The square of a number is that number multiplied by itself, written x² and read “x squared.” Squares are everywhere: the area of a room, the Pythagorean theorem, variance in statistics and the distance formula all rely on them. This calculator squares any number exactly, including whole numbers with hundreds of digits, decimals and fractions, and shows a shortcut you can use without a calculator.
How to use the square number calculator
- Type the number in the Number (x) box. You can enter whole numbers of any length, decimals such as 0.03, negative numbers, or fractions such as 3/4.
- Read x² on the tape. Long results also show their digit count and scientific notation.
- Open the steps to see the multiplication, the place-value shortcut for two- to four-digit whole numbers, and the decimal-place rule for decimals.
The square formula
Two identities make squaring easier by hand:
Worked example: 47²
Direct: 47 × 47 = 2,209.
Shortcut: split 47 into 40 + 7. Then 40² = 1,600, 2 × 40 × 7 = 560 and 7² = 49. Adding gives 1,600 + 560 + 49 = 2,209.
Check with the next square: 48² = 2,304, which is 2,209 + 95. Consecutive squares always differ by an odd number: 2 × 47 + 1 = 95.
Decimals follow the same idea. To square 0.03, square 3 to get 9, then use four decimal places (twice the two in 0.03): 0.03² = 0.0009. A common mistake is writing 0.09, which is the square of 0.3.
Squares from 1 to 20
| n | n² | n | n² |
|---|---|---|---|
| 1 | 1 | 11 | 121 |
| 2 | 4 | 12 | 144 |
| 3 | 9 | 13 | 169 |
| 4 | 16 | 14 | 196 |
| 5 | 25 | 15 | 225 |
| 6 | 36 | 16 | 256 |
| 7 | 49 | 17 | 289 |
| 8 | 64 | 18 | 324 |
| 9 | 81 | 19 | 361 |
| 10 | 100 | 20 | 400 |
For a longer table, see the list of perfect squares.
Patterns worth knowing
- Last digits. A perfect square can only end in 0, 1, 4, 5, 6 or 9. If a whole number ends in 2, 3, 7 or 8, it is not a perfect square.
- Numbers ending in 5. Take the tens part n, multiply n × (n + 1) and write 25 after it: 85² → 8 × 9 = 72 → 7,225.
- Squares near 50 or 100. 98² = (100 − 2)² = 10,000 − 400 + 4 = 9,604.
- Odd-number sums. 1 + 3 + 5 + … + (2n − 1) = n². Adding the first five odd numbers gives 25.
Squares in units
When x carries a unit, the square carries the unit squared. A room 12 ft wide has a floor area of 12 ft × 12 ft = 144 ft². Converting square units means squaring the conversion factor too: 1 yd = 3 ft, so 1 yd² = 9 ft², not 3 ft².
To undo a square, use the square root calculator. For three dimensions, the cube number calculator finds x³.
Frequently asked questions
What does it mean to square a number?
Squaring a number means multiplying it by itself: x² = x × x. The name comes from geometry, because a square with side length x has an area of x² square units.
Is the square of a negative number negative?
No. A negative times a negative is positive, so (−13)² = 169. Be careful with notation, though: −13² usually means −(13²) = −169, because the exponent is applied before the minus sign.
How do I square a decimal?
Square the digits as if there were no decimal point, then give the answer twice as many decimal places as the original. For 1.5², square 15 to get 225; 1.5 has one decimal place, so the answer has two: 2.25.
What is the quickest way to square a number in my head?
Split it into tens and ones and use (a + b)² = a² + 2ab + b². For 47², that is 40² + 2 × 40 × 7 + 7² = 1,600 + 560 + 49 = 2,209. Numbers ending in 5 have an even faster trick: 65² = 6 × 7 hundreds plus 25 = 4,225.