By Ahsan Khowaja · Updated 27 October 2026
How to use the golden ratio calculator
- Pick what you already know: the longer side, the shorter side, or a total length you want to divide.
- Type the number. Units don't matter, because a ratio is the same in pixels, millimetres, inches or feet; just read the answer in the unit you typed.
- Read the result. You get the missing side, the golden rectangle it makes, the whole length (long + short), the 61.8% : 38.2% split and a scale table of the sizes one, two and three golden steps up and down.
Example: a photo 1000 px wide becomes a golden rectangle at 1000 × 618.03 px. A 100 mm drawer front has a golden partner of 161.8 mm. A 1920 px wide page splits into a 1186.63 px main column and a 733.37 px sidebar.
The golden ratio formula
Two lengths are in the golden ratio when the longer (a) divided by the shorter (b) equals the whole (a + b) divided by the longer:
a ÷ b = (a + b) ÷ a = φ
Solving that gives φ = (1 + √5) ÷ 2 = 1.6180339887…, an irrational number usually rounded to 1.618. It has two properties that make the arithmetic easy:
- φ² = φ + 1 (2.618…): going up two golden steps is the same as adding the two lengths.
- 1 ÷ φ = φ − 1 (0.618…): dividing by φ is the same as multiplying by 0.618.
So the three calculations behind the calculator are:
- Shorter side = longer side ÷ 1.618 (or × 0.618)
- Longer side = shorter side × 1.618
- Splitting a total: longer part = total × 0.618, shorter part = total × 0.382
Worked examples
| You know | Value | Result |
|---|---|---|
| Longer side | 1000 | shorter side 1000 ÷ 1.618034 = 618.03; whole 1618.03 |
| Shorter side | 100 | longer side 100 × 1.618034 = 161.8; whole 261.8 |
| Total length | 1920 | longer part 1920 × 0.618034 = 1186.63, shorter part 1920 × 0.381966 = 733.37 |
| Shorter side (font size) | 16 | longer 16 × 1.618034 = 25.89; two steps up 41.89 |
| Longer side | 34 | shorter 34 ÷ 1.618034 = 21.01; whole 55.01 |
| Total length | 100 | 61.8 and 38.2 |
The last row is the one to remember. Whatever the total, the golden section is 61.8% and 38.2% of it.
Golden ratio calculator percentage: 61.8% and 38.2%
Dividing something in the golden ratio means the larger part is 1 ÷ φ = 61.8% of the whole and the smaller part is 1 ÷ φ² = 38.2%. Those two percentages are all you need to split a width, a height, a budget or a timeline. A 300 px tall card with a golden split has a 185.4 px image area and a 114.6 px caption area. The same numbers appear as Fibonacci retracement levels on trading charts, which is where many people first meet them.
Pick "total length" in the calculator and type 100 to see the split, or type your real total to get the parts directly.
Golden ratio calculator in pixels: layouts and screens
For web layouts, start from the content width. A 1200 px container split in the golden ratio gives a 741.64 px main column and a 458.36 px sidebar, usually rounded to 742 and 458. A 1920 px full-width hero splits 1187 / 733. For a golden rectangle image, divide the width by 1.618: 1200 × 742, 1000 × 618, 800 × 494.
No common screen is golden. A 16:9 display is 1.778:1, wider than φ; a 3:2 camera photo is 1.5:1, narrower; 16:10 (1.6:1) is the closest standard shape. The aspect ratio calculator shows where any size sits, and the image resizer can crop a photo to the exact golden size the calculator gives you. To turn the pixel sizes into print or screen measurements, use the pixels to inches and pixels to cm converters.
Golden ratio typography
A type scale built on φ multiplies each size by 1.618. From a 16 px body size the scale table in the result reads: 9.89, 16, 25.89, 41.89, 67.77. In practice you round to 10, 16, 26, 42 and 68 px for small text, body, h3, h2 and h1. Many designers also set the body line height to 16 × 1.618 ≈ 26 px, which is the "golden line height" that typography articles recommend.
