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Square Root Calculator

Finding a square root by hand is fiddly, and sometimes you need a cube root or a fourth root too. This free square root calculator computes the square root of any number and lets you choose any root — so you can get the exact result with the working shown, instantly.

Number

Root (2 = square)

What is a Square Root Calculator?

A square root calculator finds a value that, when multiplied by itself, gives the number you entered. The square root of 144 is 12 because 12 × 12 = 144; the symbol is the radical sign √. For any non-negative number it also lets you take an nth root — such as a cube root or a fourth root — with the same simple framework.

The tool computes this using the exponent form: the nth root of a number is that number raised to the power 1/n. So the cube root of 27 is 27^(1/3) = 3. This conveniently gives fractional roots and negative bases handled correctly for real numbers (a negative number has no real square root, so the tool flags it).

Roots appear everywhere in geometry, algebra, physics, finance and data analysis. Square roots turn area back into side length, cube roots convert volume into edge length, and roots show up in compounding and in the standard deviation formula. Rather than approximating by hand, students and professionals get the exact answer with the working shown.

How to use the Square Root Calculator

Enter the number you want the root of in the Number field.
Set the root in the Root field — 2 for a square root, 3 for a cube root, and so on.
Click Calculate (or the run button) to get the result.
Read the result and the working, which shows the radical form and the exponent form.
Change the root or the number and recalculate as needed.

Example

Number 144, root 2.

Result: 12, shown as √144 = 144^(1/2) = 12.

Change root to 3 on number 27 → 3 (the cube root of 27).

Who is this square root calculator for?

A square root calculator finds the square, cube or nth root of a number instantly. It is a quick check for anyone working with roots.

Students: check geometry and algebra problems that need a square or cube root.
Teachers: verify students’ answers and build root practice drills in moments.
College learners: handle roots that appear in statistics, physics and engineering formulas.

Square root table

These are the exact square roots of the perfect squares from 25 to 100:

Perfect square	Square root (√n)
25	5
36	6
49	7
64	8
81	9
100	10

Common use cases

Solving geometry and algebra problems that require a square or cube root.
Finding a side length from an area, or an edge length from a volume.
Handling roots that appear in finance, statistics and physics formulas.
Checking homework and exam answers quickly and accurately.

Pro tips

The square root of a positive number has both a positive and a negative answer; the tool returns the principal (positive) root.
A negative number has no real square root, so the calculator tells you to choose a non-negative number instead.
For a cube root of a negative number, you can still get a real answer, but this tool handles real results best for non-negative inputs.
Remember that raising a fractional power like 1/n works for any whole or fractional root, so you can also find a fourth root easily.

FAQ

What is a square root?

A square root of a number is a value that, when multiplied by itself, equals that number. The square root of 144 is 12 because 12 × 12 = 144.

What is an nth root?

An nth root is a number that, raised to the power n, gives the original value. The cube root is the third root, and the fourth root is the fourth, and so on.

How do I find a cube root?

Enter the number and set the root to 3. The tool computes the cube root as the number raised to the power 1/3.

Why can't I take a square root of a negative number?

Any real number multiplied by itself gives a positive result, so there is no real square root of a negative number. The tool lets you know to use a non-negative number.

How is the root computed?

The calculator uses the exponent form of the number raised to the power 1/n, which gives the same result as the radical form for real numbers.

What does the working show?

It shows the radical notation and the equivalent power form, such as √144 = 144^(1/2) = 12, so you can follow how the result was found.

Is it private and free?

Yes. The calculation runs entirely in your browser and is completely free, with nothing uploaded or stored.

Can it handle fractional or decimal roots?

Yes. You can enter any root value greater than zero, including a fractional root such as a half-power, and the tool computes it.