Golden Ratio Calculator
Check whether two parts split a segment in the golden ratio φ, compute the missing part, and measure the deviation.
Category: Mathematics
About this tool
What Is the golden ratio? Golden Ratio Calculator. The golden ratio calculator checks whether two lengths a and b are in the golden proportion a ÷ b = φ ≈ 1.618, and when only a is known it derives the matching b from it. The golden ratio φ = (1 + √5) / 2 ≈ 1.618 has fascinated designers for centuries. Two quantities are said to be in golden proportion when the larger divided by the smaller equals φ. The ratio shows up in architecture, art, typography, and even photo composition. The tool reports the actual ratio of your inputs and immediately flags whether it is within 0.5% of the ideal value. φ = (1 + √5) ÷ 2 ≈ 1.618 · a ÷ b = φ · b = a ÷ φ. How to Use Enter the larger value a, positive and non-zero. Optionally enter b as well to test the pair against φ. Read the ratio, the deviation from φ, and the complementary golden lengths a ÷ φ and a × φ. Worked Example Enter a = 10. The tool computes the matching smaller part b = 10 ÷ φ ≈ 6.1803 and the next golden length a × φ ≈ 16.18. Entering b = 6.18 alongside gives a ratio 1.618 within the accepted tolerance. Common Use Cases page and poster layout balancing photo cropping guides designing logos and product forms geometry and art class projects Important Notes The result shows pass when the deviation is under 0.5%. Only ratio matters here, not units — cm, inches or pixels all work. Calculations run locally. Related Tools Fibonacci