What percentage do I use to enlarge A4 to A3?

Set the copier to 141%. A3 is exactly one size larger than A4, and each A-series step up multiplies every edge by the square root of 2 (about 1.414), which is 141% as a zoom setting. Loading A3 paper and copying an A4 original at 141% fills the A3 sheet.

What percentage reduces A3 to A4?

Use 71%. Reducing one A-series step multiplies each edge by 1/√2 ≈ 0.7071, which rounds to 71%. The same 71% also reduces A4 to A5 and A5 to A6, because every adjacent step uses the identical ratio.

Why are the copier presets 141% and 71%?

Because all A-series (and B-series) paper shares a 1:√2 aspect ratio and each size is the previous one halved. Halving the area changes each edge by √2 ≈ 1.41421, so enlarging one step is 141% and reducing one step is its reciprocal, 1/√2 ≈ 0.7071 or 71%. They are exact reciprocals, which is why enlarging then reducing returns the original size.

How do I scale a custom size that is not a standard paper?

Switch to Custom size mode, enter the edge length you currently have and the length you want it to become in the same unit, and the tool returns target ÷ original × 100. For example, going from 210 mm to 297 mm gives 141%, and 100 mm to 75 mm gives 75%.

A4 to A3 Enlargement Percentage Explained: The √2 Rule

The A4 to A3 enlargement percentage is 141%, and that exact number comes from the square root of 2 (≈1.4142), which is the constant ratio between the edge lengths of any two adjacent A-series paper sizes. When you set a photocopier or printer to 141% zoom, every dimension of an A4 original multiplies by √2, producing an A3 copy with identical proportions. A3 is exactly two A4 sheets laid side by side, so the length of each edge grows by √2 and the area doubles. The opposite reduction — A3 down to A4 — uses the reciprocal, 1/√2 ≈ 0.7071, which a copier rounds to 71%. The same pair of numbers governs every adjacent step in the A-series: A5 to A4, A4 to A3, and A3 to A2 all enlarge at 141%, and the corresponding reductions all use 71%. That is why those two values sit as preset buttons on nearly every office copier. Skip one step and the factor squares to 200% (A5 to A3, for example) or its reciprocal 50% (A4 to A6), because √2 × √2 = 2 and 1/2 is the corresponding reduction. The reason this all works so cleanly is the 1:√2 aspect ratio shared by every A-series sheet and the halving rule that defines each successive size.

The 141% Number: What A4 to A3 Enlargement Actually Means

The percentage on a copier or printer is a linear zoom — it scales edge lengths, not area. Setting the zoom to 141% means every line on the page becomes 141% as long. For an A4 original, that turns the 210 mm short edge into 210 × 1.4142 ≈ 297 mm and the 297 mm long edge into 297 × 1.4142 ≈ 420 mm. Those are the two edge lengths of A3. Because both dimensions grow by exactly the same factor, the proportions of the original are preserved — the copy is not stretched, just uniformly larger.

The reason 141% is the "right" number rather than an approximation is that A3 is built from A4 by definition. ISO 216 specifies the A-series so that each size is the previous one cut in half across its long edge. Halving an A3 sheet across its long edge gives two A4 sheets; halving an A4 sheet across its long edge gives two A5 sheets. To go the other direction, you join two A4 sheets along their short edges to make one A3 sheet. The area of the resulting sheet is exactly twice the area of an A4 sheet. When the area doubles but the shape stays the same, each edge must grow by √2, and √2 × 100 = 141.4213…%.

Rounded to the nearest whole number, that is 141%. Some copiers accept a tenth-of-a-percent and let you dial in 141.4%; most just have a 141% preset that is accurate enough for everyday copying. Either way, the math behind the number is the same.

Why √2 Governs Every A-Series Enlargement and Reduction

The square root of 2 appears in the A-series because every size is a similar rectangle with the same 1:√2 aspect ratio. A sheet of A4 is 210 × 297 mm, and 297 ÷ 210 = 1.4142 ≈ √2. A3 is 297 × 420 mm, and 420 ÷ 297 = 1.4142 ≈ √2. Every other A-size has the same ratio. That single design choice is what makes 141% and 71% universal across the family.

The halving rule follows from the aspect ratio. If you cut an A4 sheet in half parallel to its short edge, you get two rectangles each measuring 210 × 148.5 mm — and 148.5 ÷ 210 = 0.7071 ≈ 1/√2. Each half is an A5 sheet with the same proportions as the original. Cutting A3 in half the same way gives two A4 sheets. Cutting A2 in half gives two A3 sheets. In every case the new sheet is exactly half the area and √2-times shorter on each edge.

