Frustum Calculator
Calculate the volume, slant height, lateral surface area and total surface area of a conical frustum from its two base radii and height, with a step-by-step derivation.
Input
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/frustum-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"radius1": "5",
"radius2": "3",
"height": "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 `frustum-calculator` tool (Frustum 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/frustum-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Frustum 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 |
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Guides
The Frustum Calculator finds the volume, slant height, lateral surface area and total surface area of a conical frustum — a cone with the pointed tip sliced off flat, leaving two parallel circular faces of different sizes. It shows the exact formula substitution for every quantity, so you can follow (and check) the working, not just copy an answer.
It's built for students working through solid-geometry problems, and for makers, woodworkers, and engineers sizing tapered buckets, lampshades, funnels, silos, or any other truncated-cone shape.
How to use it
- Enter r1, the radius of the top (smaller) circular face.
- Enter r2, the radius of the bottom (larger) circular face. Use
0if one end comes to a point — the frustum then degenerates into a plain cone. - Enter h, the perpendicular height between the two faces.
- Pick how many decimal places to round the results to.
- Read Volume and Total Surface Area directly, or the Result table for those plus the slant height, lateral (side) surface area, and each base's area individually.
- Step-by-Step Derivation shows the formula substitution for every value.
All inputs must share the same unit (all inches, all meters, etc.) — the results come out in that unit, cubed for volume and squared for area. Results update automatically as you type. For example, r1 = 5, r2 = 3, h = 10 gives a volume of ≈513.13 and a total surface area of ≈363.12.
What are the formulas?
l (slant height) = √((r1 - r2)² + h²)
Volume = (π·h/3) · (r1² + r1·r2 + r2²)
Lateral surface area = π · (r1 + r2) · l
Total surface area = Lateral surface area + π·r1² + π·r2²The slant height comes from the Pythagorean theorem applied to the right triangle formed by the height, the difference in radii, and the slanted side. The volume formula reduces to the familiar cylinder formula (π·r²·h) when r1 = r2, and to the cone formula ((π·r²·h)/3) when either radius is 0 — both are just special cases of the same frustum.
r1 vs r2 — does it matter which is "top" and "bottom"?
No — the formulas are symmetric in r1 and r2, so swapping which face you call "top" and "bottom" gives identical results. The labels are only there to help you keep track of which measurement is which while entering data.
For a liquid-holding tank shaped like a frustum — with fill percentage and volume in liters or gallons — see the Water & Liquid Tank Volume Calculator.
Privacy
This calculator runs entirely in your browser. Your measurements are never uploaded, logged, or stored — the computation happens locally on your device.