Square Root Calculator

Calculate square root, cube root, and nth root of any number.

By Konstantin Iakovlev · Updated September 2026 · Source: Khan Academy

Square Root

12.000000

Cube Root

5.241483

Root Results

Square Root12.000000
Cube Root5.241483
Root of Index 212.000000
Perfect Square?Yes

Use the Square Root Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only. Results are estimates based on the information you provide and the assumptions described on this page.

How It Works

Finding a square, cube, or nth root quickly comes up constantly for students, engineers, and anyone working with measurements, and this calculator handles all of them. The applications stretch from recovering the side of a square from its area to sizing a cube-shaped container from its volume. Automating the computation cuts both the time spent and the chance of slipping up by hand.

For a number 'x' and a root 'n', the calculator finds the value 'y' with y^n = x. It always shows the square root and the cube root, and the root you enter in the Nth Root box is computed as x^(1/n); all three come from the browser's standard double-precision math functions and are displayed to six decimal places. It also reports whether the number is a perfect square.

A negative number has no real square root (its square roots are imaginary), and for a negative number the calculator shows no real square root or other even root. With an odd root such as 3, a negative number has a real, negative root: the cube root of −27 is −3. One pitfall worth naming: an nth root is not the same as dividing by n. The square root of 9 is 3, not 4.5.

Example: Side Length of a Cube-Shaped Tank

  1. 1 A cube-shaped tank must hold 1,728,000 cm³ (1,728 liters). How long is each side?
  2. 2 Enter 1728000 (or 1,728,000) in the Number box and 3 in the Nth Root box.
  3. 3 The cube root, shown both as Cube Root and in the nth-root row, is 120.000000, because 120 × 120 × 120 = 1,728,000.
  4. 4 Each side is 120 cm. The calculator also shows the square root, 1,314.534138, and Perfect Square? No, since 1,728,000 is not the square of a whole number.

Source: Khan Academy · Last updated: September 2026

Frequently Asked Questions

How do I calculate a square root without a calculator?
Use estimation and refinement. For sqrt(50), note that 7^2=49 and 8^2=64, so it is between 7 and 8, closer to 7. Try 7.07: 7.07^2 = 49.98, very close to 50. The Babylonian method (guess, divide, average) converges quickly.
Can you take the square root of a negative number?
Not in the real number system. The square root of a negative number is imaginary. Sqrt(-1) is defined as i (the imaginary unit). Sqrt(-9) = 3i. Complex numbers (a + bi) are used in engineering and physics when square roots of negatives arise.
What is the difference between a square root and a cube root?
A square root finds what number times itself equals the input (sqrt(25) = 5 because 5x5 = 25). A cube root finds what number times itself three times equals the input (cbrt(27) = 3 because 3x3x3 = 27). Cube roots of negative numbers are real.

You might also need

Percentage Calculator

Calculate percentages three ways: what is X% of Y, X is what % of Y, and percentage change from X to Y.

Fraction Calculator

Add, subtract, multiply, and divide fractions. Results shown as fraction, mixed number, and decimal.

Standard Deviation Calculator

Calculate mean, variance, and standard deviation (population and sample) from a data set.