Golden Rectangle
Make a golden rectangle from the side you know. Type the short side and the long side is 1.618 times it (or type the long side). Start from one of our 14 designs: the rectangle with its compass-and-ruler construction, whirling squares up to 12 levels, quarter circles or the true golden spiral in the squares, a phi grid, a portrait rectangle, a colouring page, a tracing sheet or gold on navy. Set the size in inches or centimetres on US Letter or A4, print one at real size or the construction steps, and download a PDF, 300 DPI PNG or SVG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size). The info line gives both sides; the long side is the short side × 1.6180.
Rectangle
Lines and colours
Size and paper
Runs in your browser with our own code: nothing you type is uploaded or saved. The drawings are our own. You may use what you make here, including commercially, with no credit needed.
How to make and print a golden rectangle
- Pick a design to start from: with the construction, whirling squares, phi grid or steps.
- Choose the side you know (short or long) and type its length in inches or cm.
- Switch the compass construction, whirling squares, quarter circles, true spiral and phi grid on or off.
- Set the orientation, line width, colours, paper and layout.
- Download the PDF and print at 100% (Actual size), or the SVG for a design app or cutting machine.
What you can use it for
- Page, poster, frame and canvas proportions
- Logo, card and web layout sketches
- Geometry lessons: compass and ruler construction
- Photo and painting composition (phi grid)
- Woodwork and craft templates
- SVG files for laser cutting and vinyl
The 14 golden rectangle designs
| Design | Size from | Shows | Orientation | Look |
|---|---|---|---|---|
| Golden rectangle with its compass construction | Short side | construction | Landscape | Coloured lines |
| Golden rectangle only | Short side | rectangle only | Landscape | Coloured lines |
| Whirling squares, 5 levels | Short side | 5 whirling squares | Landscape | Coloured lines |
| Whirling squares, 8 levels, quarter circles | Short side | 8 whirling squares, quarter circles | Landscape | Coloured lines |
| Whirling squares with the true golden spiral | Short side | 8 whirling squares, true golden spiral | Landscape | Coloured lines |
| Phi grid (1 : 0.618 : 1) | Short side | phi grid | Landscape | Coloured lines |
| Phi grid over whirling squares | Short side | 6 whirling squares, phi grid | Landscape | Coloured lines |
| Portrait golden rectangle, whirling squares | Short side | 6 whirling squares | Portrait | Coloured lines |
| From the long side (6 in long) | Long side | 4 whirling squares | Landscape | Coloured lines |
| Colouring page: bold outlines | Short side | 7 whirling squares, quarter circles | Landscape | Coloured lines |
| Tracing sheet: light grey lines | Short side | construction, 6 whirling squares, quarter circles | Landscape | Light grey (tracing) |
| Gold on navy | Short side | 8 whirling squares, true golden spiral | Landscape | Dark background |
| Construction steps (compass and ruler) | Short side | construction | Landscape | Construction steps |
| Steps: construction, whirling squares and spiral | Short side | construction, 6 whirling squares, true golden spiral | Landscape | Construction steps |
All are our own drawings. Every design is a starting point. Our tests check that the long side is the short side × φ to 12 decimal places, that each construction step contains the one before, and that the whirling squares tile the rectangle with no gap or overlap.
Golden rectangle sizes
| Short side | Long side | In cm |
|---|---|---|
| 1 in | 1.618 in | 2.5 × 4.1 cm |
| 2 in | 3.236 in | 5.1 × 8.2 cm |
| 3 in | 4.854 in | 7.6 × 12.3 cm |
| 4 in | 6.472 in | 10.2 × 16.4 cm |
| 5 in | 8.09 in | 12.7 × 20.5 cm |
| 6 in | 9.708 in | 15.2 × 24.7 cm |
| 8 in | 12.944 in | 20.3 × 32.9 cm |
| 10 in | 16.18 in | 25.4 × 41.1 cm |
| 12 in | 19.416 in | 30.5 × 49.3 cm |
| 16 in | 25.889 in | 40.6 × 65.8 cm |
| Short side | Long side | In inches |
|---|---|---|
| 5 cm | 8.1 cm | 1.969 × 3.185 in |
| 10 cm | 16.2 cm | 3.937 × 6.37 in |
| 15 cm | 24.3 cm | 5.906 × 9.555 in |
| 20 cm | 32.4 cm | 7.874 × 12.74 in |
| 30 cm | 48.5 cm | 11.811 × 19.111 in |
| 50 cm | 80.9 cm | 19.685 × 31.851 in |
| 100 cm | 161.8 cm | 39.37 × 63.702 in |
| Screen size | Golden other side |
|---|---|
| 1080 px wide | 667 px tall (667.5) |
| 1200 px wide | 742 px tall (741.6) |
| 1920 px wide | 1187 px tall (1186.6) |
| 1000 px tall | 1618 px wide (1618) |
| 1080 px tall | 1747 px wide (1747.5) |
| 2400 px wide | 1483 px tall (1483.3) |
Long side = short side × 1.6180339887. Pixel sizes are rounded to whole pixels (exact value in brackets). The info line under the preview also gives the area, perimeter and diagonal of the size you type.
