Golden Ratio Calculator

Find golden-ratio segments from a length.

Longer part (× φ) 161.8
Shorter part (÷ φ) 61.803

Formula: φ = (1 + √5) ÷ 2 ≈ 1.618

Step-by-step with your numbers:
1. Values used:
2. Length = 100
3.
4. Longer part (× φ) = 161.8
5. Shorter part (÷ φ) = 61.803
Did we solve your problem today?

Apply the golden ratio φ ≈ 1.618, found in art, design and nature.

The math behind it

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

Worked example

100 × φ = 161.8.

FAQ

Why is it special?

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