Golden Ratio Calculator
Calculate golden ratio proportions. Enter one length to find the others so that the whole to the longer equals the longer to the shorter.
Last reviewed by the Radiatus Cloud team
Divide a length by the golden ratio φ \u2248 1.618 so the whole is to the longer as the longer is to the shorter.
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Work out golden ratio proportions
The golden ratio, written with the Greek letter phi, is approximately 1.618 and arises when a length is divided so that the whole is to the longer part exactly as the longer part is to the shorter part. This calculator takes any one of the three quantities, the longer part, the shorter part or the total, and computes the other two so they form a perfect golden proportion. It also confirms the defining ratios by showing that the longer divided by the shorter and the total divided by the longer both equal phi.
Phi is an irrational number equal to one plus the square root of five, all divided by two, and it is closely tied to the Fibonacci sequence, whose consecutive terms approach this ratio.
The golden ratio in design and nature
Designers, architects and artists use the golden ratio to create layouts and proportions that many people find naturally balanced, from page grids and logos to building facades. It also appears in nature, in the spiral arrangement of seeds, shells and leaves. Photographers apply it as an alternative to the rule of thirds.
Whether the golden ratio is objectively more beautiful is debated, but it remains a popular and convenient proportioning tool. Enter any positive length to scale a golden division to your project. All calculation runs locally in your browser.
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Frequently Asked Questions
What is the golden ratio?
It is approximately 1.618, the proportion where the whole is to the larger part as the larger part is to the smaller part. Its exact value is one plus the square root of five, over two.
How do I use it in design?
Divide a dimension by the golden ratio to split it into a pleasing larger and smaller part, useful for layouts, spacing and image composition.
How is phi related to Fibonacci numbers?
The ratio of consecutive Fibonacci numbers gets closer and closer to phi as the numbers grow, linking the sequence to the golden ratio.
Which value should I enter?
Enter whichever quantity you already know, the longer part, shorter part or total, and the tool derives the other two in golden proportion.
Is the golden ratio really found in nature?
Golden-ratio-like spirals appear in some shells and plant growth. The pattern is real in many cases, though not every claimed example holds up to scrutiny.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter any one of the longer part, shorter part or total, and compute the rest.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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