Golden Ratio Calculator

Begin with the dimension you can actually measure

A 960 px cover can be divided into roughly 593.31 px and 366.69 px. That is useful when the full width is fixed. A different job may begin with a 360 px sidebar and ask for the matching main panel and total canvas. The three modes handle these different starting points without asking you to rearrange the equations yourself.

The whole relates to the larger part as the larger part relates to the smaller one. If a is larger than b, then (a + b) / a = a / b = φ. Phi has the exact value (1 + √5) / 2 and is approximately 1.6180339887. Its digits do not terminate or settle into a repeating block.

The golden ratio formula changes with the known measurement:

• Known total T: larger a = T / φ and smaller b = T / φ².
• Known larger part a: total T = a × φ and smaller b = a / φ.
• Known smaller part b: larger a = b × φ and total T = b × φ².

The two sections occupy about 61.803% and 38.197% of the whole. A quick verification is to compare a / b with (a + b) / a; both should be close to phi. The calculator keeps the unit you supply. Enter inches and read every result as inches, or enter pixels and read pixels. It does not perform a unit conversion.

Rounding turns an ideal proportion into a buildable size

CSS allows fractional pixel lengths; they do not have to be rounded to whole numbers. A CSS pixel is not necessarily one physical device pixel. If your export format needs whole-pixel dimensions, round at that final step. The 960 px example can become 593 px and 367 px while preserving the total. A cabinet panel or printed sheet may need tenths of a millimetre instead. Rounding both parts too early can create a gap or push their sum beyond the available width.

The displayed result uses up to four decimal places for ordinary measurements. Results below 0.0001 or at least 10¹² use scientific notation. Both copying and sharing use the displayed, rounded values. Phi and the arithmetic have the finite precision of JavaScript numbers, not unlimited decimal precision. For fabrication, choose a unit that keeps the required precision visible and apply the material’s tolerance at the final step.

Enter a positive value such as 1200.5 or 1,200.5, without spaces between digits. Scientific notation such as 1e3 is not accepted as input. Zero, negative values and results too small or large to preserve a reliable ratio are rejected. Switching tabs reinterprets the same input as a total or a part; it does not convert units.

Use phi as a constraint, not an aesthetic verdict

Ratios between neighbouring Fibonacci numbers move towards phi as the sequence grows. The fractions 13 / 8, 34 / 21 and 89 / 55 give about 1.625, 1.61905 and 1.61818. They are increasingly close, but no finite pair is exactly equal to the irrational constant.

A rectangle with long side divided by short side equal to φ is a golden rectangle. Removing a square leaves another rectangle with the same proportion. Quarter-circles drawn through the nested squares create the familiar golden spiral diagram; it is an approximation rather than the exact logarithmic curve seen in the mathematical definition.

A golden ratio calculator can suggest column widths, a type scale, spacing or an image crop. It cannot judge whether the sidebar has enough room for its text or whether the type remains readable on a phone. Test the calculated split against the real content and breakpoint before committing to it.

Placing a spiral over a photograph of a building or face does not establish that its proportions were deliberately chosen. That claim needs measurements and documentation beyond a calculator result. The result here establishes a numerical relationship between measurements; it does not certify beauty, historical intent or a natural law.