How to use it
- Choose Calculate: Split a length into two parts, Whole from one part, Golden rectangle from one side or Modular type scale.
- For a split, type the Length. For a whole, type the Known part and choose Known part is.
- For a rectangle, type the Known side and choose Known side is. For a scale, type the Base size, choose the Ratio, then the Steps down and Steps up.
- Read the Larger part and Smaller part, the Whole length, the Long side and Short side, or the Type scale table.
The golden ratio
The golden ratio, φ, is (1 + √5) ÷ 2, about 1.618034. Two quantities are in the golden ratio when the whole is to the larger part as the larger part is to the smaller: (a + b) ÷ a = a ÷ b = φ (Wikipedia: Golden ratio). A line of length 100 therefore splits into 61.80 and 38.20, and 61.80 ÷ 38.20 is 1.618.
A golden rectangle has a long side φ times its short side. Cut a square the size of the short side from it, and what is left is a smaller golden rectangle, as the Wikipedia article describes.
φ = (1 + √5) ÷ 2 = 1.6180339887…
larger part = length ÷ φ; smaller part = length ÷ φ²
whole = part × φ, or part × φ² when the part is the smaller oneModular type scales
A modular scale is a series of sizes, each a fixed ratio bigger than the one before. The tool multiplies the base by the ratio for each step up and divides for each step down. The article "More Meaningful Typography" in A List Apart builds such a scale on the golden ratio: 10 × 1.618 is 16.18, and 16.18 × 1.618 is 26.18.
The fourth and third presets are musical ratios: the perfect fourth is 4:3 and the major third 5:4 in just intonation, which are 1.333 and 1.25 here (Wikipedia: Perfect fourth; Major third).
What the ratio does not decide
The golden ratio is a proportion, not a rule a design must follow. The tool gives the numbers; the choice of base size and ratio is for the design. For the shape of a picture, use the aspect ratio calculator.
Example: 100 split in the golden section
A line of 100 is split in the golden section. The larger part is 100 ÷ 1.618 = 61.80, and the smaller part is 100 − 61.80 = 38.20.
A golden rectangle with a long side of 1000 has a short side of 618.03; cutting a square of 618.03 leaves 381.97 by 618.03. A type scale from a base of 16 with the golden ratio gives 25.89 at step 1.
| Measure | Value |
|---|---|
| Larger part of 100 | 61.80 |
| Smaller part of 100 | 38.20 |
| Short side of a rectangle with a long side of 1000 | 618.03 |
| Rectangle left after a square of 618.03 | 381.97 × 618.03 |
| Step 1 of a scale from 16, golden ratio | 25.89 |
Frequently asked questions
What is the golden ratio exactly?
It is (1 + √5) ÷ 2, which is 1.6180339887…, an irrational number. The Wikipedia article on the golden ratio explains that it cannot be the ratio of two whole numbers. Its reciprocal is φ − 1, about 0.618.
What is the difference between the larger and the smaller part?
The larger part is about 0.618 of the whole and the smaller part about 0.382. The larger part divided by the smaller part is φ again, and that is what makes the split golden.
Which ratio should I use for a type scale?
No single ratio is correct. The golden ratio gives wide steps, while the perfect fourth (1.333) and the major third (1.25) give smaller ones. Both presets are musical intervals, as the Wikipedia articles on those intervals explain.
Do real designs use the golden ratio?
Some do. The Wikipedia article says that 20th-century artists and architects, including Le Corbusier and Salvador Dalí, proportioned works to approximate it, and that its use to analyse proportions has sometimes rested on doubtful fits to data.
In which unit are the results?
In the unit of the number you type. A base of 16 pixels gives sizes in pixels, a base of 16 points gives points. The scale does not change with the unit, so round to whole pixels for a screen.
Is what I type stored anywhere?
No. The numbers are worked out in your browser, and nothing is sent to us or saved.
Sources
- Wikipedia: Golden ratio
- Wikipedia: Perfect fourth
- Wikipedia: Major third
- A List Apart: More Meaningful Typography
Figures and text last checked on Tuesday, November 10, 2026.