๐ Golden Ratio Calculator: Phi (1.618) Dimensions and Proportions
By Shihab Mia ยท Updated 2026-07-18
Enter one measurement and choose what it represents. The calculator splits it into the longer and shorter parts so that longer divided by shorter equals phi (about 1.618).
phi = (1 + sqrt 5) / 2 = 1.6180339887. Results are rounded for display; the ratio is kept exact internally.
This golden ratio calculator splits any length into two parts in the proportion phi (about 1.618): enter one number, tell it whether that number is the longer part, the shorter part, or the whole, and it instantly returns the other parts. For example, a whole of 100 splits into a longer part of 61.803399 and a shorter part of 38.196601, and dividing 61.8 by 38.2 gives 1.618 again. Use it to size layouts, type scales, golden rectangles, and photo crops in a proportion many people find naturally balanced.
What is the Golden Ratio Calculator?
The golden ratio is an exact number, not a rough rule of thumb. It equals (1 + sqrt 5) divided by 2, which works out to 1.6180339887 and continues forever, so it is irrational like pi. It is usually written with the Greek letter phi. A line is divided in golden proportion when the longer segment a and the shorter segment b satisfy a / b = (a + b) / a. Both of those fractions equal phi, which is what makes the proportion self-similar: the relationship between the two parts is the same as the relationship between the larger part and the whole. This golden ratio calculator solves that relationship in any direction, so you can start from a known longer part, shorter part, or total and get the rest.
A neat property falls out of that definition. Because (a + b) / a = phi, the whole is always the longer part multiplied by phi. And because a / b = phi, the longer part is the shorter part multiplied by phi. So moving up the scale you multiply by 1.618 each step, and moving down you divide by 1.618. That is why a string of golden measurements (for example 1, 1.618, 2.618, 4.236) feels like a smooth progression: each term is phi times the one before, the same growth pattern seen in the Fibonacci sequence, whose consecutive ratios close in on phi. Divide any Fibonacci number by the one before it (for example 89 / 55 = 1.61818) and you land close to the golden ratio, getting closer the higher you go.
A golden rectangle is the most common shape this calculator feeds. It is a rectangle whose longer side divided by its shorter side equals phi, so a 1000 px wide golden rectangle is about 618 px tall. Its special feature is that if you slice off a square from one end, the piece left over is another, smaller golden rectangle with the same proportions, and repeating that cut traces the corners of the golden spiral. Designers use the golden ratio and golden rectangles as a starting proportion for page layouts, logo grids, card sizes, and spacing scales. In typography, multiplying a base font size by 1.618 (for example 16 px body text to about 26 px headings) produces a mathematically consistent type scale without guesswork.
In photography and composition the golden ratio shows up as the phi grid, an alternative to the rule of thirds. The rule of thirds divides a frame at one third and two thirds (0.333 and 0.667), while the phi grid divides it at 0.382 and 0.618, slightly closer to the centre. Placing a subject, horizon, or focal point on those golden divisions tends to read as calmer and more classical, while the rule of thirds reads a touch more dynamic. You can use this golden ratio calculator to find exactly where the phi lines fall on any image width or height: for a 1920 px wide photo the golden divisions sit at about 733 px and 1187 px.
One honest caveat: the golden ratio is a helpful proportion, not a law of good design. The popular claims that phi appears everywhere in nature, art, and the human body are frequently overstated, and many admired designs ignore it entirely. Facial golden ratio scoring, which compares distances between the eyes, nose, and chin against 1.618, is a novelty rather than a measure of real beauty or health. Treat phi as one useful proportion in your toolkit: enter a width, margin, or total size, choose which role that number plays, and let the calculator hand you the matching golden parts to work from and adjust by eye. For the underlying mathematics, see Wolfram MathWorld's entry on the golden ratio (https://mathworld.wolfram.com/GoldenRatio.html).
When to use it
- Splitting a page or canvas into a larger and smaller region (for example a content column and a sidebar) in golden proportion so the two areas relate by phi.
- Building a type scale or spacing scale where each step is 1.618 times the last, turning a 16 px base into a harmonious 26 px, 42 px, 68 px heading rhythm.
