Golden Ratio Calculator (Phi)
Start with a longer segment, shorter segment, or total length. We calculate the other two lengths plus the A/B ratio using phi = (1 + square root of 5) / 2.
Phi (φ)
1.6180
Golden constant
What you get
A, B, A + B, and A/B ratio
Proportion preview
A : B = φ
Golden split
1 / φ
0.6180
φ²
2.6180
Choose your known value
Enter one known length
Pick what you already have and we will derive the rest.
Your golden ratio split
phi = (1 + square root of 5) / 2 ~= 1.6180339887
What is the golden ratio?
The golden ratio, also called the golden mean or golden section, is a proportion where the ratio of the longer segment (A) to the shorter segment (B) equals the ratio of the whole to the longer segment. In symbols, A / B = (A + B) / A. The constant that satisfies that relationship is called phi.
Phi is approximately 1.6180339887. This calculator assumes A / B = phi and uses phi and phi^2 to derive the missing lengths from a single input. You can enter a longer segment, a shorter segment, or the total length, and the calculator fills in the other two values plus the A/B ratio so you can confirm the split.
The golden ratio is widely discussed in art, design, architecture, and nature, but it is not a strict rule. Treat it as a helpful guideline when you want a dominant element and a supporting element to feel balanced, rather than a universal law.
Common uses
- Split a canvas or artboard into a focal and supporting zone
- Set card, image, or poster proportions quickly
- Establish spacing scales for layouts and typography
- Check product or furniture dimensions for balance
- Plan logo geometry and grid relationships
These uses are about proportioning, not decoration. The golden ratio is most useful when you need a consistent relationship between a larger area and a smaller one, such as two columns in a layout, a hero image with supporting text, or a product silhouette balanced against a base.
How to use this calculator
- Select which length you know: longer (A), shorter (B), or total (A + B).
- Enter the value and optionally choose a unit.
- Read the longer, shorter, total, and A/B ratio results.
The unit selector is a label only. If you enter 120 and choose cm, the calculator outputs results in cm. No unit conversions are performed.
Key formulas
Because A / B = phi and (A + B) / A = phi, you can derive the other lengths from any single value. This is exactly what the calculator does for the three modes.
- phi = (1 + square root of 5) / 2
- A = B * phi
- B = A / phi
- A + B = A * phi
- A + B = B * phi^2
Quick ratios
- phi ~= 1.6180
- phi^2 ~= 2.6180
- 1 / phi ~= 0.6180
- 1 / phi^2 ~= 0.3819
These values are rounded for readability. The internal calculation uses higher precision before rounding results to 4 decimals for display.
When to use
Use a golden ratio split when you want a dominant element and a supporting element to feel balanced. It is useful for spacing systems, card layouts, image crops, and product proportions.
It is not a requirement for good design. If usability, constraints, or brand rules suggest a different ratio, those should take priority. Think of the golden ratio as a starting point, not a mandate.
Worked example (known longer segment)
If the longer segment A = 100, then:
- Shorter segment B = 61.8034
- Total length A + B = 161.8034
- A / B ratio = 1.6180
Rounded to 4 decimals.
Worked example (known total length)
If the total length A + B = 200, then:
- Longer segment A = 123.6068
- Shorter segment B = 76.3932
- A / B ratio = 1.6180
Rounded to 4 decimals.
FAQ
Can I use any unit?
Yes. Units are labels only and no conversion is applied.
How do I check two lengths?
This calculator takes one input. To check two lengths, divide the longer by the shorter. If the result is close to 1.618, the split is near the golden ratio.
Why do results show 4 decimals?
Calculations use extra precision internally and display rounded values for readability.
Is the golden ratio a strict rule?
It is widely discussed in art, design, and nature, but evidence varies. Treat it as a useful guideline rather than a law.
Does this calculator draw a golden rectangle or spiral?
No. It focuses on proportional lengths only. You can use the outputs to build a rectangle or grid in your own design tool.
How accurate are the results?
Internally, calculations use high precision and then round to 4 decimals for display. If you need more precision, you can use the formulas in the Key formulas section.
Why phi is unique
If A / B = (A + B) / A, then dividing both sides by A gives 1 / (B / A) = 1 + (B / A). Let x = A / B. This produces x = 1 + 1 / x, which leads to x^2 = x + 1. The positive solution is phi.
This simple equation explains why phi shows up in so many proportional systems. It is the only ratio where the whole relates to the larger part the same way the larger part relates to the smaller part. That self-similarity is why designers use it to build consistent scales.
Golden ratio and Fibonacci numbers
The ratio of consecutive Fibonacci numbers approaches phi as the numbers get larger. For example, 55 / 34 and 89 / 55 are already close to 1.618. This is an approximation, not a proof that every Fibonacci pattern is perfectly golden.
If you are using Fibonacci numbers for layout or spacing, the golden ratio can help you understand why the scale feels consistent. This calculator does not generate Fibonacci sequences, but it gives the exact phi relationship those ratios approach.
How this calculator works
There are three modes. If you know the longer segment A, the calculator sets B = A / phi and total = A * phi. If you know the shorter segment B, it sets A = B * phi and total = B * phi^2. If you know the total A + B, it computes A = (A + B) / phi and B = (A + B) / phi^2.
The A/B ratio is always displayed so you can verify the relationship. Use this ratio as a quick check when you want to test whether a split is close to the golden ratio.
Practical guidance (without hype)
The golden ratio is a useful tool when you need a consistent proportion, but it does not guarantee a better design. Factors like readability, accessibility, brand requirements, and content hierarchy often matter more. If a different ratio fits those constraints, use it.
A good workflow is to start with a golden ratio split, then adjust visually or based on your system. The ratio is a starting point for exploration, not a rule you must follow.
Golden ratio glossary (related terms)
Golden rectangle
A rectangle whose side ratio is phi. This calculator does not draw a rectangle, but you can create one by using the longer side as A and the shorter side as B.
Golden spiral
A logarithmic spiral that grows by a factor of phi every quarter turn. This page does not generate a spiral, but your A and B values can set the scale of a golden rectangle that approximates it.
Golden mean / golden section
Alternative names for the golden ratio. You will see these terms in art, geometry, and design literature, all referring to the same proportion.
Divine proportion
A historical term for the golden ratio. It is culturally significant, but the calculator treats it as a practical numeric proportion, not a guarantee of beauty.
Phi (φ)
The constant value of the golden ratio, approximately 1.6180339887. It is the positive solution to x^2 = x + 1.
Ratio vs proportion
A ratio compares two parts (A/B). A proportion states that two ratios are equal, such as A/B = (A + B)/A.
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