Cube Root Calculator

The cube root of a number x is the value y such that y³ = x. This calculator uses JavaScript's Math.cbrt() to return that value to about 15 significant digits, including for negative inputs.

When to use this calculator

You need ∛x for a number that isn't on the standard cube-root table.
You're solving for the side of a cube given its volume.
You're checking a manual cube-root step in homework or engineering work.

How it works

The cube root y of x satisfies y × y × y = x, equivalently ∛x = x^(1/3). The calculator uses Math.cbrt(x), the IEEE-754 cube root function, which accepts negative numbers natively — so ∛(−27) returns −3 directly without any complex-number tricks. Verification (result³) is shown alongside the answer.

Real-world examples

Geometry: a cube with volume 343 cm³ has a side length of ∛343 = 7 cm.
Engineering: scaling a sphere or cube proportionally by volume requires the cube root of the volume ratio.
Finance: computing the average annual growth rate over three periods uses ∛(end ÷ start) − 1.

Limitations

Results use double-precision arithmetic — accurate to ~15 significant digits, not symbolic.
Inputs near the double-precision limit (≥ 1.79e308) cannot be represented.
The calculator returns the real cube root only — not the two complex cube roots.
Irrational cube roots (∛2, ∛3) are shown rounded, not as exact algebraic forms.

Frequently asked questions

Can the cube root of a negative number be calculated?

Yes. Unlike square roots, every real number has a real cube root. ∛(−27) = −3 exactly.

What is the cube root of 0?

Zero. ∛0 = 0 because 0 × 0 × 0 = 0.

Why does the result sometimes not look exact?

Most cube roots are irrational. The display rounds to about 15 significant digits — for example ∛2 ≈ 1.2599210498948732.

Is ∛x the same as x^(1/3)?

Yes mathematically. Math.cbrt() is preferred in code because x^(1/3) returns NaN for negative x in JavaScript, while Math.cbrt handles negatives correctly.

How is this different from a square root calculator?

Square roots only exist for non-negative real numbers, while cube roots exist for every real number. The cube root preserves the sign of the input.

Calculate the Cube Root of Any Number

How to Use the Cuberoot Calculator