Square Calculator (x²)
Calculate the square of any positive or negative number (x² = x × x) with scientific notation and step-by-step arithmetic.
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What Is a Square Calculator (x²)?
In mathematics, squaring a number is the result of multiplying a number by itself: x² = x × x. The operation is an exponentiation with a power of 2.
How to Use This Calculator
- Enter any positive or negative integer or decimal number.
- View the squared result and its scientific notation.
- Review the step-by-step multiplication explanation.
Square Power Formula
x^2 = x \times x, \quad (-x)^2 = x^2Multiplying a number by itself always yields a non-negative real result, because negative times negative is positive.
Worked Example
Scenario: Calculate the square of -15
Given: x = -15
Operation: (-15)² = (-15) × (-15)
Result: 225
Tips & Key Notes
- The square of any non-zero real number is always strictly positive.
- Squaring a fraction between 0 and 1 produces a smaller number (e.g. (0.5)² = 0.25).
- Squaring is the inverse operation of finding the principal square root.
Frequently Asked Questions
Can the square of a real number ever be negative?
No. The product of two positive numbers is positive, and the product of two negative numbers is also positive. Only imaginary numbers (like i) have negative squares (i² = -1).
What are the first ten perfect squares?
1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
Why is it called "squaring"?
Because multiplying a side length by itself calculates the geometric area of a square: Area = s².
How do you square a decimal?
Multiply the decimal by itself. The result will have twice as many decimal places as the original number (e.g. 0.3 × 0.3 = 0.09).
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