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Cube Root Calculator

Enter a number to find its cube root, whether positive or negative.

How it is calculated

The cube root of a number is the value that gives the number back when multiplied by itself three times.

r = sign(x) × |x|^(1/3)

x is any real number. The tool takes the cube root of the absolute value and then puts the original sign back, so negative numbers work: the cube root of −27 is −3. Zero returns 0. The result is shown to 4 decimals, so it is a rounded value unless the number is a perfect cube such as 27 or 64. It is computed with a power function, so very large inputs still give a result.

Worked example

Suppose a cube-shaped box holds 50 litres and you want its edge length in decimetres (1 litre = 1 dm³). The edge is the cube root of the volume: r = 50^(1/3). Since 3³ = 27 and 4³ = 64, the answer must lie between 3 and 4. The tool gives 3.6840. Checking: 3.684 × 3.684 × 3.684 ≈ 49.998, which is very close to 50.

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Common mistakes

  • Confusing the cube root with the square root or with dividing by 3. The cube root of 27 is 3, the square root is about 5.196, and 27 ÷ 3 is 9.
  • Thinking negative numbers have no real cube root. They do: the cube root of −8 is −2, and the tool keeps the sign.
  • Treating the rounded 4-decimal answer as exact. For 50 the true root has infinitely many decimals, so cubing 3.6840 gives 49.998, not exactly 50.
  • Mixing up volume units when finding an edge length. A volume in litres or cm³ gives an edge in dm or cm respectively, so convert first.

About this calculator

The cube root of a number x is the value that, multiplied by itself three times, produces x; unlike a square root, a cube root is defined for negative numbers too, since a negative number multiplied by itself three times stays negative — the cube root of negative 8, for instance, is negative 2. This calculator computes cube roots for positive and negative real numbers alike, typically using an iterative numerical method that converges quickly to high precision.

Cube roots come up whenever a cubic relationship needs to be reversed: finding the side length of a cube from its known volume, working backward from a scaled-up or scaled-down volume in engineering and packaging design, and solving cubic equations in algebra classrooms all rely on this operation.

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