Golden ratio calculator: from a width to a picture size.

What each number means

Picture width is the width of the furniture divided by 1.618, which is about 60 percent — the size at which a picture belongs to the sofa or bed beneath it instead of floating above it. For an empty wall the calculator gives two numbers: the largest picture the wall wants (width ÷ 1.618) and a comfortable minimum (÷ 1.618 again). Choose toward the larger; almost everyone chooses too small.

Height at golden proportions is the picture width divided by 1.618 for a landscape format, or multiplied by it for a portrait format — the two golden rectangles that fit that width. Real prints come in standard sizes, so the last row rounds to the nearest of them; the guide on picture sizes for every room has the full table.

The golden section from the left and right is the point 38 percent in from either edge, which is where the centre of a single picture goes on a wall that has a feature — a window, a fireplace — pulling the eye to one side, and where the subject of a composition goes inside the frame. The two values add up to the width; pick the one that leaves the larger empty area on the side that deserves it.

The Fibonacci unit is the width divided by 13. Lay out squares of 1, 1, 2, 3, 5 and 8 units and they fill a 13 × 8 rectangle exactly; the spiral through their corners is the golden spiral, and the largest square (8 units) is where the main subject sits in the geometric works here. If you want to check one of them, print it, measure the largest square and the next, and divide: you will get 1.6 and change.

The arithmetic, if you want it

The golden ratio is (1 + √5) ÷ 2 = 1.6180339887… Its reciprocal is 0.618, and 1 − 0.618 = 0.382, which is why the golden section is at 38 and 62 percent. A golden rectangle is 1.618 to 1; cut a square from it and the remainder is another golden rectangle. The numbers in this calculator are those three operations — divide by 1.618, multiply by 1.618, multiply by 0.382 — applied to whatever you type.

From the number to the wall

Once you have the picture width, the hanging guide gives the height — centre at 150 cm on a bare wall, 15 to 25 cm above furniture — and the printing guide covers paper and surfaces. Every download on this site prints sharp at the sizes the calculator produces, up to about 150 cm on the long side. If you would rather see it than calculate it, send a photograph of the wall and its width and you will get three works shown in place at the size the wall wants.