Golden Spiral
Draw a golden spiral or a Fibonacci spiral at an exact size. Start from one of our 16 designs: the Fibonacci spiral in squares of 1, 1, 2, 3, 5, 8, 13 and 21, golden squares with the true golden spiral, both spirals together to compare, the eye of the spiral, a thin composition overlay, a colouring page, a tracing sheet or gold on navy. Choose 3 to 14 squares, turn or mirror it into any of 8 orientations, set the line width and colours, and set the long side in inches or centimetres on US Letter or A4. Put it over your own photo with an opacity you choose, or print the drawing steps. 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 squares, quarter circles and the true golden spiral all use the same corners, so you can trace them or check them with a ruler.
On your photo (stays in this browser)
Spiral
Lines and colours
Size and paper
Runs in your browser with our own code: nothing you type or choose (including your photo) 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 spiral
- Pick a design to start from: Fibonacci spiral, true golden spiral, both, overlay, colouring or tracing.
- Choose Fibonacci or golden squares and how many (3 to 14).
- Switch the squares, numbers, quarter circles, true spiral and eye on or off, and pick one of 8 orientations.
- Set the long side in inches or cm, the paper and the layout (one figure or the construction steps).
- Download the PDF and print at 100% (Actual size), or the SVG; or add a photo and save it with the spiral.
What you can use it for
- Composition guides for photos, paintings and layouts
- Logo, poster and web layout sketches
- Maths lessons on Fibonacci numbers and the golden ratio
- Tracing and drawing practice with a compass
- SVG files for laser cutting, engraving and vinyl
- Wall art, tattoo outlines and colouring pages
The 16 golden spiral designs
| Design | Squares | How many | Shows | Orientation | Look |
|---|---|---|---|---|---|
| Fibonacci spiral: 8 squares (1 to 21) with numbers | Fibonacci | 8 | squares, quarter circles | Landscape, eye lower right | Coloured lines |
| Fibonacci spiral: 10 squares (1 to 55) | Fibonacci | 10 | squares, quarter circles | Landscape, eye lower right | Coloured lines |
| Fibonacci spiral: 6 squares, big numbers | Fibonacci | 6 | squares, quarter circles | Landscape, eye lower right | Coloured lines |
| Fibonacci spiral line only (no squares) | Fibonacci | 8 | quarter circles | Landscape, eye lower right | Coloured lines |
| True golden spiral in golden squares | Golden | 8 | squares, true golden spiral | Landscape, eye lower right | Coloured lines |
| Both spirals on golden squares (quarter circles and the true spiral) | Golden | 7 | squares, quarter circles, true golden spiral | Landscape, eye lower right | Coloured lines |
| Golden squares with quarter circles | Golden | 9 | squares, quarter circles | Landscape, eye lower right | Coloured lines |
| True golden spiral with its eye (two diagonals) | Golden | 8 | squares, true golden spiral, eye | Landscape, eye lower right | Coloured lines |
| Composition overlay: spiral and squares, thin lines | Golden | 10 | squares, true golden spiral | Landscape, eye lower right | Coloured lines |
| Fibonacci spiral, portrait | Fibonacci | 9 | squares, quarter circles | Portrait, eye lower left | Coloured lines |
| Fibonacci spiral, mirrored | Fibonacci | 8 | squares, quarter circles | Landscape, eye lower left | Coloured lines |
| Colouring page: bold outlines | Fibonacci | 9 | squares, quarter circles | Landscape, eye lower right | Coloured lines |
| Tracing sheet: light grey lines | Fibonacci | 9 | squares, quarter circles | Landscape, eye lower right | Light grey (tracing) |
| Gold on navy | Golden | 9 | squares, true golden spiral | Landscape, eye lower right | Dark background |
| How to draw the Fibonacci spiral (steps) | Fibonacci | 7 | squares, quarter circles | Landscape, eye lower right | Construction steps |
| How to draw the golden spiral (steps) | Golden | 6 | squares, quarter circles, true golden spiral | Landscape, eye lower right | Construction steps |
All are our own drawings. Every design is a starting point: change the squares, what is shown, the orientation, line width and colours. Our tests check that the squares tile the rectangle exactly, that each arc’s radius is its square’s side, and that the true spiral passes through every corner.
