Golden Ratio Calculator
Enter a length and split it into golden proportion, or read off the golden-rectangle dimensions built from the same number.
Golden-proportion split
Golden rectangle
Why divide by φ instead of multiplying?
Dividing the total length by φ (≈1.618) directly gives the longerof the two pieces, which can feel backwards at first. It works because φ is defined so that the whole is to the larger part as the larger part is to the smaller part — dividing the whole by φ “removes” exactly the smaller-to-larger step, leaving the larger piece.
This is the same arithmetic used to lay out a golden rectangle, mark a golden-spiral starting square, or find a proportionally pleasing crop line inside a photograph or page layout.
Frequently Asked Questions
What exactly is the golden ratio?
The golden ratio, φ (phi), is the number (1 + √5) / 2 ≈ 1.6180339887. Two lengths a and b (with a the larger) are in golden ratio when a/b equals φ, which is the same as saying the whole (a+b) divided by a also equals φ. It's the one proportion where 'the whole is to the larger part as the larger part is to the smaller part.'
How does the split calculation work?
Given a total length L, the longer piece is a = L / φ and the shorter piece is b = L − a. Because of how φ is defined, this guarantees a / b works out to φ exactly (up to rounding), and a + b always equals the original length L.
What's a golden rectangle?
A golden rectangle is one whose long side divided by its short side equals φ. This calculator treats your entered length as the long side and reports the short side (length ÷ φ) needed to complete a golden rectangle — the same rectangle you'd get by unfolding the golden-proportion split above.
Is the golden ratio really everywhere in nature and art?
Some claims are solid (it's the limiting ratio of consecutive Fibonacci numbers, and it genuinely describes the growth angle in plant phyllotaxis), while many popular claims about specific artworks or buildings being deliberately designed around φ are disputed or unsupported by historical evidence. This calculator is a proportion tool — it doesn't take a position on any particular historical claim.
Educational tool for proportion and design work. It does not verify or endorse any specific historical claim about the golden ratio's use in a particular artwork or building.