The Complete Golden Ratio Calculator
Professional precision for designers, architects, and artists. Instantly calculate proportions, check ratios, and scale your designs using the divine proportion.
Enter Values
* Values are linked by the Golden Ratio (φ ≈ 1.618)
Formula Relationship
(A+B) : A = A : B = φ ≈ 1.618
Results
Visual Proportion
See how your values translate into the classic Golden Rectangle geometry. The larger gold section (A) and the smaller cream section (B) maintain a perfect φ ratio.
Ratio A/B
1.618
Ratio (A+B)/A
1.618
Golden Angle
137.5°
Phi (φ)
1.61803
How to Use the Calculator
Follow these simple steps to bring divine proportion to your projects.
Enter a Known Value
Type any dimension you already know into the A (longer), B (shorter), or Total field. For example, if your layout container is 1200px wide, enter 1200 in the Total field.
See Instant Results
The calculator fills in all missing values automatically in real-time. Results show the exact golden-ratio proportions for your specific measurement.
Apply to Your Design
Copy any value with one click. Use the longer segment (A) for your dominant element and the shorter segment (B) for secondary elements like sidebars or margins.
Tip: Use the unit selector to work in pixels, inches, or centimeters.
Tip: Check the Fibonacci table for quick whole-number approximations.
Tip: Use Check Ratio mode to verify existing designs and measurements.
| Pair (A / B) | Ratio | Action |
|---|---|---|
| 1/1 | 1.000 | |
| 2/1 | 2.000 | |
| 3/2 | 1.500 | |
| 5/3 | 1.667 | |
| 8/5 | 1.600 | |
| 13/8 | 1.625 | |
| 21/13 | 1.615 | |
| 34/21 | 1.619 | |
| 55/34 | 1.618 | |
| 89/55 | 1.618 |
Did you know?
The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21...) has a special relationship with the Golden Ratio. As you go higher in the sequence, the ratio between consecutive numbers gets closer and closer to exactly 1.618.
Mathematical Fact
"The Golden Ratio is the limit of the ratio of two consecutive Fibonacci numbers."
What is the Golden Ratio?
The Golden Ratio, represented by the Greek letter φ (phi), is a mathematical constant approximately equal to 1.618. Often called the "divine proportion," it is found when the ratio of two quantities is the same as the ratio of their sum to the larger of the two quantities.
The Formula
Where A is the longer segment and B is the shorter segment.
Why is 1.618 called the Golden Ratio?
It is mathematically unique: φ = 1 + 1/φ. It's the only positive number whose reciprocal is exactly 1 less than itself. Ancient Greek mathematicians first studied this "mean and extreme ratio" for its aesthetic properties in geometry and architecture.
What Does a Golden Ratio Calculator Do?
A golden ratio calculator simplifies the math for designers. You enter one known dimension, and it instantly finds the other two segments (A and B) that maintain the divine proportion. This ensures your layouts, logos, and crops feel naturally balanced and professional.
Applying the Golden Ratio
The divine proportion isn't just for math—it's a tool for beauty. Here's how to apply it across different creative disciplines.
Web Design
Use the ratio for main content vs sidebar widths. If your layout is 1200px, set content to 741px and sidebar to 459px.
Typography
Create a type scale using φ. If body text is 16px, multiply by 1.618 for your h2 (≈26px), and again for h1 (≈42px).
Photography
Position subjects along the golden ratio split rather than centered. Divide image width by 1.618 to find the ideal focal line.
Architecture
Apply to window heights, doorway proportions, and room ratios. Golden ratio rooms feel naturally comfortable and balanced.
Logo Design
Size logo elements using the ratio. A primary mark at 100px pairs with a wordmark at 162px for natural visual balance.
UI/UX Spacing
Base your spacing scale on φ: 4px, 6px, 10px, 16px, 26px, 42px — a perfectly scaled golden Fibonacci spacing system.
Frequently Asked Questions
Everything you need to know about φ and our calculator.
More Calculation Tools
Professional tools for precision-driven creators.
Golden Rectangle Calculator
Design perfect containers and cards using classic geometry.
Rule of Thirds Calculator
Quickly find optimal focal points for photography and layout.
Fibonacci Sequence Generator
Generate natural numerical sequences for dynamic designs.
Aspect Ratio Calculator
Convert and scale any resolution while preserving proportions.
