Results

Short Side (a)

Long Side (L)

Remainder Segment (b)

Area

Perimeter

Diagonal

Golden Rectangle Calculator

Our Golden Rectangle Calculator finds every dimension of a golden rectangle — a rectangle whose side ratio equals the golden ratio — from just one known side.

What Is a Golden Rectangle?

A golden rectangle is a rectangle whose long side (L) and short side (a) are in the same proportion as the golden ratio: L ÷ a = φ, where φ = (1+√5)÷2 ≈ 1.618. It has a remarkable property: if you cut off a square with side a from one end, the piece left over — width b, height a — is itself another, smaller golden rectangle. Repeating this forever traces out the golden spiral.

Golden Rectangle Formulas

From Short Side: L = a × φ, b = a ÷ φ
From Long Side: a = L ÷ φ, b = L ÷ φ²
Area = a × L
Perimeter = 2(a + L)
Diagonal = √(a² + L²)

Example Calculation

Short Side: a = 10

L = 10 × 1.618 ≈ 16.18

Area = 10 × 16.18 ≈ 161.80

Diagonal = √(10² + 16.18²) ≈ 19.02

✓ Long Side ≈ 16.18, Area ≈ 161.80, Diagonal ≈ 19.02

Features of Our Golden Rectangle Calculator

✅ Works from either the short or long side

✅ Labeled diagram showing the recursive square split

✅ Instant, accurate results

✅ Free to use, no sign-up required

Who Can Use This Calculator?

Students & Teachers – For geometry and golden ratio lessons

Designers & Artists – For layouts, logos, and compositions

Architects – For proportion-driven design work

Photographers – For framing and composition guides

👉 Try our Golden Rectangle Calculator to find every dimension in seconds.