Golden Ratio Calculator

Worked example: splitting 100 and a 36-inch shelf

Choose Whole as the part you entered and type 100. The longer part is 61.803399 and the shorter part is 38.196601. The arithmetic is 100 divided by 1.618034, which gives 61.8034, and the shorter part is what is left: 100 minus 61.8034 is 38.1966. Divide 61.803399 by 38.196601 and you get 1.618034 again, which is the defining property of a golden section.

For something physical, enter a 36-inch wide shelf as the whole. The split point lands at 22.249224 inches from one end, leaving 13.750776 inches on the other side. In practice you would mark it at about 22 1/4 inches. If you enter 10 as the shorter part instead, the whole comes out as 26.18034, which is 2.618 times the shorter part. That is phi squared, and it equals phi plus 1.

Where designers actually use it

The length field has no unit, so pixels, inches and millimeters all work the same way. The most useful habit is deciding which part you already know before you start.

• Page layouts: a 1,200 px content area split as a whole gives a 741.64 px main column and a 458.36 px sidebar.
• Type scales: enter a 16 px body size as the shorter part and the longer part is 25.888544, so a heading of about 26 px follows the same ratio. Repeating the step gives a scale of 16, 26, 42 and 68 px.
• Photo and print layouts: on an 8.5-inch wide page, entering 8.5 as the whole puts the golden line about 5.25 inches from one edge.
• Furniture and framing: use the height of a cabinet or the width of a mat as the whole to place a shelf or a divider.

Ratios that get mistaken for golden

Plenty of everyday rectangles are close to 1.618 and plenty are not. A credit card (3.370 by 2.125 inches) is about 1.586 and a 5 by 3 index card is 1.667, both near the golden ratio. A US business card, 3.5 by 2 inches, is 1.75, and a 16:9 screen is 1.778, so both are noticeably wider. US Letter paper is only 1.294, and A4 paper uses 1.414, the square root of 2, which keeps the same shape when folded in half.

To test a rectangle, enter its long side as the longer part and compare the shorter part the tool returns with the real short side. A 3.5-inch card would need a short side of 2.163119 inches to be golden, so the actual 2 inches is a little short.

When you need whole-number dimensions, neighboring Fibonacci numbers are a good stand-in: 5 to 8 is 1.6, 8 to 13 is 1.625 and 13 to 21 is about 1.615.

A note of caution

A golden section splits a length at about 61.8 percent, which is not the same as a 60/40 split, although the difference is small enough that many layouts labeled golden are really just close. Check the longer part divided by the shorter part if you need to be exact.

Claims that the Parthenon or famous paintings were built on the golden ratio are widely repeated, but the result depends heavily on which points you choose to measure, and many are disputed. Treat the ratio as a useful starting point for proportion rather than a rule of beauty, and round the six-decimal results to whatever precision your material allows.