Use the free Cube Root Calculator below: your data never leaves your browser — all work happens on your device, and nothing is uploaded to any server.
What This Calculator Does
A cube root calculator finds the number that, multiplied by itself three times, gives your number. The cube root of 27 is 3, because 3 times 3 times 3 is 27. The cube root of negative 27 is negative 3, because negative 3 cubed is negative 27. Unlike square roots, cube roots work for negative numbers too, because three negatives multiply to a negative. Cube roots undo cubing, and they appear in volume problems, scaling problems, and algebra wherever a quantity depends on a cube.
This tool tells you whether your number is a perfect cube, meaning its root is a whole number, and if not, it shows the two nearest perfect cubes that bracket it. For example, 30 is not a perfect cube, but it sits between 27 (3 cubed) and 64 (4 cubed), so its root sits between 3 and 4, at about 3.107. The tool also checks its answer by cubing the root. That check matters, because cube roots of non-perfect cubes are irrational decimals that are easy to mistype.
How to Use It
Type any number, positive, negative, or zero, and click Calculate. Zero gives zero. Positive numbers give positive roots. Negative numbers give negative roots, which is correct and expected for cube roots. If your school problem says to give only real roots, this tool’s answer is the real root. If it asks for complex roots, remember that every non-zero number actually has three cube roots in complex numbers, but only one of them is real, and that is the one this tool shows.
Perfect Cubes and Scaling, Explained
Perfect cubes are the cubes of whole numbers: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, and so on. They grow fast, which is why cube roots are useful for scaling. If you double the side of a cube, its volume grows eight times, because 2 cubed is 8. Conversely, if a tank’s volume grows eight times, its side only doubles. That is the cube root at work. Engineers use this when scaling models: a model one tenth the size of the real thing has one thousandth of the volume, because one tenth cubed is one thousandth.
A Worked Example
Suppose a cubic box holds 125 litres. Its side is the cube root of 125, which is 5 units, because 5 cubed is 125. Now suppose a box holds 200 litres. Its side is about 5.848 units, because 5.848 cubed is about 200. If you want a box with double the volume of the 125-litre box, you need 250 litres, and the side is the cube root of 250, about 6.3 units, not 10. Doubling the side would give eight times the volume, not double. That surprise is exactly why cube roots matter in design and packaging.
Common Mistakes
The most common mistake is thinking a negative number has no cube root. It does, and it is negative. That rule belongs to square roots, not cube roots. Another mistake is confusing cube roots with dividing by three: the cube root of 27 is 3, but 27 divided by 3 is 9, a different number. A third mistake is rounding the root and then cubing the rounded value to check, which gives a slightly different number. Small differences after rounding are normal; large ones mean an error. Keep extra digits until the last step.
Frequently Asked Questions
What is the cube root of 0? Zero. What is the cube root of 1? One. What is the cube root of negative 8? Negative 2, because negative 2 cubed is negative 8. How is a cube root different from a square root? A square root asks what number times itself gives the value; a cube root asks what number times itself three times gives the value. Are cube roots ever fractions? Yes. The cube root of 1/8 is 1/2, because one half cubed is one eighth.
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