Math

Golden Rectangle Calculator

Find the dimensions of a golden rectangle from one side.

Parameters Live Compute
Calculated Output
Long side 16.18
Area 161.8
Formula: length = width × φ, φ ≈ 1.618
Step-by-Step Breakdown
1. Values used:
2. Short side (width) = 10
3.
4. Long side = 16.18
5. Area = 161.8
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A golden rectangle has its sides in the golden ratio φ, a proportion found throughout art and nature.

The math behind it

The long side is the short side times φ = (1 + √5)/2 ≈ 1.618. Removing a square leaves a smaller golden rectangle.

Worked Example

Width 10 → length 16.18.

Frequently Asked Questions

Why is it special?

It is self-similar — cutting off a square leaves another golden rectangle, repeating forever.

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