To enlarge A4 to A3, set your photocopier or printer zoom to 141%. The exact figure is √2 × 100, which rounds to 141.4%, and it comes from the way ISO 216 paper sizes are built: every A-series sheet shares the same 1:√2 aspect ratio, and each larger size is exactly the previous one doubled in area — so A3 is two A4 sheets placed side by side, A4 is two A5 sheets, A5 is two A6 sheets, and so on up to A0. Because area doubles at each step, every edge length grows by the square root of two, about 1.41421. Multiplying that factor by 100 gives the percentage the copier needs: 141.4%, almost always shown as 141% on the machine's preset buttons. Dial in 141%, load A3 paper, and an A4 original fills the A3 sheet exactly with no cropping on either edge. The Paper Enlargement Percentage Calculator returns the same 141% the moment you pick A4 under From and A3 under To in paper-sizes mode.
Where the 141% Number Comes From
Every sheet in the ISO 216 A-series is built from one rule: the long edge is √2 times the short edge, and each larger size is exactly twice the area of the previous one. A0 is the largest, then A1, A2, A3, A4, A5, A6, and so on. A3 measures 297 × 420 mm, A4 measures 210 × 297 mm, and A5 measures 148 × 210 mm. Each pair shares its shorter edge with the previous size's longer edge, which is why you can fold an A3 sheet exactly in half and end up with two A4 sheets, or fold an A4 sheet and end up with two A5 sheets.
When area doubles, each edge length has to grow by the square root of two, because doubling one dimension without changing the aspect ratio means multiplying length and width by the same factor, and (factor)² = 2. That factor is √2 ≈ 1.41421. So jumping one step up multiplies every edge by about 1.41421, which is the 141% the copier needs to enlarge A4 to A3. Jumping one step down divides every edge by √2, giving 1/√2 ≈ 0.7071, or 71%. The two percentages are reciprocals, so enlarging at 141% and then reducing at 71% returns the original size.
The same ratio governs the ISO B-series, which is also built on the 1:√2 proportion. Skipping a size squares the factor: two steps up multiplies edges by √2 × √2 = 2 (so 200%), and two steps down multiplies by 0.5 (so 50%). Those four numbers — 141%, 71%, 200%, and 50% — are the reason most office copiers label them as preset buttons right next to "Auto".
A4 to A3 Enlargement Percentage Example: The Calculation
The general formula for any photocopy scaling is the same, no matter which paper sizes you start with:
Zoom percentage = (target edge length ÷ original edge length) × 100
Pick one edge — either the short side or the long side, as long as you use the same edge on both numbers — divide the target by the original, then multiply by 100.
Worked example for A4 → A3, using the long edge:
- Long edge of A3 (target) = 420 mm
- Long edge of A4 (original) = 297 mm
- 420 ÷ 297 = 1.41414…
- 1.41414 × 100 = 141.414%
- Rounded to the nearest whole percent on the copier: 141%
Checking the same calculation on the short edge gives 297 mm ÷ 210 mm × 100 = 141.428%, which matches within rounding because A3 and A4 share the same 1:√2 shape — so a single zoom percentage fits both edges at once. The Paper Enlargement Percentage Calculator returns the same 141% the moment you select A4 under From and A3 under To, which is a quick way to confirm the arithmetic before walking over to the machine.
Setting 141% on a Copier or Printer
Once the percentage is known, the rest is a routine copier operation. Use the calculator to confirm the figure, then dial it in:
- Open the Paper Enlargement Percentage Calculator in paper-sizes mode.
- Pick A4 in the From dropdown and A3 in the To dropdown — the tool displays 141%.
- On the photocopier or printer control panel, press the "Reduce/Enlarge", "Zoom", or "Copy Ratio" button.
- Enter 141 using the number pad, or pick the "141%" preset if your machine shows one on the touchscreen.
- Load A3 paper into the bypass tray or main paper tray and confirm the tray setting matches A3.
- Place the A4 original face-down on the scanner glass, aligned with the corner guide, or face-up in the automatic document feeder.
- Press Start and collect the enlarged copy.
If your machine only takes whole-number ratios in steps of 5 — a common limitation on older office copiers — 140% is close enough that the difference will not be visible to the eye. Most modern machines, including the Epson inkjet models documented in their support pages, accept 141 directly through the custom-ratio entry.
Adjacent and Skipped-Size Scaling Factors
Because the A-series runs on the √2 ratio, every adjacent step uses the same two percentages, and every skipped step uses the squares of those percentages. The table below lists the values that come up most often at the office copier. For a complete chart of every A-to-A and B-to-B percentage, see the A4 to A3 Enlargement Percentage Chart reference.
| From → To | Edge factor | Zoom setting |
|---|---|---|
| One step up (e.g. A4 → A3, A5 → A4) | √2 ≈ 1.4142 | 141% |
| One step down (e.g. A3 → A4, A4 → A5) | 1/√2 ≈ 0.7071 | 71% |
| Two steps up (e.g. A4 → A2, A5 → A3) | 2 | 200% |
| Two steps down (e.g. A4 → A6, A3 → A5) | 0.5 | 50% |
These four numbers come directly from √2 × √2 = 2 and 1/√2 × 1/√2 = 0.5, so any A-to-A or B-to-B pair follows the same rules regardless of which specific sizes are involved. The Paper Enlargement Percentage Calculator covers A2 through A6, B4, B5, Letter (8.5 × 11 in), Legal (8.5 × 14 in), and Tabloid/Ledger (11 × 17 in), so most standard pairs you meet at the copier are already in the dropdowns.
When Source and Target Shapes Don't Match
All A-series sheets share the 1:√2 shape, and all B-series sheets share it too, which is why a single percentage like 141% or 71% works for both edges at once. The US sizes do not follow that pattern: Letter, Legal, and Tabloid all share an 8.5-inch short edge, but their long edges vary (11, 14, and 17 inches), so the proportions are different between pairs.
For pairs with different aspect ratios, no single zoom percentage can fit the whole page on both edges. A4 to US Letter, for example, has a long-edge ratio of about 94% and a short-edge ratio of about 103%, so a single percentage cannot satisfy both at the same time. The Paper Enlargement Percentage Calculator handles this by returning the largest percentage that still fits the whole page and flagging which edge will leave a margin. For A4 to US Letter the tool returns roughly 94% and notes that the short edge has white space. If you need pixel-perfect output, use "Fit to page" in your printer driver instead, which crops digitally rather than scaling.
Custom Sizes Beyond the Standard Sheets
When the original is an unusual size — a child's drawing, a piece of artwork, a magazine clipping, or a poster trimmed to a non-standard dimension — the standard dropdowns do not apply. Switch the Paper Enlargement Percentage Calculator to Custom size mode, enter the edge length of what you have and the edge length of what you want (in the same unit), and the tool returns the percentage using the same target ÷ original × 100 formula shown above.
For example, going from a 100 mm edge to a 75 mm edge returns 75%, and going from 210 mm to 297 mm returns 141% — the same number you would get for A4 → A3. Custom mode is also useful when scaling a print to fill a frame or poster tube, or when resizing artwork to fit a mat board. Everything is computed locally in the browser using the exact ISO 216 dimensions, so the measurements never leave your device.
For a deeper look, see Age Calculator Example: What the Result Looks Like.