This is also why the A-series is a widely used paper system where one percentage fits every scaling job between any two adjacent sizes. The Letter and Legal sizes in the US do not share a single aspect ratio, and neither does Tabloid. A-to-A and B-to-B scaling always collapses to one clean percentage; mixed-shape scaling does not.

Skipping Sizes: How 141%, 71%, 200%, and 50% Connect

Because each A-series step changes edges by √2, skipping a step squares the factor. The most useful fixed percentages on any office copier come straight from this rule:

Source → Target	Zoom %	Edge factor
A4 → A3 (one step up)	141%	√2
A3 → A4 (one step down)	71%	1/√2
A5 → A3 (two steps up)	200%	√2 × √2 = 2
A4 → A6 (two steps down)	50%	1/2
A6 → A4 (two steps up)	200%	2
A3 → A5 (two steps down)	50%	1/2

The 141% and 71% values are exact reciprocals: enlarge at 141% then reduce at 71% and you are back where you started. The 200% and 50% values are reciprocals of each other in the same way. Going three steps up is √2 × √2 × √2 = 2√2 ≈ 2.828, or 283%; three steps down is 1 / 2√2 ≈ 35%. These are the same four "B-series-aware" scaling values too, because B-series sheets share the same 1:√2 aspect ratio.

In practice this means a copier with only four preset buttons — 71%, 100%, 141%, and 200% — can handle almost every office scaling job without trial and error. For a comprehensive lookup across every standard pair, see the A4 to A3 enlargement percentage chart guide. For anything outside those four cases, or for non-adjacent jumps beyond two steps, a tool such as the Paper Enlargement Percentage Calculator returns the exact percentage to dial in.

Using the 141% Setting on a Copier or Printer

The fastest way to enlarge an A4 original to fill an A3 sheet is:

Place the A4 original face-down on the copier glass or feed it through the document feeder.
Open the Paper Enlargement Percentage Calculator and confirm A4 → A3 returns 141%, or pick the 141% preset directly on the machine.
On the copier, set the zoom or "Reduce/Enlarge" setting to 141%.
Load A3 paper into the correct tray and confirm the paper-size selector matches.
Press start. The output is a clean A3 copy with the same proportions as the A4 original.

The same five steps work in reverse for an A3 → A4 reduction at 71%. If the machine offers Auto Paper Select, leaving it on will not change the percentage — it only picks the paper tray that matches the zoom. The percentage you dial in determines the size of the image; the paper tray determines where that image is printed.

For a non-adjacent jump such as A5 → A3, dial 200% instead. The machine produces an A3-sized copy that is exactly four times the area of an A5 original.

When One Zoom Cannot Match Both Edges

A single zoom percentage only works cleanly when the source and target paper have the same aspect ratio. A4 and A3 both share the 1:√2 ratio, so 141% (or 71%) fits both edges with no cropping or margin. The same is true for A3 and A2, A4 and A5, and any B-to-B pair.

The moment the shapes differ, no single zoom can match both edges. The most common case is between A-series and US sizes:

Source → Target	Aspect match	How the zoom behaves
A4 → A3 (and any A→A or B→B pair)	Yes — same 1:√2 ratio	One zoom fits both edges exactly.
A4 → US Letter	No — different proportions	Largest fit leaves a margin on one edge.
US Letter → Legal	Same width, different length	Fit-by-width leaves top/bottom margins.

When you ask the Paper Enlargement Percentage Calculator for a mixed-shape pair, it returns the largest zoom that still fits the entire source page onto the target. Whichever edge scales smaller is the one that limits the result; the other edge leaves a margin. For A4 to US Letter, the page cannot fill both the Letter width and height at one setting, so a band of white space appears on one pair of sides.

Custom Sizes That Are Not Standard Paper

The same logic works for any pair of edges you can measure. Switch the calculator to Custom size mode and enter the edge length you currently have and the length you want it to become, in the same unit. The tool returns target ÷ original × 100.

A worked example: going from a 210 mm edge to a 297 mm edge — the same as A4 to A3 — gives 297 ÷ 210 × 100 = 141.42…, which rounds to 141%. That is the same percentage the copier applies for the standard A4 → A3 jump, so the formula reproduces the preset.

For non-adjacent custom sizes, the tool handles the unit-matching automatically as long as both edges use the same unit. Use it whenever the source or target is not on the standard list — posters, photographs, scanned artwork, engineering drawings, or a sheet trimmed to a non-standard size. The calculation is one division and one multiplication, and the result is the zoom you dial into the machine.