- Sizing a golden rectangle for a card, logo, or frame so its width divided by its height equals 1.618 for a balanced look.
- Placing a subject on the phi grid (the 0.382 and 0.618 divisions) when cropping or framing a photo, as an alternative to the rule of thirds.
- Stepping a measurement up or down a golden scale by feeding the longer part back in to grow the sequence, mirroring Fibonacci growth.
- Setting margins and gutters in a layout so the printed or negative space relates to the content block by the golden ratio.
How to use the Golden Ratio Calculator
- Enter the one measurement you already know, such as a total width, a column width, or a single segment length.
- Choose what that number represents: the longer part, the shorter part, or the whole (longer plus shorter).
- Read off the longer part, the shorter part, and the whole, all in golden proportion, in the same unit you entered.
- Apply the parts as your dimensions, or feed the longer part back in as a new whole to step the scale up or down again.
Formula & method
Worked examples
You have a total width of 100 px and want to split it into golden proportion.
- The value is the whole, so total = 100.
- Longer part a = total / phi = 100 / 1.6180339887 = 61.803399
- Shorter part b = total - a = 100 - 61.803399 = 38.196601
- Check: a / b = 61.803399 / 38.196601 = 1.618034 (phi)
Result: Longer 61.803399, shorter 38.196601, which add back to 100.
You know the longer part is 50 and want the matching shorter part and whole.
- The value is the longer part, so a = 50.
- Shorter part b = a / phi = 50 / 1.6180339887 = 30.901699
- Whole = a x phi = 50 x 1.6180339887 = 80.901699 (also a + b)
- Check: a / b = 50 / 30.901699 = 1.618034 (phi)
Result: Shorter 30.901699, whole 80.901699.
You are designing a golden rectangle and know the shorter part is 10.
- The value is the shorter part, so b = 10.
- Longer part a = b x phi = 10 x 1.6180339887 = 16.180340
- Whole = b x phi^2 = 10 x 2.618034 = 26.180340 (also a + b)
- Check: a / b = 16.180340 / 10 = 1.618034 (phi)
Result: Longer 16.180340, whole 26.180340. A rectangle 16.18 by 10 is a golden rectangle.
You want a golden type scale from a 16 px base font size.
- Treat 16 as the shorter part and step up: 16 x 1.618034 = 25.888544, round to about 26 px.
- Step up again: 25.888544 x 1.618034 = 41.887902, round to about 42 px.
- Step up once more: 41.887902 x 1.618034 = 67.770252, round to about 68 px.
Result: A four-step golden type scale of roughly 16, 26, 42, and 68 px.
Powers of phi: each step multiplies the one before by 1.618
| Expression | Value | Meaning |
|---|---|---|
| phi^0 | 1.000000 | Starting unit |
| phi^1 | 1.618034 | One golden step up |
| phi^2 | 2.618034 | Two steps (also phi + 1) |
| phi^3 | 4.236068 | Three steps |
| phi^4 | 6.854102 | Four steps |
| 1 / phi | 0.618034 | One golden step down (the shorter share of 1) |
Splitting a whole into golden parts (longer plus shorter)
| Whole | Longer part (a) | Shorter part (b) |
|---|---|---|
| 10 | 6.180340 | 3.819660 |
| 100 | 61.803399 | 38.196601 |
| 720 | 444.984472 | 275.015528 |
| 960 | 593.310424 | 366.689576 |
| 1000 | 618.033989 | 381.966011 |
| 1920 | 1186.625614 | 733.374386 |
Phi grid vs rule of thirds: where the composition lines fall
| Frame width | Rule of thirds (0.333, 0.667) | Phi grid (0.382, 0.618) |
|---|---|---|
| 1080 px | 360, 720 | 413, 667 |
| 1920 px | 640, 1280 | 733, 1187 |
| 3000 px | 1000, 2000 | 1146, 1854 |
Common mistakes to avoid
- Using 1.6 instead of 1.618. Rounding phi to 1.6 is close but not exact, and small errors compound when you step a scale several times. Use 1.618 (or more digits) for anything that has to add back up cleanly.
