Math

Golden Ratio Calculator

Find golden-ratio segments from a length.

Calculated Output

Longer part (× φ) 161.8

Shorter part (÷ φ) 61.803

Formula: φ = (1 + √5) ÷ 2 ≈ 1.618

Step-by-Step Breakdown

1. Values used:

2. Length = 100

4. Longer part (× φ) = 161.8

5. Shorter part (÷ φ) = 61.803

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The math behind it

φ = (1 + √5) ÷ 2. Multiply by φ to extend, divide by φ to shrink, keeping the golden proportion.

100 × φ = 161.8.

Why is it special?

A line split so the whole-to-long ratio equals the long-to-short ratio gives φ.