Number Square Calculator
Perfect Squares (1-20)
Quick Guide
Calculate squares, square roots, cubes, and any power instantly. Features visual grid representation for perfect squares.
- Enter any number and select operation
- Visual grid shows square representation (up to 20×20)
- Automatic perfect square detection
- Calculate any power (x^n)
- View calculation history
Frequently Asked Questions
Square means multiplying a number by itself (5² = 5 × 5 = 25). Square root is the opposite - finding what number multiplied by itself gives you the original number (√25 = 5). They're inverse operations.
A perfect square is a number that results from multiplying an integer by itself. Our calculator instantly tells you if your number is a perfect square. For example, 16 is a perfect square (4²), but 17 is not.
In real numbers, you can't take the square root of a negative number. However, in complex numbers, this gives an imaginary result. Our calculator shows when a result would be imaginary.
The calculator can handle very large numbers up to JavaScript's maximum safe integer (2^53 - 1). For most practical purposes, this is more than sufficient.
Our calculator provides square roots accurate to 10 decimal places. For irrational square roots (like √2), we show the decimal approximation.
Squares are everywhere! Area calculations (square footage), physics (E=mc²), statistics (standard deviation), computer graphics (distance calculations), and engineering (structural loads) all use squares.
Because 1 × 1 = 1. By definition, a perfect square is any number that can be expressed as n², where n is an integer. Since 1 is 1², it's a perfect square.
The square root of 0 is 0, because 0 × 0 = 0. Zero is unique in that it's the only number that equals its own square root.