Perfect Cube Calculator - Cube Root and Reference List

A perfect cube calculator tests any integer you enter and tells you in one step whether the value can be written as the cube of an integer. The tool returns a Yes or No verdict, the exact integer root for exact cubes, the real cube root at your chosen precision, and the nearest perfect cubes above and below the input.

• • Class homework and number theory: Confirm whether a specific integer is a perfect cube before a proof or Diophantine equation.
• • Practice and quiz checking: Cross-check a candidate answer during algebra exercises against the cube sequence below.
• • Volume and capacity sanity checks: Confirm whether a side length in meters produces a clean volume in cubic meters.
• • Programming and cryptography work: Filter candidates in number-theoretic algorithms with the integer-cube-root test.

The underlying rule: N is a perfect cube exactly when N = a^3 for some integer a. The positive sequence 1, 8, 27, 64, 125, 216, ... extends in both directions with zero and negative integers. The calculator reduces every test, including negatives, to a single integer-cube-root comparison.

For a^3 in geometry, Cube Volume Calculator solves the full side-length, volume, surface-area, and diagonal profile of a cube from one measurement.

The calculator takes your input, computes the real cube root, rounds to the nearest integer, cubes the result, and compares it with the original. If they match, the input is a perfect cube; otherwise, the real cube root is shown at the chosen precision.

• N: The integer you entered.
• a: The candidate integer root, from rounding the real cube root of N.
• cubeRoot(N): The real cube root of N.
• precision: Decimal places for the real cube root when N is not a perfect cube.

For exact cubes, the verdict is Yes and the integer root is shown without decimals. For inputs between two cubes, the verdict is No and the real cube root is shown at the chosen precision. The previous and next cubes come from cubing one step below and one step above the candidate root, which works for negative numbers too.

According to Wolfram MathWorld, the volume of a cube with edge length a equals a^3, so any cube-of-integer value is a perfect cube.

As Wikipedia notes, a perfect cube is the cube of an integer, including zero and negatives, with sequence 0, 1, 8, 27, 64, 125, ...

For integer powers beyond the third, Exponent Calculator evaluates a^n for any positive integer exponent.

Four ideas show up every time you talk about perfect cubes.

The cube-volume calculator solves for the full cube profile when the geometry is the actual question.

To turn a cube back into its integer side length, Root Calculator handles cube roots, square roots, and nth roots.

Five short steps take you from a raw integer to a clear yes/no answer plus the surrounding cube values.

1. 1 Enter the number to test: Type any whole number from -999999999 to 999999999 in the first field. The default 64 is itself a perfect cube.
2. 2 Pick a decimal precision: The second field sets decimal places for the real cube root. The default of 4 is enough for most textbook work.
3. 3 Read the verdict: Yes means the input is a perfect cube; No means it is not, and the real cube root is shown at the chosen precision.
4. 4 Read the integer root and real cube root: The integer root is what you cube to get the closest cube. The real cube root is the actual root, shown when the input is not a perfect cube.
5. 5 Check the previous and next perfect cube: The bottom of the result panel shows both.

Try 500 with the default precision. The calculator reports No, integer root 8, real root 7.9370, previous 343 (7^3), next 512 (8^3).

For a parallel rapidly growing sequence, Factorial Calculator returns n! and double factorials for any positive integer n.

Five concrete benefits make the calculator more useful than working the test by hand.

• • One-line answer for yes/no questions: 'Is 64 a perfect cube' or 'is 216 a perfect cube' are answered in a glance.
• • Exact cube root without long division: The integer root for exact cubes and a precise decimal root for the rest.
• • Previous and next cubes included: The values around your input are shown next to the verdict.
• • Negative-number support: Negative inputs are handled as naturally as positive ones, so -8, -27, -64, and -1000 are recognized.
• • Quick reference of the first 100 cubes: The page lists the first 100 perfect cubes below the calculator.

The prime-factorization-calculator shows why perfect cubes have prime exponents that are multiples of 3, and the factorial-calculator gives another rapidly growing integer sequence for comparison.

If you want to dig deeper into the prime structure of a perfect cube, Prime Number Checker tells you whether each prime factor appears an integer number of times in the factorization.

Three factors and two practical limits decide whether the test gives a clean result.

• • The calculator treats each number independently, so it does not show a continuous list or a graph. Use the reference table below the calculator for a longer view.
• • The verdict compares the integer cube of the rounded root with the input, so 0.0001 will not be flagged as a perfect cube. Stay with integers.

The integer-cube-root identity is the same one used in the cube-volume calculator, so you can move from the verdict to a full cube geometry analysis without re-learning the math.

MDN Web Docs notes that Math.cbrt() returns the cube root of a number, which is what the calculator rounds and recubes to produce its verdict.

For the 1/3 power that defines a cube root, Fractional Exponent Calculator shows the radical form and a decimal value for any base and rational exponent.