Cube and Cube Root Calculator
Calculate a number's cube (n³) and cube root (∛n) together, with a perfect-cube check, a simplified radical form for whole numbers, and a step-by-step breakdown of both.
Input
Any real number — its cube and cube root are computed together.
Output
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/cube-and-cube-root-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"number": "8"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `cube-and-cube-root-calculator` tool (Cube and Cube Root 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/cube-and-cube-root-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Cube and Cube Root 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 Cube and Cube Root Calculator computes both directions at once: a number's cube (n³) and its real cube root (∛n) from a single input, plus a perfect-cube check, a simplified radical form for whole numbers, and a step-by-step breakdown of both operations.
It's built for students and teachers who want both answers side by side instead of running two separate calculators, or looking up one to check the other.
How to use it
- Enter any number — positive, negative, or zero. Cube roots of negative numbers are real, so there's no restriction.
- Read Cube (n³) for the number multiplied by itself three times, and Cube Root (∛n) for the real cube root.
- Check Perfect Cube? to see whether your input number is itself a perfect cube, and Simplified Radical Form for its cube root written in simplest terms.
- Step-by-Step Solution shows the arithmetic for both the cube and the cube root, plus the perfect-cube/simplification reasoning.
Results update automatically as you type. For example, entering 8 returns a cube of 512 and a cube root of 2 — since 8 is itself a perfect cube (2³), Perfect Cube? reads Yes and the simplified radical form is 2. Entering 72 instead returns a cube of 373248 and a cube root of 4.16017, with a simplified radical form of 2∛9.
Why compute both at the same time?
Cubing and cube-rooting are inverse operations, so checking one against the other is a common way to verify homework or a quick mental-math estimate: if ∛n rounds to a whole number k, then k³ should land back on (or very near) n. Running both from one input saves re-entering the number into a second calculator.
What is a perfect cube?
A perfect cube is a number that's the cube of an integer — 1, 8, 27, 64, 125, and so on (or their negatives, like -8 and -27). Its cube root is a whole number with no remaining radical. Any other number has an irrational cube root, which can only be approximated as a decimal or written in simplified radical form.
What does "simplified radical form" mean?
For a whole number that isn't a perfect cube, the cube root can often still be simplified by pulling the largest perfect-cube factor out from under the radical. For example, 72 = 8 × 9, and 8 is a perfect cube, so ∛72 = ∛8 × ∛9 = 2∛9 — a shorter, exact form instead of an infinite decimal. Numbers with no perfect-cube factor greater than 1 (like 9 or 10) are already in simplest form.
Only need the root by itself, with the two nearest bounding perfect cubes shown too? Use the Cube Root Calculator. Need a root of a different degree — square, fourth, fifth, or beyond? Use the Nth Root Calculator.
Privacy
This calculator runs entirely in your browser. Your number is never uploaded, logged, or stored — the computation happens locally on your device.