Cube Root Button on Calculator: How to Use It

The cube root button on a calculator (often labeled ∛x or 3√x) computes the number that, when multiplied by itself three times, equals the value you enter. You press the button, type the number, and press equals (or the button may work after entering the number, depending on the model) to get the cube root. This article explains how to find cube roots on standard, scientific, and graphing calculators, what the button does, and how to check your answer.

Formula

The cube root of a number x is written as ∛x or x^1/3. It is the inverse operation of cubing a number. If y = ∛x, then y³ = x. For example, ∛8 = 2 because 2 × 2 × 2 = 8. Unlike square roots, cube roots exist for negative numbers: ∛(−8) = −2 because (−2)³ = −8.

In the calculator above, the formula is simply cbrt(x), where x is the number you enter. The result is displayed as a decimal, rounded to four decimal places. The cube root of 27 is exactly 3, so the default input gives 3.0000.

Worked Example

Using the default value of x = 27:

1. Enter 27 into the calculator.
2. Press the cube root button (∛x) or use the cbrt function.
3. The calculator computes ∛27.
4. Since 3 × 3 × 3 = 27, the result is 3.

The calculator above shows 3.0000, which matches the exact value.

How the Cube Root Button Works on Different Calculators

Calculator designs vary, so the button may work in one of two ways:

• Function first (scientific calculators): You press the ∛x button, then type the number, then press equals. This is common on Casio and Texas Instruments scientific models.
• Number first (some graphing and iPhone calculators): You type the number, then press the cube root button. For example, on the iPhone calculator in landscape mode, you enter 27, then tap the ∛x button.
• Shift or second function: On many calculators, the cube root is not a dedicated button but is accessed by pressing SHIFT or 2nd followed by the ^ or x√ button. The label above the button usually shows ∛x.

If you cannot find a cube root button, you can always use the exponent function: type the number, press the ^ or xʸ button, then enter (1/3) or 0.3333. For example, 27^(1/3) = 3.

Common Mistakes and How to Avoid Them

One frequent error is confusing cube root with square root. The square root button (√) only gives the number that multiplies by itself twice. For cube roots, you must use the ∛ button or the exponent 1/3.

Another mistake is entering the exponent as 3 instead of 1/3. If you type 27^3, you get 19683, not 3. Always use parentheses around the fraction: 27^(1/3).

Also, remember that cube roots of negative numbers are negative. If you enter −8 and get an error on a basic calculator, it may be because the calculator does not support odd roots of negatives. Use a scientific calculator or the cbrt function instead.

When to Use Cube Roots in Real Life

Cube roots appear in geometry, physics, and engineering. For example, to find the side length of a cube given its volume, you take the cube root of the volume. If a cube has a volume of 64 cubic centimeters, each side is ∛64 = 4 cm.

In physics, the cube root is used in formulas for gravitational time dilation (though that is more advanced) and in calculating the radius of a sphere from its volume. The formula for the radius r of a sphere with volume V is r = ∛(3V / 4π).

In statistics, cube roots are sometimes used to transform skewed data to make it more normally distributed.

Limits of the Cube Root Button

The cube root button on a calculator gives a decimal approximation for most numbers. For perfect cubes (like 8, 27, 64), the result is exact. For non-perfect cubes (like 2 or 10), the result is a long decimal that the calculator rounds. For example, ∛2 ≈ 1.2599.

Some calculators only show a limited number of digits, so if you need more precision, use a calculator that displays more digits or use the exponent method with a high-precision tool.

Also, the cube root button on a basic four-function calculator may not exist at all. In that case, you need a scientific or graphing calculator, or you can use the online calculator above.

Comparing Cube Root to Other Roots

Square roots (√) and cube roots (∛) are the most common roots. The square root of a number x is the number that, when squared, gives x. It only works for non-negative numbers. The cube root works for all real numbers, including negatives.

Higher roots, like the fourth root (∜) or fifth root, follow the same pattern. The nth root of x is the number that, when raised to the nth power, gives x. On a calculator, you can compute any root using the exponent 1/n.

Frequently Asked Questions

How do I type cube root on a phone calculator?

On the iPhone calculator, rotate your phone to landscape mode to reveal the scientific calculator. Look for the ∛x button. On Android, the default calculator may have a scientific mode; swipe or rotate to access it. If not, download a scientific calculator app or use the online calculator above.

What is the cube root of 0?

The cube root of 0 is 0, because 0 × 0 × 0 = 0. This is true for any root of zero.

Why does my calculator give an error for cube root of a negative number?

Some basic calculators only handle square roots of positive numbers and may not support odd roots of negatives. Use a scientific calculator or the cbrt function, which correctly returns a negative result for negative inputs.

Can I use the cube root button to find the side length of a cube?

Yes. If you know the volume of a cube, the side length is the cube root of the volume. For example, a cube with volume 125 cubic inches has side length ∛125 = 5 inches.

Is the cube root of a number always smaller than the number?

No. For numbers greater than 1, the cube root is smaller (e.g., ∛8 = 2). For numbers between 0 and 1, the cube root is larger (e.g., ∛0.125 = 0.5). For negative numbers, the cube root is negative and its absolute value is smaller than the number’s absolute value (e.g., ∛(−8) = −2).

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in x | Number | - | 27 | 0
out cbrt | Cube root | - | cbrt(x) | 4