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Find the cube root of any number
Use the free cube root calculator to work through the number relationship, preserve exact values, and check the result with estimation. Calculate with natural scientific notation, reusable history, angle modes, memory, probability functions, and familiar calculator layouts.
Arithmetic
Cube Root Calculator explained
The short version
- The cube root of a number is what you multiply by itself three times to get it, so ∛216 = 6.
- Unlike square roots, cube roots of negative numbers exist: ∛(−125) = −5.
- Pull out the biggest perfect cube inside to keep the answer exact, as in ∛432 = 6∛2.
The formula this page uses
∛a = the number that multiplies by itself three times to give a ∛(m³ × n) = m∛n ∛(−a) = −∛a
What each part means
SymbolWhat it means
a — The number under the signIt may be positive, negative or zero. All three give a real answer.
∛ — The cube root signThe small 3 says how many copies get multiplied. Without it the sign means a square root.
m³ — The perfect cube you pull out1, 8, 27, 64, 125, 216 and so on. The biggest one that divides a.
side length — What a cube root often meansIf a box holds 216 cm³, each side is ∛216 = 6 cm.
Show your work: a full example
- Find ∛216 and ∛(−125)∛216
- Test the cubes you know5³ = 125, too small
- Try the next one6³ = 216, exactly right, so ∛216 = 6
- Now the negative one5³ = 125, so 5 is the right size
- Put the sign in(−5) × (−5) × (−5) = 25 × (−5) = −125
- Read the answer∛(−125) = −5, which no square root could ever do
A second, different case
- A different case: simplifying and estimating∛432
- Look for a perfect cube inside432 = 216 × 2, and 216 = 6³
- Split the root∛432 = ∛216 × ∛2 = 6∛2
- As a decimal∛2 = 1.2599, so 6 × 1.2599 = 7.5595
- Now estimate ∛60 by hand3³ = 27 and 4³ = 64, so the answer is just under 4
- Try 3.93.9 × 3.9 × 3.9 = 59.319, a little too small
- Settle it∛60 = 3.9149 to four decimal places
Copy-ready example
∛216
Find ∛216 and ∛(−125)
Questions about the Cube Root Calculator
How many cube roots does a number have?
Just one real cube root, and that is the big difference from square roots. Since 4³ = 64 and (−4)³ = −64, no negative number can cube to a positive one. So ∛64 = 4 with no ± needed anywhere.
Is ∛a the same as a to the power 1/3?
Yes, they are two ways of writing the same thing. It works because a^(1/3) × a^(1/3) × a^(1/3) = a^(1/3 + 1/3 + 1/3) = a¹. That is also how to type a cube root into a calculator that only has a power key.
How do I estimate a cube root between two whole numbers?
Trap it between the cubes you know. Since 27 and 64 sit either side of 60, ∛60 is between 3 and 4, and much closer to 4 because 60 is near 64. Then test decimals: 3.9³ = 59.319 is just under, so the answer is a shade over 3.9.
A cube-shaped box holds 1,000 cm³. How long is each side?
Take the cube root: ∛1000 = 10, so each side is 10 cm. This is the most common real use of the operation, and it is also why volume answers get a small 3 written after the unit.
How to use a scientific calculator accurately
The calculator executes the expression entered; mathematical judgment still determines the correct expression, mode, and interpretation.
Set the angle mode
Use degrees for degree-labelled angles and radians for calculus or unit-circle work unless the problem states otherwise. A correct key sequence in the wrong mode produces a wrong value.
Group the expression
Use parentheses around numerators, denominators, exponents, and negative substitutions. Read the full display before evaluating.
Keep precision until the end
Reuse the stored answer instead of a rounded display value during multi-step work, then round once to the requested precision and units.
Estimate and verify
Predict sign and scale, use identities or inverse operations, and compare a second entry when the result matters.
About the calculator layouts
The MathGPT, TI-84 Plus-style, HP Prime-style, Casio fx-CG50-style, and Casio fx-9860GIII-style key arrangements share one independent calculation engine. They provide familiar practice layouts and do not emulate proprietary firmware or imply affiliation with those manufacturers.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.