Cube Root Calculator
Cube Root Calculator
Enter any number to find its cube root. Unlike square roots, cube roots are defined for negative numbers too — this calculates the real cube root for any input and flags whether your number is a perfect cube.
The cube root of −27 is exactly −3, since (−3)³ equals −27 — a real result exists here because multiplying three negative numbers together (an odd count) produces a negative result, unlike squaring where an even number of negative factors always turns positive. This distinction is why square roots of negative numbers require imaginary numbers while cube roots don't, and it's a useful fact whenever solving equations that involve cubing, like finding the side length of a cube from its volume.
- Definition: ∛x is the value that, multiplied by itself three times, equals x.
- Works for negative numbers, unlike square roots: the cube root of −27 is −3 (since (−3)³ = −27) — a real result exists because an odd number of negative factors multiplies to a negative number.
- Perfect cubes have whole-number roots: numbers like 8, 27, 64, and 125 have cube roots that are themselves whole numbers.
Why does the cube root of a negative number have a real answer, unlike the square root?
Cubing a negative number keeps the result negative (since you multiply three negatives together, and the product of three negative numbers is negative), so a real number can always satisfy x³ = negative value — that's not true for squaring, where the result is always positive.
How can I quickly check if a number is a perfect cube?
Compare it to the cubes of small whole numbers (1, 8, 27, 64, 125, 216...) — if it matches one exactly, it's a perfect cube; this calculator does that check automatically for you.
Cube Root Calculator
Enter any number to find its cube root. Unlike square roots, cube roots are defined for negative numbers too — this calculates the real cube root for any input and flags whether your number is a perfect cube.
The cube root of −27 is exactly −3, since (−3)³ equals −27 — a real result exists here because multiplying three negative numbers together (an odd count) produces a negative result, unlike squaring where an even number of negative factors always turns positive. This distinction is why square roots of negative numbers require imaginary numbers while cube roots don't, and it's a useful fact whenever solving equations that involve cubing, like finding the side length of a cube from its volume.
- Definition: ∛x is the value that, multiplied by itself three times, equals x.
- Works for negative numbers, unlike square roots: the cube root of −27 is −3 (since (−3)³ = −27) — a real result exists because an odd number of negative factors multiplies to a negative number.
- Perfect cubes have whole-number roots: numbers like 8, 27, 64, and 125 have cube roots that are themselves whole numbers.
Why does the cube root of a negative number have a real answer, unlike the square root?
Cubing a negative number keeps the result negative (since you multiply three negatives together, and the product of three negative numbers is negative), so a real number can always satisfy x³ = negative value — that's not true for squaring, where the result is always positive.
How can I quickly check if a number is a perfect cube?
Compare it to the cubes of small whole numbers (1, 8, 27, 64, 125, 216...) — if it matches one exactly, it's a perfect cube; this calculator does that check automatically for you.