Golden ratio calculator — split any length by φ ≈ 1.618

How to use the golden ratio calculator

1. Type the Known length.
2. In This length is the, choose Whole (a + b), Longer part (a) or Shorter part (b).
3. Read the Longer part (a), Shorter part (b) and Whole (a + b). The main answer is highlighted.
4. For a golden rectangle, use the longer part and the whole (or the shorter and longer parts) as its two sides.

What it does and when to use it

Designers use the golden ratio to split a page, a photo or a shelf into two parts that feel balanced. Typical uses: a two-column web layout, the position of a horizon line in a photo, the height of a drawer front compared with the one above it, or a logo grid. In a maths class it links to the Fibonacci sequence and to quadratic equations, since φ solves x² = x + 1.

For general ratios such as 16:9, use the ratio simplifier. The Fibonacci calculator shows terms whose ratios get closer and closer to φ. For a missing value in any proportion, try the proportion solver.

How it works

The tool uses φ = (1 + √5)/2 ≈ 1.61803398875 and the rule a/b = (a + b)/a = φ.

• If you give the whole W: a = W ÷ φ, then b = a ÷ φ.
• If you give the longer part a: b = a ÷ φ.
• If you give the shorter part b: a = b × φ.

The whole is always a + b, which equals a × φ, so a and a + b (or b and a) are the sides of a golden rectangle.

Worked examples

Splitting a 1920-pixel screen, step by step.

1. Divide the whole by φ: 1920 ÷ 1.61803398875 = 1,186.625258. This is the main column.
2. Divide that by φ again: 1,186.625258 ÷ 1.61803398875 = 733.3747416. This is the sidebar.
3. Check: 1,186.625258 + 733.3747416 = 1,920.

The tool shows Longer part (a): 1,186.625258. In practice you would round to 1187 and 733 pixels.

From the longer part. A shelf is 50 cm tall and you want a shorter shelf above it in the golden ratio. The tool gives Shorter part (b): 30.90169944 and a total of 80.90169944 cm.

From the shorter part. A card is 8 cm wide. For a golden rectangle, the long side is Longer part (a): 12.94427191, about 12.9 cm.

Limits and tips

• The length must be greater than zero. There is no unit menu; answers use the unit you typed.
• Results show up to 10 significant figures. Round to what you can actually cut, print or draw.
• The tool splits lengths only. It does not draw spirals or grids.
• The calculation runs in your browser.