Fibonacci spiral vs golden spiral
| Fibonacci spiral | True golden spiral | |
|---|---|---|
| Made of | Quarter circles, one per square | One smooth logarithmic spiral |
| Squares | Fibonacci sides 1, 1, 2, 3, 5, 8 … | Golden squares, each 1.618 times the next |
| Growth per quarter turn | Changes: 1, 2, 1.5, 1.667, 1.6 … (closer to 1.618 each time) | Always φ = 1.6180… |
| Passes through the square corners | Yes | Yes (to 1 billionth, tested) |
| Between the corners | Strays from the true spiral by up to 1.2% of a side | Exact |
| Ends | At the first 1 × 1 square | Never: turns forever round the eye |
| Quarter turn | Fibonacci growth F(n+1) / F(n) | Golden growth |
|---|---|---|
| 1 | 1.0000 | 1.6180 |
| 2 | 2.0000 | 1.6180 |
| 3 | 1.5000 | 1.6180 |
| 4 | 1.6667 | 1.6180 |
| 5 | 1.6000 | 1.6180 |
| 6 | 1.6250 | 1.6180 |
| 7 | 1.6154 | 1.6180 |
| 8 | 1.6190 | 1.6180 |
Both spirals use the same corners, so they look alike from a distance. Switch on both in golden squares (the Both spirals design) to see where they part.
Fibonacci squares
| Squares | Newest side | Rectangle | Ratio | Minus φ |
|---|---|---|---|---|
| 1 | 1 | 1 × 1 | 1.000000 | −0.618034 |
| 2 | 1 | 2 × 1 | 2.000000 | +0.381966 |
| 3 | 2 | 3 × 2 | 1.500000 | −0.118034 |
| 4 | 3 | 5 × 3 | 1.666667 | +0.048633 |
| 5 | 5 | 8 × 5 | 1.600000 | −0.018034 |
| 6 | 8 | 13 × 8 | 1.625000 | +0.006966 |
| 7 | 13 | 21 × 13 | 1.615385 | −0.002649 |
| 8 | 21 | 34 × 21 | 1.619048 | +0.001014 |
| 9 | 34 | 55 × 34 | 1.617647 | −0.000387 |
| 10 | 55 | 89 × 55 | 1.618182 | +0.000148 |
| 11 | 89 | 144 × 89 | 1.617978 | −0.000056 |
| 12 | 144 | 233 × 144 | 1.618056 | +0.000022 |
| 13 | 233 | 377 × 233 | 1.618026 | −0.000008 |
| 14 | 377 | 610 × 377 | 1.618037 | +0.000003 |
The ratio of the rectangle’s sides gets closer to φ = 1.6180339887 with every square, from above and below in turn, but never reaches it. That is why a Fibonacci rectangle is never quite a golden rectangle.
How to draw it (steps)
| Step | Fibonacci spiral |
|---|---|
| 1 | Draw two 1 × 1 squares side by side (use squared paper, or measure). |
| 2 | Add a 2 × 2 square along the long side: the rectangle is now 3 × 2. |
| 3 | Add a 3 × 3 square along the long side: the rectangle is now 5 × 3. |
| 4 | Add a 5 × 5 square along the long side: the rectangle is now 8 × 5. |
| 5 | Add a 8 × 8 square along the long side: the rectangle is now 13 × 8. |
| 6 | Add a 13 × 13 square along the long side: the rectangle is now 21 × 13. |
| 7 | In each square draw a quarter circle with the compass point on a corner and the radius = the side, so each arc starts where the last one ended. |
| Step | Golden spiral |
|---|---|
| 1 | Draw a golden rectangle (long side = short side × 1.618…; see the compass steps on our golden rectangle page). |
| 2 | Cut off a square at the left: what is left is a smaller golden rectangle (1 square). |
| 3 | Cut off a square at the top: what is left is a smaller golden rectangle (2 squares). |
| 4 | Cut off a square at the right: what is left is a smaller golden rectangle (3 squares). |
| 5 | Cut off a square at the bottom: what is left is a smaller golden rectangle (4 squares). |
| 6 | Cut off a square at the left: what is left is a smaller golden rectangle (5 squares). |
| 7 | Cut off a square at the top: what is left is a smaller golden rectangle (6 squares). |
| 8 | In each square draw a quarter circle with the compass point on a corner and the radius = the side, so each arc starts where the last one ended. |
| 9 | The true golden spiral: it grows by the golden ratio every quarter turn and passes through the same corners. |
The steps are made from the same squares and arcs as the finished figure: each step contains the one before, and the last step is the figure you print.
