Golden Rectangle Calculator
Calculate a golden rectangle's short side, long side, area, perimeter, and diagonal from any single known measurement — the short side, the long side, or the diagonal. A golden rectangle's sides are always in the golden ratio, φ ≈ 1.618.
Input
Pick the value you know; the rest of the rectangle is calculated from it.
Output
| Metric | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/golden-rectangle-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"solveFrom": "short",
"shortSide": "10",
"unit": "cm",
"precision": "4"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `golden-rectangle-calculator` tool (Golden Rectangle Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/golden-rectangle-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Golden Rectangle Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
Guides
A golden rectangle is a rectangle whose sides are in the golden ratio — the long side divided by the short side equals φ ("phi"), an irrational constant that works out to φ ≈ 1.6180339887…. Golden rectangles show up throughout classical architecture, typography, photo composition, and logo design because that particular proportion tends to read as naturally balanced rather than arbitrary. One well-known property: cut the largest possible square off a golden rectangle (the "golden gnomon") and the remaining piece is itself a smaller golden rectangle, in the same proportion — a subdivision you can repeat forever.
How to use it
- Pick which measurement you already know — the short side, the long side, or the diagonal.
- Enter that one number. Units don't matter for the ratio itself (mm, inches, pixels), but pick one so the area/perimeter/diagonal outputs carry the right label.
- Choose a decimal precision. φ is irrational, so more decimals means less rounding error if you're laying out a print piece or a UI grid to the calculated dimensions.
The tool derives the other side and reports the full rectangle: both sides, area, perimeter, diagonal, and the aspect ratio (which always comes back as φ ≈ 1.618, shown for confirmation).
The math
Because a golden rectangle's long side is always the short side times φ, each mode reduces to a simple multiply or divide:
- From the short side
s: long sidel = s × φ. - From the long side
l: short sides = l ÷ φ. - From the diagonal
d: sinced² = s² + l² = s²(1 + φ²), the short side iss = d ÷ √(1 + φ²).
From there: area = s × l, perimeter = 2(s + l), diagonal = √(s² + l²).
How is this different from a general rectangle calculator?
The Rectangle Calculator solves an arbitrary rectangle from any two known measurements and can tell you how close the result sits to golden — useful when you're checking an existing rectangle. This tool goes the other way: it builds the rectangle from φ directly, so you only ever need one measurement to get a guaranteed golden rectangle.
How is this different from the Golden Ratio Calculator?
The Golden Ratio Calculator splits a single length into two golden-ratio segments (a larger part and a smaller part) — useful for things like a golden-ratio crop line or column split. This tool treats the two golden-ratio quantities as the two sides of a rectangle and also reports area, perimeter, and diagonal, which a segment split doesn't have.