Times tables, square numbers and a printable chart — with the shortcuts that make them stick and a drill to make them fast
Mental arithmetic is one skill made of a few hundred small facts. Once each fact is instant, everything built on top of it — long multiplication, dividing, fractions, percentages, unit conversion — stops being slow. This section gathers those facts into three references you can actually learn from, and a timed drill to turn recognition into recall.
There are 190 distinct multiplication facts from 2 × 2 to 20 × 20, but they are not 190 separate things to learn. Order does not matter (7 × 8 is 8 × 7), the 1s, 2s, 5s, 10s and 11s follow rules, and every fact is one step from a square. Strip those out and fewer than twenty genuinely hard facts remain.
The ones that cause the most trouble are the middle of the grid: 7 × 8 = 56, 6 × 8 = 48, 7 × 9 = 63, 6 × 7 = 42, 8 × 9 = 72, 4 × 7 = 28, 6 × 9 = 54, 3 × 8 = 24. None of them has a neat digit pattern to lean on, which is exactly why they need drilling rather than reciting.
A few facts people search for most have a page of their own with the story behind them — 7 × 8, the one most adults admit to tripping on; 8 × 9 and the finger trick; 19 × 19 and the Go board — linked below.
All twenty tables are written out in full on one page, from the 1 times table to the 20 times table, each with the patterns hiding inside the row, a line of advice for that row, and a drill you can point at any table.
Anchors are the fastest way in. The 1, 2, 5 and 10 steps of any table come almost free, and every other fact in that row is one addition or one subtraction away from an anchor. Building from anchors beats counting up from the start of the row, because it works when the facts arrive out of order — which is how they arrive in real arithmetic.
Every perfect square up to 25² is listed with its root, alongside the non-square roots people most often look up — each with its decimal value and simplified form — and a method for bracketing any root in your head.
Squares and roots are the same fact read in opposite directions, so learning them together halves the work: knowing 12 × 12 = 144 is the same as knowing √144 = 12.
Reading an answer is not learning it. Recall improves with the number of times a fact is retrieved under a little pressure, which is why every page here ends in a drill rather than a summary.
Sixty seconds a day, shuffled, beats twenty minutes once a week. The arcade has timed arithmetic drills, a times-tables sprint and a mental addition game, all free, all instant, and none of them asking for an account.
Learn the 1, 2, 5 and 10 anchors of each row first, then build every other fact by adding or subtracting one lot. Drill shuffled rather than in order, for a minute a day, checking each answer immediately.
The middle of the grid causes the most trouble because it has no digit pattern to lean on: 7 × 8 = 56, 6 × 8 = 48, 7 × 9 = 63, 6 × 7 = 42, 8 × 9 = 72. Drill those on their own rather than inside a full row.
Not to get by, but the 13 to 20 rows are quick once you split them: 17 × 6 is 10 × 6 plus 7 × 6. Learning the split is more useful than memorising eight extra rows.
A calculator answers the question you already know how to ask. Mental arithmetic is what lets you notice an answer is wrong, estimate before committing, and keep a longer calculation moving without stopping to type.
No. Every page and every drill here is free, instant, and works without signing in or giving an email address.
Start with the multiplication chart if you want the whole grid on one screen, pick a times table and drill it, or read how to learn the times tables without chanting.