φ makes big jumps, so sites with many heading levels often use a smaller ratio such as 1.25 or 1.333 and keep φ for one or two display sizes. Enter your base size as the "shorter side" to get the next size up, or divide it to get caption sizes. The font size calculator and px to rem converter turn the result into CSS values.
Golden ratio in photography
The golden ratio in photography appears as the phi grid and the golden spiral. The phi grid is the rule of thirds with the lines moved inward: instead of cutting the frame at 33.3% and 66.7%, the lines sit at 38.2% and 61.8%, so the subject lands a little closer to the centre. The golden spiral is drawn through a golden rectangle divided into ever-smaller squares, and compositions place the point of interest where the spiral tightens. Many editors, including Lightroom's crop overlays, let you switch between these guides.
To use the calculator for a crop: enter the image width as the longer side to get a golden-rectangle height, then crop to that size. For a 6000 × 4000 photo, the golden height for the full width is 3708 px.
Golden ratio calculator for logo design
Logo tutorials use golden circles and golden rectangles as construction guides: a set of circles whose diameters follow the scale table (for example 34, 55, 89, 144 units), with curves of the mark traced along them. The calculator gives you the sizes: type the largest diameter as the longer side and read down the table, or type the smallest and read up. It also sizes the clear space around a mark (logo width ÷ 1.618) and the gap between a symbol and its wordmark.
Treat it as a tidy way to pick sizes rather than a guarantee. A logo built on a golden grid isn't automatically good, and the famous logos said to be golden were mostly analysed that way after the fact.
Golden ratio calculator for woodworking
Furniture makers use φ to proportion pieces: a table top, a cabinet door, a picture frame or a box lid that is a golden rectangle looks balanced to most eyes. Type the dimension that's fixed by the room or the material and let the calculator give the other. A side table that has to be 30 inches wide gets a depth of 30 ÷ 1.618 = 18.54 inches, or 18 1/2 in once you reach for a tape measure.
Graduated drawers are the classic woodworking use. Set the shallowest drawer height, then multiply by 1.618 for each drawer below it: 4 in, 6.47 in, 10.47 in. The scale table gives all of them from one entry. Working the other way, divide a case height in the golden ratio to place a rail or shelf. The ratio calculator handles any other proportion you prefer.
Fibonacci sequence and the golden ratio
In the Fibonacci sequence each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. Divide any number by the one before it and you get closer and closer to φ:
| Pair | Ratio |
|---|---|
| 3 ÷ 2 | 1.5 |
| 5 ÷ 3 | 1.667 |
| 8 ÷ 5 | 1.6 |
| 13 ÷ 8 | 1.625 |
| 21 ÷ 13 | 1.615 |
| 34 ÷ 21 | 1.619 |
| 55 ÷ 34 | 1.6176 |
| 89 ÷ 55 | 1.61818 |
This is why Fibonacci numbers work as a ready-made golden scale for sizes and spacing (8, 13, 21, 34 px), and why a golden rectangle can be approximated with squares of Fibonacci sides. The calculator's example of 34 → 21.01 → 55.01 shows how close the whole-number version is.
Golden ratio calculator face: what the evidence says
A golden ratio calculator for the face takes measurements such as face length divided by face width, or the spacing of eyes, nose and mouth, and scores how close they come to 1.618, often for men and women separately. The idea is popular, and it is fine as entertainment, but it isn't supported by good evidence: the measurements chosen vary from one calculator to the next, and no reliable study shows that faces closer to 1.618 are judged more attractive. This page measures lengths, not people; if you want the number anyway, divide the longer measurement by the shorter and compare it with 1.618.
Golden ratio in design: where it helps and where it doesn't
Used well, φ gives a consistent family of sizes: widths, type, spacing and image proportions that relate to each other. That consistency is what people respond to, and the calculator's scale table is the quickest way to get it. The limits are practical. Rounding is unavoidable (you can't have 618.03 pixels), screens and paper aren't golden (A4 is 1:√2, a credit card is 1.586:1), and content doesn't always fit a 61.8% column. Use the numbers as a starting point and adjust by eye.
