How this calculation works
The cube root is the real number that produces the input when multiplied by itself three times. Negative numbers have negative real cube roots.
Result = ∛numberA worked example
The cube root of −27 is −3.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
Eight times the volume means twice the side
A cube with side length 2 has volume 8. A cube with side length 4 has volume 64: doubling every dimension multiplies the volume by eight. Cube roots reverse that relationship, so an eightfold volume increase corresponds to a twofold length increase for similar cubes.
Unlike an even root, an odd root can stay in the real-number system for negative inputs. The real cube root of −27 is −3, since three negative factors multiply to a negative result.
A signed algebra result is not a negative physical volume
Negative cube roots are useful in algebra, but a physical volume is normally non-negative. Keep the mathematical sign convention separate from the measurement you are modeling.
For measurements, converting cubic units before taking a cube root is essential. A volume in cubic centimetres produces a length in centimetres; reading that number as metres would introduce a large unit error.
A few questions, answered
Can I enter a negative number?
Yes. Every finite real number has one real cube root.
Why does doubling the volume not double the root?
The cube root scales with the cube root of the multiplier. A factor of 8, rather than 2, doubles the root.