proportions, and each one is exactly half the area of the size above it. For both of those to be true at once, the sheet has to be √2 times longer than it is wide — about 1.414. Halve the area and the linear dimensions shrink by √2, which is a factor of 1 ÷ 1.414 = 0.7071.
Check it against the actual sizes. A1 is 594 × 841 mm and A2 is 420 × 594 mm. Divide 420 by 594 and you get 0.707. The long side of one size is the short side of the next, which is why the series nests so neatly and why a plan set folds down so tidily.
Copiers usually label the button 70% or 71%. Either is close enough for a check print, but 70% leaves about a millimetre of slack per 100 mm — which matters if you are about to measure off the result. More on that below.
ISO A-series reductions
Every step down is another factor of 0.7071, so the percentages simply compound.
| From | To | Steps | Exact | Copier setting |
|---|---|---|---|---|
| A0 | A1 | 1 | 70.7% | 71% |
| A0 | A2 | 2 | 50.0% | 50% |
| A0 | A3 | 3 | 35.4% | 35% |
| A0 | A4 | 4 | 25.0% | 25% |
| A1 | A2 | 1 | 70.7% | 71% |
| A1 | A3 | 2 | 50.0% | 50% |
| A1 | A4 | 3 | 35.4% | 35% |
| A2 | A3 | 1 | 70.7% | 71% |
| A2 | A4 | 2 | 50.0% | 50% |
| A3 | A4 | 1 | 70.7% | 71% |
Going the other way, enlargement is the same sequence inverted: one size up is 141.4%, two sizes is 200%, three is 282.8%, four is 400%.
B-series reductions
The B series sits between the A sizes and is built on the same √2 proportion, so B-to-B steps are also 70.7%. Mixing B and A is where it gets untidy, because the two series are not simple multiples of each other.
These are worked from ISO 216 sizes — B1 is 707 × 1000 mm:
| From | To | Reduction |
|---|---|---|
| B1 | A1 | 84% |
| B1 | B2 | 70.7% |
| B1 | A2 | 59.4% |
| B1 | B3 | 50% |
| B1 | A3 | 42% |
| B1 | B4 | 35.4% |
| B1 | A4 | 29.7% |
If your chart disagrees with this one, check which B you are using. There is a separate and incompatible Japanese B series. JIS defines its B sizes as 1.5 times the area of the corresponding A size, which makes them √1.5 ≈ 1.22 times the A-series lengths — so JIS B1 works out around 728 × 1030 mm against ISO B1 at 707 × 1000 mm.
Run B1→A1 off JIS sizes and you get 82%; off ISO sizes you get 84%. Neither is wrong — they are answers to different questions. That one difference is behind most of the conflicting reduction charts in circulation, and it is worth knowing which series your office chart was built from before you trust it on a job.
Changing drawing scale
Different job, same arithmetic. Here you are not fitting a sheet, you are moving between drawing scales:
| From | To | Change |
|---|---|---|
| 1:1000 | 1:500 | 200% |
| 1:500 | 1:250 | 200% |
| 1:250 | 1:200 | 125% |
| 1:200 | 1:100 | 200% |
| 1:100 | 1:50 | 200% |
The rule is just the ratio of the two denominators. Going from 1:200 to 1:100 doubles everything, so 200%. From 1:250 to 1:200 is 250 ÷ 200 = 1.25, so 125%. Halving the scale number always means doubling the print.
The part that catches people out
Reduce a sheet and you change the drawing scale whether you meant to or not.
Take an A1 plotted at 1:100 and copy it down to A3 at 50%. The paper is now A3 and the drawing is now at 1:200 — but the title block still says 1:100, because that text got reduced along with everything else. Anyone who scales off that print with a 1:100 rule reads every dimension at double its true value.
This is exactly why drawings carry a graphic scale bar. The bar reduces with the drawing, so it stays correct at any reduction — and it is the only thing on a reduced print you can trust for measuring. It is also why “DO NOT SCALE FROM DRAWING” earned its place on the title block, and why figured dimensions always win over anything you measure.
Two related traps worth knowing:
- “Fit to page” is not a reduction ratio. Printing a PDF with fit-to-page or shrink-to-fit applies whatever percentage it likes, usually something like 96% to clear the printer’s margins. The result is at no scale at all. If you need a true half-size print, set 50% explicitly and turn scaling off.
- Half size is not always 50%. “Half size” on an A1 sheet means A3, which is two A-steps — so 50%. But half of A1 by area is A2, which is 70.7%. Worth agreeing which one is meant before someone plots forty sheets.
The short version
- One A size down: 70.7%. One up: 141.4%.
- Two sizes down: 50%. Three: 35.4%. Four: 25%.
- Scale change = the ratio of the two scale denominators.
- Reducing a sheet silently changes the drawing scale. The printed scale text becomes wrong; the scale bar stays right.
- Never measure off a reduced print without checking the scale bar.
Related on this site: standard paper sizes, ANSI and ARCH sheet sizes with a printable chart, how to fold an A1 drawing, and text heights in drawings, which is the other thing that goes wrong when you reduce a sheet.
References
- ISO 216:2007 — Writing paper and certain classes of printed matter: Trimmed sizes, A and B series, and indication of machine direction — International Organization for Standardization. The standard that defines the A and B series.
- ISO 216 — Wikipedia. A- and B-series dimensions in millimetres; the √2:1 aspect ratio; each size being half the area of the next larger; and the incompatible JIS B series defined as 1.5 times the area of the corresponding A size, giving lengths √1.5 ≈ 1.22 times those of A-series paper.
- Standard paper sizes — blog.draftsperson.net. The full ISO A and B size tables.
- Paper sizes chart: ANSI, ARCH & ISO A — blog.draftsperson.net. The inch-based equivalents, with a printable chart.