Square Root Calculator
Free square root calculator with high precision results. Find the square root of any positive number instantly. Perfect for math, science, and engineering.
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Calculate Square Roots with Precision
Finding square roots doesn't have to be complicated. Our calculator instantly computes the square root of any positive number with high precision, perfect for students, engineers, and anyone working with mathematical calculations.
What Is a Square Root?
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Square roots are fundamental in geometry (calculating distances and areas), physics (wave equations), statistics (standard deviation), and many other fields. Every positive number has two square roots: one positive and one negative, though we typically refer to the positive root.
Mathematical Notation
√x = y, where y² = xWhy Use Our Square Root Calculator?
High Precision Results
Get square roots calculated to many decimal places for accurate scientific and engineering work.
Perfect & Imperfect Squares
Works with any positive number, whether it's a perfect square like 16 or an imperfect square like 7.
Educational Insights
Learn whether your number is a perfect square and understand the mathematical relationship.
How to Calculate Square Roots
Square Root Applications
Geometry & Construction
Calculate diagonal distances, determine side lengths from area, and solve Pythagorean theorem problems.
Statistics
Compute standard deviations and root mean square values for data analysis.
Physics & Engineering
Solve equations involving velocity, energy, electrical calculations, and wave mechanics.
Finance
Calculate volatility, risk metrics, and compound annual growth rates (CAGR).
Frequently Asked Questions
A perfect square is a number whose square root is a whole number. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Perfect squares result from multiplying an integer by itself.