About the Golden Ratio Calculator
Golden Ratio Calculator splits a length into two parts that are in the golden ratio, about 1 to 1.618. Enter any one of the three numbers, the longer part, the shorter part or the whole length, and the page gives the other two so that the whole divided by the longer part equals the longer part divided by the shorter part. Designers use it for layouts, logos, photo crops and typography, and it is also a popular topic in maths. Enter the length in any unit: centimetres, inches or pixels.
Updated October 2026
How to use the Golden Ratio Calculator
- 1Choose which length you already know: the longer part, the shorter part or the whole.
- 2Type the length in any unit.
- 3Read the other two lengths.
- 4Use the values in your layout, drawing or crop.
- 5Copy the result.
The idea in one picture
Take a line and cut it into a long part and a short part so that the whole line compared with the long part is the same ratio as the long part compared with the short part. That ratio is φ, about 1.618. It is the only ratio with this property, and it has the neat feature that φ squared equals φ plus 1.
Using it in design
Designers use the ratio to choose proportions that feel balanced. A page 1,000 pixels wide can have a main column of 618 pixels and a sidebar of 382. A photo cropped to 1.618 to 1 is close to a golden rectangle. Logos and typography scales use it too. Treat it as a starting point and trust your eyes.
- Layout: 61.8% content and 38.2% sidebar
- Type: scale headings by 1.618 steps
- Photos: crop to a 1.618 to 1 frame
- Furniture and shelves: choose a long and short side
Maths and Fibonacci
The sequence 1, 1, 2, 3, 5, 8, 13, 21 makes ratios 1, 2, 1.5, 1.667, 1.6, 1.625, 1.615, which tend towards φ. This is why the ratio shows up in spirals, in the arrangement of seeds and in many puzzles.
Related tools
Explore the sequence with the Fibonacci Calculator, work with proportions in the Ratio Calculator and the Aspect Ratio Calculator, and make matching colours with the Color Palette Generator.
Features
- Start from the long part, short part or whole
- All three lengths shown
- Shows the ratio to six decimals
- Any unit
- Instant result
- Private: nothing is uploaded
Frequently asked questions
What is the golden ratio?
About 1.6180339887, written φ (phi). Two lengths are in the golden ratio when the whole is to the longer part as the longer part is to the shorter part.
What is the formula?
φ = (1 + √5) / 2. If a is the longer part and b is the shorter part, a / b = φ and (a + b) / a = φ.
How do I find the shorter part from the longer?
Divide the longer part by 1.618. For example 10 gives 6.18.
How do I split a total in the golden ratio?
Multiply the total by 0.618 to get the longer part, and take that away from the total to get the shorter part.
Is the golden ratio really found in nature and art?
It appears in some plants and shells in approximate form, and designers use it, but many claims about it in famous art and in the human body are exaggerated. Use it as a pleasing guide, not a law.
How is it related to Fibonacci numbers?
The ratio of two neighbouring Fibonacci numbers gets closer and closer to the golden ratio: 8/5 = 1.6, 13/8 = 1.625 and 21/13 = 1.615.
What is a golden rectangle?
A rectangle whose sides are in the golden ratio, such as 161.8 by 100. If you cut a square off it, the rest is another golden rectangle.
Is anything uploaded?
No. It runs in your browser.