- Mixing up which part the longer ratio applies to. The longer part divided by the shorter equals phi, not the other way round. If your shorter part comes out bigger than the longer one, you have divided in the wrong direction.
- Forgetting the parts must sum to the whole. The longer and shorter parts always add up to the total. If you size two regions independently and they do not sum to your canvas, they are not in true golden proportion to the whole.
- Confusing the phi grid with the rule of thirds. The golden divisions sit at 0.382 and 0.618, not at one third and two thirds (0.333 and 0.667). They look similar but land in slightly different places, so pick one grid and stay consistent.
- Building a golden rectangle by adding instead of dividing. A golden rectangle height is the width divided by phi, not the width minus some fixed amount. For a 1000 px width the height is 618 px, and subtracting a flat margin will not give the right proportion.
- Treating the golden ratio as a rule that guarantees good design. Phi is a helpful starting proportion, not a guarantee. Context, content, and balance matter more, so use it as a guide and adjust by eye.
Glossary
- Golden ratio
- The proportion in which the longer part divided by the shorter equals the whole divided by the longer, about 1.618.
- Phi
- The Greek letter naming the golden ratio, equal to (1 + sqrt 5) / 2 = 1.6180339887.
- Golden section
- A line divided so the two segments are in the golden ratio; another name for the split this tool produces.
- Golden rectangle
- A rectangle whose longer side divided by its shorter side equals phi, so cutting off a square leaves a smaller golden rectangle.
- Golden spiral
- A logarithmic spiral that grows by a factor of phi every quarter turn, traced through nested golden rectangles.
- Phi grid
- A composition grid dividing a frame at 0.382 and 0.618, a golden-ratio alternative to the rule of thirds.
- Longer part (a)
- The bigger of the two segments. It equals the shorter part times phi and the whole divided by phi.
- Fibonacci sequence
- The series 1, 1, 2, 3, 5, 8, 13 and so on, where the ratio of each term to the previous one closes in on phi.
Frequently asked questions
What is the golden ratio?
The golden ratio is the number phi, about 1.618, where two lengths relate so the longer divided by the shorter equals the whole divided by the longer. Exactly, phi = (1 + sqrt 5) / 2 = 1.6180339887.
How do I calculate the golden ratio of a number?
Decide whether your number is the longer part, the shorter part, or the whole. To split a whole into golden parts, the longer part is the whole divided by 1.618 and the shorter part is what remains. This golden ratio calculator does all three cases for you.
What is phi exactly?
Phi is (1 + the square root of 5) divided by 2. Written out that is 1.6180339887 and the digits continue forever, so it is an irrational number, much like pi.
How do I make a golden rectangle?
Divide the width by phi to get the height. For a width of 1000 the height is about 618, so a 1000 by 618 rectangle is a golden rectangle where width divided by height equals 1.618.
How is the golden ratio related to Fibonacci numbers?
In the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13 and so on) each number is the sum of the two before it. As the numbers grow, the ratio of one term to the previous one gets closer and closer to phi, so 89 divided by 55 is already 1.6182.
What is 1 divided by phi?
1 divided by phi is about 0.618, which also equals phi minus 1. If you split a length of 1 in golden proportion, the longer part is 0.618 and the shorter part is 0.382, and 0.618 divided by 0.382 is again 1.618.
What is the difference between the phi grid and the rule of thirds?
The rule of thirds divides a frame at 0.333 and 0.667, while the phi grid divides it at 0.382 and 0.618, slightly closer to the centre. The phi grid tends to read as calmer and more classical, and the rule of thirds a touch more dynamic.
How do I use the golden ratio for font sizes?
Multiply your base font size by 1.618 for each step up. Starting from 16 px body text gives headings of about 26, 42, and 68 px, producing a consistent golden type scale.
Is the golden ratio actually used in design?
Yes, designers often use it as a starting proportion for layouts, type scales, logos, and crops. It is a guide rather than a strict rule, and many good designs do not rely on it, so treat it as one useful tool.
Does the golden ratio really appear everywhere in nature and the human face?
Not as often as popular claims suggest. Some spirals and growth patterns approximate phi, but many famous examples are cherry-picked or measured loosely, and facial golden ratio scores are a novelty rather than a real measure of beauty.