Cube Root on a Calculator: Quick Steps and Examples

A cube-root calculator finds the number that, when multiplied by itself three times, equals your input. Enter a number and the calculator returns its cube root; for example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. You can also use the steps below on a scientific calculator or a basic calculator with an exponent key.

Formula

The cube root of a number x is the value y such that y³ = x. In symbols, y = ∛x = x^1/3. Here, x is the number you enter and y is the cube root result; both use the same units, if the input represents a measured quantity. The calculator block uses cbrt(x), a cube-root function that handles negative inputs as well as positive ones.

Worked Example

Using the block’s default input, x = 27:

1. Write the cube-root expression: ∛27.
2. Find a number that gives 27 when multiplied by itself three times: 3 × 3 × 3 = 27.
3. Therefore, ∛27 = 3. The calculator displays 3.

What You’ll Need

• A scientific calculator with a cube-root key (often shown as ∛), or a calculator with a power key marked xʸ, yˣ, or ^.
• The number whose cube root you want to find. You do not need to change the number into a different unit first.

Step-by-Step

1. Enter the number. Type the value whose cube root you need. For instance, enter 64 to find ∛64. If the number is negative, include the minus sign as part of the value.
2. Look for a cube-root key. Check the main keys and any secondary functions printed above them. A cube-root key may be marked ∛x or ³√x. On some calculators, you access a secondary function with Shift, 2nd, or another labeled key.
3. Use the key in the correct order. Depending on the calculator, either press the cube-root key, enter the number, and press equals, or enter the number first and then press the cube-root key. Follow the display: if the key opens an expression such as ∛( ), type the number inside the parentheses before calculating.
4. Read the displayed result. For 64, the answer is 4, since 4³ = 4 × 4 × 4 = 64. If your calculator shows a long decimal, it may be approximating a root that is not a whole number.
5. Check the answer by cubing it. Multiply the result by itself three times, or use the calculator’s power key to calculate result³. It should match the original input, apart from small rounding differences.

If there is no cube-root key: use the power function. Enter the number, press the key marked xʸ, yˣ, or ^, enter 1 ÷ 3 (or 0.333333…), then press equals. On a calculator that accepts a complete expression, enter x^(1/3), using parentheses around the fraction. For example, 64^(1/3) gives 4. Parentheses matter: entering 64^1/3 may be interpreted as (64¹) ÷ 3, which is not a cube root.

Common Mistakes

• Using the square-root key. The square root undoes a number raised to the second power; a cube root undoes a number raised to the third power. For example, √64 is 8, but ∛64 is 4.
• Entering the wrong exponent. A cube root uses the fractional exponent 1/3, not 1/2 or 3. Enter the fraction as (1 ÷ 3) if the calculator’s order of operations is unclear.
• Leaving out parentheses. The calculator may divide the result by 3 instead of using 1/3 as the exponent. Use x^(1/3), not x^1/3, unless your calculator clearly groups the exponent.
• Misreading the sign of a negative input. A negative number has a negative real cube root: ∛(−8) = −2. Keep the negative sign inside the cube-root operation or exponent expression.
• Rounding too early. Keep the calculator’s full displayed result while doing further calculations, and round only the final answer to the required precision.

Tips

• Memorize common perfect cubes: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, and 10³ = 1,000. These make quick checks easier.
• For a negative input using a power key, use parentheses around the number too: (−8)^(1/3). Without parentheses, some calculators apply the exponent before the negative sign.
• When the root is not exact, give a sensible number of decimal places. For example, ∛2 is approximately 1.260, not exactly 1.260.
• Use the cube function or x³ key to verify your result. If the cube differs slightly from the input, the difference is usually due to rounding.

Troubleshooting

• The calculator shows an error for a negative number. Some basic calculators define fractional powers only for positive inputs. Use a calculator with a dedicated cube-root function, or find the root of the positive value and restore the negative sign. For example, ∛(−8) = −∛8 = −2.
• The result is one-third of the input or otherwise unexpected. Check that you entered the exponent as a grouped fraction, x^(1/3). If the calculator has a dedicated ∛ key, use that instead.
• The answer is a long decimal rather than a whole number. The input may not be a perfect cube. Check by cubing the displayed result; a rounded decimal should get close to the original value.
• The calculator gives a positive answer for a negative input. It may be interpreting a negative base with fractional powers in a way that does not return real roots. Use the dedicated cube-root function or calculate the positive root and add the negative sign.
• The key sequence does not work. Clear the current expression and try again, checking whether the calculator expects the number before or after the root key. Consult the calculator’s key labels or manual for the secondary-function method.

Frequently Asked Questions

What is a cube root?
A cube root is a number that, multiplied by itself three times, equals the original number. Since 5³ = 125, the cube root of 125 is 5.

How do I find a cube root without a cube-root button?
Raise the number to the power 1/3. Enter x^(1/3), with parentheses around the exponent; use a calculator that supports negative bases if x is negative.

Can you take the cube root of a negative number?
Yes. The real cube root of a negative number is negative: ∛(−27) = −3, because (−3)³ = −27.

Is a cube root the same as dividing by three?
No. A cube root reverses cubing; it does not divide the input by 3. For example, ∛27 = 3, while 27 ÷ 3 = 9.

Why does my calculator show an approximate answer?
Many numbers do not have exact cube roots that can be written as finite decimals. The calculator displays a rounded approximation, so cubing it may give a value very close to, but not exactly, the input.

How can I check a cube-root answer?
Multiply the answer by itself three times or raise it to the third power. The result should equal the original number, allowing for rounding.

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in x | Number | - | 27 | 
out root | Cube root | - | cbrt(x) | 6