Golden Ratio Calculator

What are a, b and a+b?

A line of total length a+b is cut so that the long part b is to the short part a as the whole is to b. In symbols (a+b) ÷ b = b ÷ a = φ. So b = φ·a and a+b = φ²·a. Pick whichever of the three lengths you already know and the calculator returns all three.

What is the value of φ used?

φ = (1 + √5) ÷ 2, computed in full precision and displayed as 1.618034. It satisfies φ² = φ + 1 and 1 ÷ φ = φ − 1, which is why entering b = 1000 returns a = 618.033989.

Is the answer exact?

φ is irrational, so the results are decimals rounded to 6 places. The “Verification (a+b)/b” row recomputes the ratio from your result and shows 1.618034. If you need whole pixels or millimetres, round the output yourself; the split will then be only approximately golden.

Does 13 ÷ 8 equal the golden ratio?

Not quite. Ratios of consecutive Fibonacci numbers approach φ but never reach it: 13 ÷ 8 = 1.625. Entering b = 13 gives a = 8.034442 rather than 8. Larger neighbouring Fibonacci numbers get closer.

What units does it use?

None; the value is a pure length in whatever unit you typed, whether pixels, inches, centimetres or metres. All three outputs use the same unit.

What input is rejected?

The value must be greater than zero. Zero or negative input returns “Value must be positive”. Blank fields are not valid either.

Can it draw a golden rectangle or spiral?

No. It only splits one length into two parts. For a golden rectangle, enter the shorter side as a and use the b output as the longer side. The spiral construction, angles (such as the golden angle) and areas are outside its scope.

Is the golden ratio the best proportion for design?

It is one option, not a rule. Whether it looks better than other proportions is a matter of taste and context, and the tool makes no claim about that. Treat it as a way to generate a ratio, then judge the result visually.