Enter a width and height — the calculator returns the phi divisions at 38.2% and 61.8%, the golden-section crop points, and the nearest root rectangle, with a live preview. A free PhiMatrix alternative.
The Golden Ratio Calculator takes any width and height and returns the golden divisions — the lines at 38.2% and 61.8% along each side where phi, about 1.618, splits the frame. It also names the nearest root rectangle and the exact dimension for a perfect golden rectangle, then opens the live overlay on your own image.
How phi divisions work — three steps
The golden ratio splits a length so the whole is to the larger part as the larger part is to the smaller. In an image that lands at 38.2% and 61.8% along each axis.
1
Enter dimensions
Type the width and height of your photo, canvas, page, or logo box in any unit. The proportions are the same whatever the unit.
2
Read the divisions
The calculator multiplies each side by 0.382 and 0.618 to find the golden lines, marks the four intersections, and names the nearest root rectangle.
3
Overlay and compose
Open the Golden Ratio overlay on your own reference and align your focal point to a golden intersection.
What this calculator gives you that a number alone cannot
Phi is one number. Using it on a real image means turning that number into division lines, crop points, and a proportion class — which is what this calculator draws.
Both axes, both lines
The 38.2% and 61.8% divisions for width and height, in your unit — ready to mark on a canvas or a digital file.
Golden-section crop points
The four intersections where the golden lines cross — the phi equivalent of the rule-of-thirds power points.
Nearest root rectangle
Whether your frame is closest to root-2, phi, root-3, or root-5 — so you can pick the matching dynamic-symmetry overlay.
Make it a golden rectangle
The exact height or width that would turn your dimensions into a true golden rectangle, if you want to resize the frame.
Live preview
A drawing of your exact aspect ratio with the golden lines, spiral guide, and intersection dots — updated as you type.
One click into the tool
Open the same golden ratio as a live overlay on your reference image, free, with no signup and no watermark.
From the field·Three users
How people use the calculator
A photographer, a muralist, and a logo designer on where the phi divisions earn their keep.
I crop to the golden section when thirds feels too loose. The calculator gives me the exact pixel lines so I can set guides in Lightroom precisely.
— Elena Fors · landscape photographer, Bergen
For a wall I enter the real centimetres and mark the golden lines with chalk. No licence, no app to install — it just gives me the numbers.
— Hassan All · muralist, Cairo
Logo work lives and dies on proportion. I check the bounding box against phi here before committing to a construction grid.
— Greta Lim · brand designer, Singapore
Phi, in plain terms — and a free way to use it
The golden ratio has a long history and a simple definition. Here is what the calculator is actually computing, and how it compares to the paid tools.
Phi (φ) is the number, roughly 1.618, that satisfies a single condition: divide a line into two parts so that the whole length is to the longer part exactly as the longer part is to the shorter. Euclid wrote it down around 300 BC as a line cut "in extreme and mean ratio"; Luca Pacioli called it the divine proportion in 1509. The same number appears as the limit of the Fibonacci sequence, which is why the two ideas are taught together — see the golden ratio glossary entry and the Fibonacci and phi guide for the full derivation.
On an image, the practical consequence is small but specific: the golden division of a side falls at 0.382 and 0.618 of its length, slightly closer to the centre than the rule-of-thirds lines at one third and two thirds. That is the entire difference in placement between the two systems, and it is why the golden ratio reads as calmer and more classical while thirds reads as a touch more dynamic. The golden ratio in art and photography pillar walks through worked examples.
The proportion is not magic, and it is not a guarantee of beauty. It is a reliable place to put the important thing — slightly off centre, in a way the eye has been trained by centuries of pictures to find restful.
— Grid Maker Pro studio notes
The best-known dedicated golden-ratio tool, PhiMatrix, is a paid desktop overlay. Grid Maker Pro covers the same ground — phi grid, golden spiral, golden triangles, and the root rectangles of dynamic symmetry — free and in the browser.
The golden ratio, written with the Greek letter phi, is approximately 1.618. A line is divided in the golden ratio when the whole is to the longer part as the longer part is to the shorter — that is, (a+b)/a = a/b. It was defined by Euclid around 300 BC. In images, the golden divisions fall at about 38.2% and 61.8% along each side. See the glossary entry for the full definition.
How do you calculate the golden ratio of an image?
Multiply each dimension by 0.382 and by 0.618 to get the two golden division lines along that axis. The four points where the vertical and horizontal lines cross are the golden-section intersections — the phi equivalent of the rule-of-thirds power points. This calculator does that arithmetic and draws the result live.
Is this a free alternative to PhiMatrix?
Yes. PhiMatrix is a paid golden-ratio overlay application. This calculator, and the live Golden Ratio overlay in Grid Maker Pro, are free with no signup and no watermark, and they run in any browser — phi grid, golden spiral, golden triangles, and root rectangles without a licence.
What is a golden rectangle?
A golden rectangle is one whose long side divided by its short side equals phi, about 1.618. Remove a square from it and the remaining rectangle is also golden — which is what generates the golden spiral. The calculator tells you whether your dimensions form a golden rectangle and, if not, the exact height or width that would make them golden.
What are root rectangles?
Root rectangles are the proportions used in dynamic symmetry: root-2 (about 1.414), root-3 (1.732), root-4 (2.0), and root-5 (2.236), alongside the golden rectangle phi (1.618). The calculator reports which your image is closest to, so you can choose the matching dynamic-symmetry overlay.
Golden ratio or rule of thirds — which should I use?
The rule of thirds places interest at one-third lines and is quick and forgiving; the golden ratio places it slightly closer to centre, at phi, for a calmer, more classical balance. Many photographers use thirds for speed and the golden ratio for a more deliberate feel. You can switch between both overlays on the same image in the tool.
Does the calculator change with units?
The phi divisions are proportional, so the percentages are identical in any unit. The calculator reports the division lines in whatever unit you enter — pixels, centimetres, or inches — so you can mark them on a digital canvas or a physical surface.
Do my image dimensions get uploaded anywhere?
No. The calculator runs entirely in your browser. Nothing you type is sent to a server, and when you open the overlay your reference image is processed locally too — it never leaves your device.
Can I use this for canvas sizing, not just photos?
Yes. Painters, muralists, and designers use it to find golden divisions on a physical canvas, a wall, a page layout, or a logo box. Enter the real dimensions in centimetres or inches and mark the returned division lines on the surface.
A free PhiMatrix alternative
Compose with phi
Free forever. No signup. The golden ratio overlay opens on your own image, processed entirely on your device.
Built by Sarah Chen
Founder and lead developer, Grid Maker Pro. Fine-arts background, self-taught developer. Built Grid Maker Pro in 2019 to put every classical construction method into one free browser tool. Read our methodology for how each overlay was derived.
Page last updated: 1 June 2026 · Golden Ratio Calculator version 2026.6
