Cube Root Calculator
Calculate real cube roots for integers and decimals with exact perfect-cube checks, simplified radical form, and decimal approximation.
Last Updated: May 2026
Enter a finite integer or decimal. Negative numbers are supported.
Whole number from 0 to 12.
Decimal approximation
5.00
Exact root
5
Simplified radical
5
Input as fraction
125
| Item | Value | Meaning |
|---|---|---|
| Input | 125 | Integer input. |
| Rational form | 125 | Exact value used for cube-root checks. |
| Perfect cube? | Yes | Both numerator and denominator must be perfect cubes for a rational exact root. |
| Exact root | 5 | Shown when the exact real cube root is rational. |
| Simplified radical | 5 | Cube factors are pulled outside the radical when practical. |
| Decimal approximation | 5.00 | Rounded for display to 6 decimal places. |
| Check | 5^3 = 125 | Cubing the exact root returns the input when a rational root exists. |
The cube root is the number that returns the input when multiplied by itself three times.
Perfect cubes return exact rational roots. Other values are shown as simplified radicals and decimals.
Every real number has one real cube root, so negative inputs produce negative real roots.
Real Cube Root Notice
This calculator focuses on the real cube root of real inputs. Complex cube roots are not listed here.
Reviewed For Methodology, Labels, And Sources
Every CalculatorWallah calculator is published with visible update labeling, linked source references, and founder-led review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.
Reviewed By
Jitendra Kumar, Founder & Editorial Standards Lead, oversees methodology standards and trust-sensitive publishing decisions.
Review editor profileTopic Ownership
Sales tax and tax-sensitive estimate tools, Education and GPA planning calculators, Health, protein, and screening-formula pages, Platform-wide publishing standards and methodology
See ownership standardsMethodology & Updates
Page updated May 2026. Trust-critical pages are reviewed when official rates or rules change. Evergreen calculator guides are checked on a recurring quarterly or annual cycle depending on topic volatility.
How to Use the Cube Root Calculator
Enter an integer or finite decimal and choose the decimal precision for the approximation. Negative values are supported because real cube roots can be negative.
Read the decimal approximation first, then compare the exact root when the input is a perfect cube, the simplified radical form, and the rational input form.
Step 1: Enter a number
Use an integer or finite decimal such as 125, -64, 20, or 15.625.
Step 2: Set precision
Choose 0 to 12 decimal places for the displayed approximation.
Step 3: Check exactness
If the input is a perfect cube, the exact rational cube root is shown.
Step 4: Review the radical
For non-perfect cubes, use the simplified radical form when available.
How This Cube Root Calculator Works
The calculator parses finite decimals as exact rational numbers. It checks whether both the numerator and denominator are perfect cubes to determine whether the root is exact.
When the cube root is not a rational value, it still simplifies cube factors outside the radical where practical and displays a decimal approximation.
Negative inputs are handled with the real cube root rule: cuberoot(-a) = -cuberoot(a) for positive a.
Cube Root Guide
Cube Root Rules
| Concept | Formula or Example | Meaning |
|---|---|---|
| Definition | cuberoot(x) = y means y^3 = x | A cube root reverses cubing. |
| Perfect cube | cuberoot(125) = 5 | Because 5^3 = 125. |
| Negative input | cuberoot(-64) = -4 | Real cube roots preserve the sign of negative real inputs. |
| Decimal input | cuberoot(15.625) = 2.5 | Finite decimals are checked as rational values. |
| Non-perfect cube | cuberoot(20) = 2 cuberoot(5) | Cube factors can be pulled outside the radical. |
| Approximation | cuberoot(2) ~= 1.259921 | Irrational cube roots need decimal approximations. |
Cube Root Examples
| Input | Cube Root | Notes |
|---|---|---|
| 125 | 5 | Perfect cube. |
| -64 | -4 | Negative perfect cube. |
| 20 | 2 cuberoot(5) | Simplified radical form. |
| 15.625 | 2.5 | Decimal perfect cube because 2.5^3 = 15.625. |
| 0.001 | 0.1 | Small decimal perfect cube. |
Volume Connection
Cube roots often appear in geometry. If a cube has volume V, its side length is cuberoot(V), because side x side x side equals volume.
Keep the research moving with Scientific Calculator, Decimal Calculator, Integer Calculator, and Factor Calculator.
Frequently Asked Questions
Related Calculators
Scientific Calculator
Evaluate roots, powers, logarithms, trigonometry, and scientific expressions.
Use Scientific CalculatorDecimal Calculator
Add, subtract, multiply, divide, round, and convert decimals exactly.
Use Decimal CalculatorInteger Calculator
Calculate signed integer arithmetic, quotient and remainder, GCD, LCM, and powers.
Use Integer CalculatorFactor Calculator
Find all factors, factor pairs, prime factorization, and proper factors.
Use Factor CalculatorScientific Notation Calculator
Convert numbers to and from scientific notation with significant figures.
Use Scientific Notation CalculatorSources & References
- 1.Wikipedia - Cube root(Accessed May 2026)
- 2.Khan Academy - Roots, exponents, and scientific notation(Accessed May 2026)