The golden ratio, explained simply

What the golden ratio is

Take a line and cut it into two pieces, a longer one a and a shorter one b. The cut is in the golden ratio when the whole line divided by the longer piece equals the longer piece divided by the shorter piece:

Solving that gives a single value, written with the Greek letter phi:

It is an irrational number, so the decimals never end or repeat. In practice, 1.618 is plenty.

How to split a length in the golden ratio

Divide the total by φ to find the longer part. The shorter part is whatever is left.

Check it: 61.8 ÷ 38.2 = 1.618. If you know only the shorter piece, multiply it by 1.618 to get the longer one.

The golden rectangle

A golden rectangle has sides in the ratio 1.618 : 1. If the shorter side is 618 pixels, the longer is about 1000. Or the other way round: a 1000-pixel-wide banner in a golden rectangle would be 1000 ÷ 1.618 ≈ 618 pixels tall.

The Fibonacci connection

The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13, 21, 34, and each number is the sum of the two before it. Divide each number by the one before and the answers close in on φ:

The ratios swing above and below 1.618 and get closer each time. That is the neat link between the sequence and the ratio.

Using it in design, with some honesty

Designers use the golden ratio as a starting point, not a rule. A few sensible uses:

• Layouts: a main column about 61.8% wide and a sidebar 38.2% wide.
• Type scale: a heading around 1.618 times the body size, so 16 px body text pairs with a heading of about 26 px.
• Picture frames and crops: a 1.618 : 1 rectangle is close to a 3 : 2 photo, so it often feels natural.

You will also read that the Parthenon, the Mona Lisa and nautilus shells are built on the golden ratio. Many of those claims are loose or measured selectively. A nautilus spiral, for example, is a different kind of spiral and does not match φ. Treat the golden ratio as a pleasant proportion that is worth knowing, not a secret behind all beauty.

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