Want to find golden ratio pairs or check if two values form a golden ratio? This golden ratio calculator finds the golden partner for any number and checks if your dimensions are in golden proportion.
Golden Ratio Calculator
Using the calculator
The calculator has two modes:
Find Golden Pair: Enter any value and get both its golden partners – the larger value (your number × φ) and smaller value (your number ÷ φ). These three numbers form a perfect golden proportion.
Check Ratio: Enter two values to see if they form a golden ratio. The calculator shows how close your ratio is to φ and whether it qualifies as "golden."
What is the golden ratio?
The golden ratio (φ, phi) is the ratio where the whole to the larger part equals the larger part to the smaller part:
\frac{a + b}{a} = \frac{a}{b} = \phiSolving this gives:
\phi = \frac{1 + \sqrt{5}}{2} \approx 1.6180339887...This irrational number has fascinated mathematicians, artists, and architects for millennia.
Properties of φ
The golden ratio has remarkable properties:
- Self-similar:
φ² = φ + 1(about 2.618) - Reciprocal relation:
1/φ = φ - 1(about 0.618) - Fibonacci connection: Consecutive Fibonacci numbers approach φ as they grow
- Continued fraction: φ = 1 + 1/(1 + 1/(1 + 1/...)) – the simplest infinite continued fraction
The golden rectangle
A golden rectangle has sides in the ratio φ:1. When you remove a square from a golden rectangle, the remaining rectangle is also golden – infinitely self-similar.
Example: designing with golden proportions
To create a golden rectangle with width 800 pixels:
- Enter 800 in the calculator
- Larger partner: 1294.4 (the length if 800 is the width)
- Smaller partner: 494.4 (the height if 800 is the length)
So an 800 × 494 rectangle, or a 1294 × 800 rectangle, both have golden proportions.
Where you'll find the golden ratio
φ appears in nature (sunflower seed spirals, nautilus shells, leaf arrangements) and design (the Parthenon, Renaissance art, typography). The "rule of thirds" in photography approximates golden divisions.
Whether these appearances are coincidental or fundamental is debated (on other sites, not here...), but the ratio remains a useful design tool.