Construction steps (compass and ruler)
| Step | What to do |
|---|---|
| 1 | Draw a square with the short side you want (here ABCD with A at the bottom left). |
| 2 | Mark the midpoint M of the bottom side and draw a line from M to the top right corner C. |
| 3 | Put the compass point on M, open it to C and swing an arc down to the extended bottom line at E. |
| 4 | Extend the top line and draw a line straight up from E to meet it: the golden rectangle (long side ÷ short side = 1.618…). |
| 5 | Cut the rectangle into whirling squares: each square cut off leaves a smaller golden rectangle. |
| 6 | The true golden spiral through the corners of the squares. |
The steps are made from the same lines and arcs as the finished drawing: each step contains the one before, and the last step is the figure you print. The construction is in Euclid’s Elements (Book VI, 30).
Phi grid positions
| Frame | Vertical lines at | Horizontal lines at |
|---|---|---|
| 1920 × 1080 px | 733.4 and 1186.6 px | 412.5 and 667.5 px |
| 1080 × 1080 px | 412.5 and 667.5 px | 412.5 and 667.5 px |
| 1080 × 1350 px | 412.5 and 667.5 px | 515.7 and 834.3 px |
| 3000 × 2000 px | 1145.9 and 1854.1 px | 763.9 and 1236.1 px |
| 4000 × 6000 px | 1527.9 and 2472.1 px | 2291.8 and 3708.2 px |
Lines at 1 / φ² ≈ 0.382 and 1 / φ ≈ 0.618 of each side. To put a phi grid over a photo and crop it, use the Rule of Thirds Grid.
The numbers
| Value | Exact | Decimal |
|---|---|---|
| φ (phi) | (1 + √5) / 2 | 1.6180339887… |
| 1 / φ | φ − 1 | 0.6180339887… |
| φ² | φ + 1 | 2.6180339887… |
| 1 / φ² | 2 − φ | 0.3819660113… |
Every value is exact in the drawing (worked out from √5, not typed in). To split a length or a type size by φ, use the Golden Ratio Calculator.
Sizes
| Paper | Largest short side, portrait page | Landscape page |
|---|---|---|
| US Letter | 4.625 in (11.7 cm) | 6.125 in (15.6 cm) |
| A4 | 4.375 in (11.4 cm) | 6.5 in (16.7 cm) |
Every page has a 1 in (or 2 cm) bar at the bottom to check the print is at 100%. For bigger prints, download the SVG and tile it with the Poster Tiler.
What prints
| Download | What is in it |
|---|---|
| Every page at real size, vector: rectangle, squares, arcs, the true spiral, grid lines and the size bar | |
| PNG 300 DPI | One picture per page (a ZIP when there are several) |
| SVG | The page on screen at real size, with squares, arcs, spiral and grid in separate groups (good for cutting machines, laser cutters and design apps) |
Which tool to use
| You want | Use |
|---|---|
| A spiral template, Fibonacci or true golden, at an exact size | Golden Spiral |
| A golden rectangle from one side, with the compass steps, whirling squares or a phi grid | Golden Rectangle |
| To split one length or a type size by 1.618 | Golden Ratio Calculator |
| Thirds, phi grid or spiral lines over a photo, then crop | Rule of Thirds Grid |
| Golden circles and Fibonacci squares round a logo | Logo Grid Generator |
The Golden Ratio Calculator works out lengths and a type scale, the Rule of Thirds Grid lays composition guides over a photo and crops it, and the Logo Grid Generator builds circle grids round a logo. These two pages draw the spiral and the rectangle themselves, exactly, at the size you set, with the construction steps.
More free tools
Proportion, grids and composition?
Design and print tools that run privately in your browser, with no sign-up and no watermark.
Frequently asked questions
What is a golden rectangle?
A rectangle whose long side divided by its short side is the golden ratio, φ = (1 + √5) / 2 ≈ 1.6180. Cut a square off one end and what is left is a smaller golden rectangle, which is why it can be cut into whirling squares forever.
How do I work out the other side?
Long side = short side × 1.6180. Short side = long side ÷ 1.6180 (or × 0.6180). A 4 in short side gives 6.472 in; a 10 cm short side gives 16.18 cm. The tables below list common sizes.
How do I construct a golden rectangle with a compass?
Draw a square. Mark the middle of its bottom side, put the compass point there and open it to a top corner on the far side. Swing an arc down to the extended bottom line and draw a line straight up from that point to the extended top line. The long rectangle you now have is golden. The construction steps layout prints this in four pictures.
Why does the construction work?
If the square’s side is 1, the distance from the midpoint to the far top corner is √(1² + ½²) = √5 / 2. The long side is ½ + √5 / 2 = (1 + √5) / 2, which is φ.
What is the phi grid?
Like the rule of thirds, but the lines sit at 0.382 and 0.618 of the width and height, so the middle part is 0.618 of each outer part (1 : 0.618 : 1). It comes from the golden ratio, and the page draws it exactly.
What are whirling squares?
The squares you get by cutting a square off a golden rectangle again and again, going round in turn. Quarter circles in them make a spiral close to the golden spiral; the true golden spiral passes through all their corners.
Is A4 paper a golden rectangle?
No. A4 and the other A sizes use √2 ≈ 1.414 so they halve into the same shape; US Letter is 1.294. Neither is 1.618. Cards of 85.6 × 54 mm (1.585) come close.
Is the golden ratio the most beautiful proportion?
That is often claimed, but studies disagree and many famous examples are measured loosely. We draw it as an exact construction and leave the taste to you.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. The rectangle is drawn by JavaScript in your browser. Nothing you type is sent anywhere or saved when you close the page.