Squares 1 to 30
The squares of numbers from 1 to 30 range from 1² = 1 to 30² = 900. A square number is the result of multiplying a whole number by itself (n × n). The full table of all 30 values is below.
Squares of 1 to 30 (n and n²)
| Number (n) | Square (n²) |
|---|---|
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
| 17 | 289 |
| 18 | 324 |
| 19 | 361 |
| 20 | 400 |
| 21 | 441 |
| 22 | 484 |
| 23 | 529 |
| 24 | 576 |
| 25 | 625 |
| 26 | 676 |
| 27 | 729 |
| 28 | 784 |
| 29 | 841 |
| 30 | 900 |
What is a square number?
A square number is what you get when you multiply a whole number by itself. So the square of 7 is 7 × 7 = 49, written 7². It is called a 'square' because that many dots can be arranged into a perfect square grid — 49 dots make a 7-by-7 square.
Knowing squares 1 to 30 by heart speeds up almost everything else in maths: square roots, areas, the Pythagoras theorem, and quadratic equations all lean on them.
The pattern in the squares
The gap between one square and the next is always the next odd number. 1, then +3 → 4, then +5 → 9, then +7 → 16, and so on. This is why 1 + 3 + 5 + 7 + … always adds up to a perfect square.
It also means you can build the next square from the last one: 25² = 625, so 26² = 625 + 25 + 26 = 676.
Worked examples
Find 24² without a calculator.
- Split 24 into 20 + 4.
- 24² = (20 + 4)² = 20² + 2·20·4 + 4²
- = 400 + 160 + 16
- = 576.
Struggling with squares, roots or algebra? Learn it 1-to-1 with a maths mentor.
Related concepts
Frequently asked questions
30² = 30 × 30 = 900.
Every number from 1 to 30 has a square: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841 and 900.
Learn 1–10 first, then use the odd-number pattern (each square is the previous one plus the next odd number) and the (a + b)² trick to build the rest — you rarely need to memorise all 30 outright.