TablesTrophy → Square Numbers
Square Numbers
Drill 2², 3² … up to 12² with instant feedback, and see the full list of squares from 1×1 to 12×12 — the diagonal of the times table, made automatic.
How it works
Practise first, read after. Press Begin for ten "n × n = ▢" questions drawn from 2² to 12², with instant right/wrong feedback. Then keep scrolling for the full squares list, the odd-number pattern, and answers to common questions. Nothing you type is stored.
The squares drill
A square number is a number multiplied by itself: 6 × 6 = 36, so 36 is the square of 6 (written 6²). The squares from 1 to 12 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144. They form the diagonal of the multiplication grid, and knowing them by heart speeds up area, algebra and mental maths.
Key takeaways
- A square is n × n — a number times itself.
- The squares 1–12 run 1, 4, 9 … up to 144.
- The gaps are the odd numbers (+3, +5, +7 …).
- They’re the grid’s diagonal — worth knowing on sight.
- No account, no data — it runs in the browser.
The square numbers 1 to 12
- 1 × 1 = 1
- 2 × 2 = 4
- 3 × 3 = 9
- 4 × 4 = 16
- 5 × 5 = 25
- 6 × 6 = 36
- 7 × 7 = 49
- 8 × 8 = 64
- 9 × 9 = 81
- 10 × 10 = 100
- 11 × 11 = 121
- 12 × 12 = 144
The odd-number pattern
You don't have to memorise the squares cold. Each one is the previous square plus the next odd number:
- 1, then +3 → 4
- 4, then +5 → 9
- 9, then +7 → 16
- 16, then +9 → 25, and so on.
Spotting that pattern turns a list to memorise into a rule to apply — and it explains why squares grow so quickly.
Why squares matter
Square numbers show up everywhere: the area of a square (side × side), the x² in algebra, square roots, and quick mental-maths tricks. They are also the diagonal of the multiplication chart — the line where the row and column match. Get them automatic now and later maths feels much lighter.
Frequently asked questions
What is a square number?
A square number is what you get when you multiply a number by itself. For example 5 × 5 = 25, so 25 is the square of 5, written 5². The squares from 1 to 12 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144.
How does the square-numbers drill work?
Press Begin and you get ten "n × n = ▢" questions — for example "7 × 7 = ▢" — drawn from 2² up to 12². Type the answer and press Check for instant feedback; a wrong answer shows you the correct square.
Why are square numbers worth practising on their own?
The squares are the diagonal of the multiplication grid, and they appear constantly — in area, in algebra (x²), and in mental-maths shortcuts. Knowing them by heart speeds up everything else.
Is there a pattern to the square numbers?
Yes — the gaps between consecutive squares are the odd numbers: 1, 4 (+3), 9 (+5), 16 (+7), 25 (+9)… So each square is the previous one plus the next odd number. Many children find that pattern easier than rote memorising.
Is it free, and is anything stored?
It is completely free, needs no account, and stores nothing. Questions are generated in your browser and nothing you type is sent anywhere.
What should we practise next?
Once the squares are automatic, practise full tables, then mix several together, then try a timed speed test to build all-round fluency.
Square numbers are mathematical facts (12 × 12 = 144 is exact). The odd-number gap pattern is a standard property of the squares.
Last reviewed 2026-06-28