Cube Root Calculator

Calculate the cube root of any number (∛x).

Last updated: 10/8/2026

The cube root of a number x is the number y whose cube equals x, written ∛x or x^(1/3). Because a negative number cubed stays negative, every real number has exactly one real cube root; this is the main way cube roots differ from square roots. Enter any number and the calculator returns its cube root to six decimal places, with a verification line that cubes the result back.

Calculator Inputs

Enter Number*

Results

Enter values above to see your results

How It Works

For a perfect cube such as 27 or −8 the root is exact (3 and −2). For other inputs the root is irrational and the calculator returns a rounded decimal using the standard cbrt function, which handles negative inputs correctly. The verification row shows the rounded root cubed; small differences from the input in the last decimal places are rounding, not error.

Estimating a cube root by hand

Bracket the answer between two perfect cubes, then refine. For ∛50: 3³ = 27 and 4³ = 64, so the root is between 3 and 4, closer to 4. Try 3.7: 3.7³ = 50.65, slightly high. Try 3.68: 3.68³ = 49.84, slightly low. The root is about 3.684. One step of Newton's method gives the same result faster: new guess = (2 × guess + x ÷ guess²) ÷ 3; starting from 3.7, (7.4 + 50 ÷ 13.69) ÷ 3 = 3.6841.

Cube roots of large numbers can be read from the digit count: a number with 1 to 3 digits has a one-digit cube root, 4 to 6 digits a two-digit root, 7 to 9 digits a three-digit root. For a perfect cube, the last digit of the root follows from the last digit of the number (1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0).

Where cube roots turn up

Any quantity that scales with volume needs a cube root to recover a length: the side of a cube of volume V is ∛V, and the radius of a sphere of volume V is ∛(3V ÷ 4π). Doubling the volume of a container multiplies each dimension by ∛2 ≈ 1.26, not by 2. Cube roots also appear in the geometric mean of three numbers, ∛(a × b × c), and in compound growth over three periods: a quantity that grows from 100 to 150 in three years grows by a factor of ∛1.5 ≈ 1.1447, or 14.47% a year.

Worked example

Cube root of 125

Find y with y³ = 125:Try nearby integers= 4³ = 64 is too small, 6³ = 216 too large

Check 5:5 × 5 × 5= 125

Result:∛125= 5

Side of a cube-shaped tank holding 2,000 litres

Volume in cubic metres:2,000 L ÷ 1,000 L/m³= 2 m³

Side length:∛2= 1.259921 m

Check:1.259921³= 2.0000 m³

Perfect cubes 1 to 15

n	n³	n	n³	n	n³
1	1	6	216	11	1,331
2	8	7	343	12	1,728
3	27	8	512	13	2,197
4	64	9	729	14	2,744
5	125	10	1,000	15	3,375

Tips & Best Practices

•∛27 = 3 because 3 × 3 × 3 = 27, and ∛−8 = −2 because (−2) × (−2) × (−2) = −8.
•A cube root of a fraction is the cube root of numerator over the cube root of denominator: ∛(8⁄27) = 2⁄3.
•On a scientific calculator without a ∛ key, raise the number to the power 1⁄3 (for negatives, take the root of the positive value and restore the sign).

Frequently Asked Questions

Why can I take the cube root of a negative number but not the square root?

Squaring any real number gives a non-negative result, so no real number squares to −9. Cubing keeps the sign, so (−3)³ = −27 and ∛−27 = −3 is a perfectly good real number.

Why does my calculator or spreadsheet give an error for (−8)^(1/3)?

The general power function works through logarithms, which are undefined for negative numbers, so some tools return an error or a complex number for a negative base with a fractional exponent. Use a dedicated cube-root function (CBRT in most languages) or compute −(8^(1/3)) = −2 instead.

Is the cube root of 2 a rational number?

No. ∛2 ≈ 1.259921 is irrational; its decimal expansion never repeats. Only perfect cubes (and ratios of perfect cubes) have rational cube roots.

How accurate is the result?

The cube root is computed in double-precision floating point (about 15 to 16 significant digits) and then displayed to six decimals. For practical work that is far more precise than any measurement you would feed in.