Cube Root Calculator
Use the Cube Root Calculator for positive, negative, zero, and decimal inputs, with four-decimal results, worked examples, and cited guidance.
Formula: ∛x = y, where y³ = x
Enter any finite real number. Negative inputs return negative real cube roots; results are rounded to four decimal places.
The Cube Root Calculator finds the real cube root of a number. Enter any finite real number. Negative inputs return negative real cube roots; results are rounded to four decimal places. Decimal inputs and zero are supported. Select Calculate after entering or changing the value.
The default input 27 returns 3.0000 because 3 × 3 × 3 = 27. A negative input of −8 returns −2.0000, not an undefined value, because (−2)³ = −8. For a decimal example, 0.125 returns 0.5000.
How to Use the Cube Root Calculator
- Enter a finite positive, negative, zero or decimal number.
- Select Calculate.
- Read the real cube root shown to four decimal places.
Changing the input clears the earlier result until you calculate again. Blank, nonnumeric and non-finite entries are rejected with an accessible field error. The calculator does not impose a positive-only rule or an arbitrary maximum inside the browser’s finite numeric range.
Cube Root Formula and Worked Examples
∛x = y, where y³ = xThe cube root is the number y whose cube equals x. The OpenStax College Algebra 2e section on radicals and rational exponents explains nth roots and the treatment of negative radicands for odd indices. Because 3 is odd, every real input has one real cube root, including negative inputs.
For 125, the result is 5.0000 because 5³ = 125. For −125, it is −5.0000 because (−5)³ = −125. For 0, it is 0.0000. These checks use the defining equation rather than treating a negative input as a fractional power that could lose its real result in JavaScript.
For a positive cube volume V, ∛V gives the side length in the corresponding linear unit when the units are consistent. Negative values are valid algebraic inputs but do not describe a physical volume. Cube roots also undo cubing when solving equations such as x³ = 64.
Input Limits, Rounding and Related Calculators
The widget uses standard browser floating-point numbers. MDN’s Number.MAX_VALUE reference documents JavaScript’s largest positive finite numeric value. Inputs outside the finite range are invalid; Number.MAX_VALUE itself still has a finite real cube root.
Results are displayed to four decimal places, so 2 returns approximately 1.2599. Display formatting does not add precision, and a very small nonzero cube root can appear as 0.0000 after rounding. Use more precision elsewhere when downstream work depends on digits beyond the display.
Use the Square Root Calculator for principal square roots, the Exponential Calculator for powers, or the Nth Root Calculator when you need a configurable root index and its domain rules.
Frequently asked questions
What is a real cube root?
The real cube root of x is the unique real number y for which y³ = x. For example, the real cube root of 8 is 2.
What formula does the Cube Root Calculator use?
It evaluates ∛x = y, where y³ = x, through the audited real nth-root operation with a fixed degree of 3.
Can the calculator find cube roots of negative numbers?
Yes. Because the cube-root index is odd, a negative input has a negative real result. For example, ∛(−8) = −2 and ∛(−125) = −5.
Can I enter zero or a decimal number?
Yes. Zero and finite decimal values are supported. For example, ∛0 = 0 and ∛0.125 = 0.5.
How can I check a cube-root result?
Cube the result. A correct real cube root y satisfies y × y × y = x, subject to the displayed rounding.
How are results rounded?
Results are displayed to four decimal places using standard browser floating-point arithmetic. Display rounding does not add precision to the calculation.
What input limits apply?
The input must be a finite browser number. Blank, nonnumeric and non-finite values are rejected; finite positive, negative, zero and decimal values are accepted without an arbitrary maximum.