Golden Ratio Calculator
How it works
The golden ratio, φ, is (1 + √5) / 2 — approximately 1.618033988749895. A golden rectangle's longer side is always the shorter side multiplied by φ, so if you know the shorter side, the longer one is one multiplication away. If instead you know the longer side, the shorter one comes from dividing by φ, which undoes that same multiplication exactly.
Which of those two happens here depends only on which side you say you already have. Enter the shorter side and choose "Shorter side" to get the longer one back; enter the longer side and choose "Longer side" to get the shorter one back.
Frequently asked questions
What is the golden ratio actually used for?
It is a proportion — about 1 : 1.618 — that some designers and photographers reach for when a rectangle needs to feel balanced rather than square or stretched. A frame mat, a cropped photo panel or a layout column sized at that ratio is a common example; it is a starting point for pleasing composition, not a rule anything is required to follow.
What is φ, exactly, and why can't this show an exact answer?
φ = (1 + √5) / 2, which works out to approximately 1.618033988749895. It is an irrational number — its decimal expansion never ends or repeats — so any decimal shown for it, here or anywhere else, is necessarily a rounded approximation rather than the exact value.
How do the two solve directions relate to each other?
They are exact inverses of the same constant. Solving for the longer side multiplies the known dimension by φ; solving for the shorter side divides it by φ. Multiplying by a number and then dividing by that same number always cancels out, so going one direction and then the other returns you to where you started.