Golden Ratio Calculator
Split a length into golden-ratio segments from its total, larger part, or smaller part — a/b = (a+b)/a = φ ≈ 1.618. Solve for whichever one value you know and get the other two, plus the ratio itself, at your chosen decimal precision.
Input
Pick the value you know; the other two are 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-ratio-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"solveFrom": "total",
"total": "10",
"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-ratio-calculator` tool (Golden Ratio 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-ratio-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Golden Ratio 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
The golden ratio (φ, "phi") splits a length into two segments — a larger part a and a smaller part b — so that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part: (a + b) / a = a / b = φ. That constant works out to an irrational number, φ ≈ 1.6180339887…, and it shows up everywhere from classical architecture and typography to photo composition and logo design because a split at that proportion tends to read as naturally balanced rather than arbitrary.
How to use it
- Pick which value you already know — the total length, the larger segment, or the smaller segment.
- Enter that one number. Units don't matter (mm, inches, pixels, percentages) — the ratio is the same regardless.
- 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 segment sizes.
The tool solves the other two segments plus the golden ratio itself, so you can sanity-check that a ÷ b really does land on 1.618…
The math
Because φ + 1 = φ², each mode reduces to a simple multiply or divide:
- From the total
T = a + b: larger segmenta = T / φ, smaller segmentb = T / φ². - From the larger segment
a: totalT = a × φ, smaller segmentb = a / φ. - From the smaller segment
b: larger segmenta = b × φ, totalT = b × φ².
Why 1.618 and not something rounder?
φ is the unique positive solution to x² = x + 1 — the only ratio where removing the smaller piece from the whole leaves a piece in the same proportion to what's left. That self-similar property is also why it's tied to the Fibonacci sequence: the ratio of consecutive Fibonacci numbers converges to φ as the numbers grow.
Can I use this for aspect ratios or design grids?
Yes — feed it a canvas width as the total and the larger segment gives you a golden-ratio column split (or crop point). If you're picking screen or print dimensions from a fixed ratio more generally (16:9, 4:3, or a custom width:height pair) rather than splitting a single length, use the Aspect Ratio Calculator instead. And since φ is the limit of the ratio between consecutive Fibonacci numbers, the Fibonacci Generator is a natural next stop if you want to see that convergence in the raw sequence.