The 8 orientations
| # | Name | How it is made |
|---|---|---|
| 1 | Landscape, eye lower right, turns clockwise inward | Turn 0° |
| 2 | Portrait, eye lower left, turns clockwise inward | Turn 90° |
| 3 | Landscape, eye upper left, turns clockwise inward | Turn 180° |
| 4 | Portrait, eye upper right, turns clockwise inward | Turn 270° |
| 5 | Landscape, eye lower left, turns anticlockwise inward | Mirror, then turn 0° |
| 6 | Portrait, eye upper left, turns anticlockwise inward | Mirror, then turn 90° |
| 7 | Landscape, eye upper right, turns anticlockwise inward | Mirror, then turn 180° |
| 8 | Portrait, eye lower right, turns anticlockwise inward | Mirror, then turn 270° |
Every orientation is the same drawing turned and mirrored exactly; nothing is stretched. Portrait versions suit tall photos and posters.
Sizes
| Paper | Largest long side, portrait page | Landscape page |
|---|---|---|
| US Letter | 7.5 in (19 cm) | 10 in (25.4 cm) |
| A4 | 7.25 in (18.4 cm) | 10.625 in (27.1 cm) |
Every page has a 1 in (or 2 cm) bar at the bottom to check the print is at 100%. For a wall-size print, download the SVG and split it over several sheets with the Poster Tiler; to work out other lengths in the golden ratio, use the Golden Ratio Calculator.
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 the golden spiral?
A logarithmic spiral that gets wider by the golden ratio, φ ≈ 1.618, every quarter turn. It never ends: going in, it turns round a point (the eye) forever. It passes through the corners of a golden rectangle cut again and again into squares.
What is the Fibonacci spiral?
Quarter circles drawn in squares whose sides are Fibonacci numbers (1, 1, 2, 3, 5, 8, 13 …), each centred on a corner of its square with the side as radius. It looks almost the same as the golden spiral, and the two are often mixed up.
Are the golden spiral and the Fibonacci spiral the same?
No. The Fibonacci spiral is made of circle arcs, so its curve changes in steps at each square; the golden spiral curves smoothly and grows by exactly 1.618 every quarter turn. Even drawn in the same golden squares, quarter circles stray from the true spiral by up to 1.2% of a square’s side between the corners. The page can draw both on top of each other so you can see it.
How do I draw a Fibonacci spiral?
Draw two 1 × 1 squares side by side, then keep adding a square along the long side: 2, 3, 5, 8, 13 and so on. In each square draw a quarter circle with the compass point on a corner and the radius set to the side, so each arc starts where the last one ended. The construction steps layout prints this.
What are the 8 orientations?
A rectangle can be turned four ways and mirrored, so a spiral can end in any corner and turn either way: 4 landscape and 4 portrait. They are exact turns and mirror images of one drawing; the menu names each by where the eye sits.
How do I use it on a photo?
Choose a photo under On your photo. It is drawn in your browser only, with the spiral on top at the opacity you set. The spiral is the largest exact golden (or Fibonacci) rectangle that fits, centred; it is never stretched, because a stretched spiral is no longer golden. For thirds, phi grids and cropping, use the Rule of Thirds Grid.
Is the golden spiral in nature?
Some shells, plants and galaxies grow in logarithmic spirals, but most are not golden ones (the nautilus shell is a well-known example that is not). Claims that the golden ratio is the secret of beauty are disputed; we treat it as a useful construction, nothing more.
Can I use it for a cutting machine or laser?
Yes. Download the SVG: it is at real size, with squares, arcs and the spiral in separate groups. The arcs are exact quarter circles and the true spiral is a smooth curve, not traced pixels.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. The spiral is drawn by JavaScript in your browser, and a photo you add stays on your device. Nothing is sent anywhere or saved when you close the page.