Golden Ratio Calculator

How to Use the Calculator

1. Choose Golden split when you know one line value and want the shorter, longer, and total lengths.
2. Choose Golden rectangle when you know one rectangle dimension and want width, height, area, perimeter, and diagonal.
3. Choose Check two lengths to test whether two segment lengths are close to the golden ratio.

Formulas

Let s be the shorter segment, l the longer segment, and L = s + l the total. A golden split means l / s = L / l = φ.

• Given total L: l = L / φ, s = L / φ².
• Given longer segment l: s = l / φ, L = φl.
• Given shorter segment s: l = φs, L = φ²s.
• Golden rectangle from height h: w = φh. From width w: h = w / φ.
• Rectangle area A = wh, perimeter P = 2(w+h), diagonal d = √(w²+h²).

Worked Examples

Split 100 cm into golden parts

For L = 100, longer = 100 / φ = 61.803 cm and shorter = 100 / φ² = 38.197 cm.

Make a golden rectangle from 500 px width

For w = 500, height = 500 / φ = 309.017 px, area = 154,508.497 px², perimeter = 1,618.034 px, and diagonal = 587.785 px.

Golden Rectangle

A golden rectangle has side ratio width / height = φ in landscape orientation. Removing the largest possible square leaves a smaller rectangle with the same proportion. This is why golden rectangles are often used for page layouts, image crops, product cards, and canvas dimensions.

Fibonacci Connection

Ratios of consecutive Fibonacci numbers approach φ: 1/1, 2/1, 3/2, 5/3, 8/5, 13/8. Larger Fibonacci pairs give closer approximations, which is why designers sometimes use practical ratios such as 8:5 or 13:8.

Design Applications

• Layouts: Split a 1920 px canvas into about 1186.633 px and 733.367 px columns.
• Sidebars: If a longer content column is 500 px, the matching shorter column is about 309.017 px.
• Type scales: A 16 px base can scale to 25.889 px by multiplying by φ.
• Crops: Use a golden rectangle as one possible image or card proportion.

Common Misconceptions

The golden ratio is not automatically the best proportion for every design, and many historical claims about φ are overstated. Treat it as a useful mathematical option, then check readability, available space, content needs, and real user behavior.

Golden Ratio Calculator FAQs

What is the golden ratio phi?

The golden ratio phi is (1+√5)/2, approximately 1.61803398875. In a golden split, longer divided by shorter equals φ, and total divided by longer also equals φ.

How do I find the shorter part from a total length?

Divide the total length by φ². The longer part is L / φ, and the shorter part is L / φ².

How do I find the longer part from the shorter part?

Multiply the shorter part by φ. The total is the shorter part multiplied by φ².

How do I calculate golden rectangle width from height?

For a landscape golden rectangle, multiply the height by φ to get the width. If you know the width, divide it by φ to get the height.

What does 0.618 mean in the golden ratio?

0.618 is approximately 1 / φ. It is the fraction of the total length occupied by the longer part in a golden split.

How accurate is the rounding?

The calculator uses the full JavaScript floating-point value of φ and rounds only the displayed result to your selected decimal places.

Is the golden ratio always best for design?

No. It is a useful proportion, not a design law. Use it when it fits the content and constraints.

How do Fibonacci ratios approximate phi?

Ratios of consecutive Fibonacci numbers, such as 8/5 and 13/8, get closer to φ as the numbers increase.

Is my data private?

Yes. Everything runs locally in your browser; nothing is uploaded.