Cube Root of -343 = -7.0000

Cube Root Calculator

Use the calculator above to find the cube root of any real number (positive, negative, or decimal). See below the step-by-step method using Newton's iteration, plus a table of common perfect cubes.

-343 Is a Perfect Cube

∛-343 = -7  because  -7³ = -7 × -7 × -7 = -343

Formula

The cube root of a number a is the value x such that:

x³ = a  ⇔  ∛a = x

Every real number has exactly one real cube root. Unlike the square root, the cube root is defined for negative inputs: ∛(−a) = −∛a.

How to Calculate Cube Roots

For perfect cubes (8, 27, 64, 125, …) the cube root is an integer — just recall the cube of small integers.

For other numbers, use Newton's Method:

1. Start with a rough estimate (e.g. x₀ = a / 3).
2. Apply x_n+1 = (2x_n + a/x_n²) / 3.
3. Repeat 3–4 times — the value converges fast (each step roughly doubles the digits of precision).

Nearby Cube Roots

Perfect Cube Roots Table

Common perfect cubes from 1 to 1000. For the full table 1–100, see our cube root chart 1 to 1000.

Inverse Operation: Cubing

Since ∛-343 = -7, the inverse operation is cubing: -7³ = -343.

See our Cubed Calculator for more details on this and related cubed values.

References

• [1] Cube root (Wikipedia)
• [2] Newton's Method (Wikipedia)

Popular Cube Root Calculations

Top cube root calculations based on search data: