Torus Calculator
Calculate the volume, surface area, outer/inner radius and circumferences of a torus (donut shape) from its major radius (center to tube) and minor radius (tube radius).
Input
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/torus-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"unit": "cm",
"majorRadius": "5",
"minorRadius": "2"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `torus-calculator` tool (Torus 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/torus-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Torus 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
Enter the major radius (center of the torus to the tube's centerline) and the minor radius (the tube's own radius) and get the volume, surface area, outer/inner radius, and both circumferences in one pass.
What are major and minor radius?
Picture a donut lying flat. The major radius is the distance from the very center of the hole to the center of the ring of dough. The minor radius is the radius of the dough itself — half the thickness of the tube. Together they fully describe a standard "ring" torus (one where the tube doesn't overlap the center hole).
Formulas
For major radius R and minor radius r (with r < R):
Outer radius = R + r
Inner radius = R − r
Volume = 2 × π² × R × r²
Surface area = 4 × π² × R × r
Tube circumference = 2 × π × r (perimeter of the circular cross-section)
Centerline circumference = 2 × π × R (path traced by the tube's center)How to use it
- Choose a unit.
- Enter the major radius and the minor (tube) radius.
- Results update instantly as you type.
FAQ
Why does the minor radius have to be smaller than the major radius?
If the tube radius is greater than or equal to the major radius, the tube would overlap itself through the center — that's a different shape (a "horn" or "spindle" torus), not the standard donut these formulas describe.
What's the difference between outer/inner radius and the two circumferences?
Outer and inner radius are straight-line distances from the torus's center to its farthest and nearest points. Tube circumference is the distance around the tube's circular cross-section (like the seam on a rubber ring); centerline circumference is the distance around the whole donut, traced through the middle of the tube.
Privacy
Everything runs locally in your browser — nothing you enter is uploaded or stored anywhere.