Root Calculator
Calculated using standard mathematical and industry formulas.
Free online Root Calculator calculator and unit conversion tool for everyday, engineering, and home projects.
How to use this calculator?
- Enter the radicand x — the number under the root sign.
- Enter the root degree n: 2 for square root, 3 for cube root, etc.
- Read the result, plus square root and cube root shown as reference.
Formula & calculation method
Nth root formula
ⁿ√x = x^(1/n) · Verification: (ⁿ√x)ⁿ = x
Negative radicand allowed only for odd n. n = 0 is undefined.
Step-by-step calculation example
∛64 = 64^(1/3) = 4 (verification: 4³ = 64). √144 = 12 (verification: 12² = 144).
Key insights to remember
- Square root (n = 2) is the most common root: √64 = 8 because 8² = 64.
- Cube root (n = 3) is the only real odd root of a negative number: ∛(-8) = -2.
- The nth root of x equals x^(1/n) — a fractional exponent.
- Irrational numbers like √2 ≈ 1.41421 cannot be expressed as exact fractions.
How to interpret your results?
Square root vs cube root
Square root undoes squaring (n = 2). Cube root undoes cubing (n = 3) and accepts negative inputs.
Even roots of negative numbers
Even-degree roots (n = 2, 4, 6, …) of negative numbers are complex and not supported here.
Frequently asked questions
- How do I use the Root Calculator calculator?
- Enter your numerical input and select desired units to get instant accurate results.
- How accurate are the conversions?
- Conversions use official ISO conversion factors for maximum precision.
- Does it convert metric and imperial units?
- Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.
- Is my data stored?
- No, all calculations execute 100% locally in your browser with zero data logging.
- Can I use this for DIY or engineering projects?
- Yes, it provides reliable estimates for construction, crafting, science, and everyday math.
- What if I enter invalid inputs?
- The calculator will display a friendly error prompt if non-numeric values are entered.
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