Sphere Calculator
Calculate a sphere's radius, diameter, circumference, surface area and volume from any single known value — enter one measurement and the other four are derived instantly.
Input
Pick the value you know; the other four are calculated from it.
Output
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/sphere-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"unit": "cm",
"precision": "2",
"solveFrom": "radius",
"radius": "5"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `sphere-calculator` tool (Sphere 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/sphere-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Sphere 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
Find every measurement of a sphere from just one known value. Pick "Solve from" and enter whichever of radius, diameter, circumference, surface area, or volume you already have — the calculator inverts the formula to find the radius first, then derives the rest.
Formulas
For a sphere with radius r:
Diameter = 2r
Circumference = 2πr (a great circle around the sphere)
Surface Area = 4πr²
Volume = (4/3)πr³To solve for the radius from a different known value, the calculator inverts each formula:
From diameter: r = d / 2
From circumference: r = C / 2π
From surface area: r = √(A / 4π)
From volume: r = ∛(3V / 4π)How to use it
- Pick a unit (millimeters, centimeters, meters, inches, feet, or yards) — it's a label on the results only; no unit conversion happens, so enter your value in the unit you want the results shown in.
- Choose how many decimal places to display.
- Pick which value you're solving from and enter it.
- Results update instantly as you type.
FAQ
What counts as a sphere's "circumference"?
The distance around a great circle — a circle passing through the sphere's center, like the equator on a globe. Every great circle on a sphere has the same circumference, 2πr.
Does the unit dropdown convert my measurement?
No. It only labels the output — surface area is shown in squared units (e.g. cm²) since it measures a two-dimensional surface, volume in cubed units (e.g. cm³) since it measures a three-dimensional space, and every other result stays in the plain unit you entered.
What if I enter a negative, zero, or blank value?
The calculator requires a positive value for whichever measurement it's solving from — a blank, zero, or negative entry is flagged with a validation message asking for a value greater than 0, rather than silently returning a result.
What if I need a different 3D shape?
For a cylinder, cone, or cube, see the Volume & Surface Area Calculator. For circles and ellipses (2D shapes), use the Circle & Ellipse Calculator.
Privacy
Everything runs locally in your browser — nothing you enter is uploaded or stored anywhere.