By Tim King · Updated
Multiplication Chart
Square Numbers and Any Single Times Table Listed Beside the Grid
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How the Multiplication Chart works
This multiplication chart builds a times table grid for any run of whole numbers, from the classic 1 to 12 up to 30 numbers wide. It also lists the square numbers along the diagonal and writes out any single times table you name, ready to copy for homework or print for the wall.
A multiplication chart is a square grid with the same numbers along the top and down the side. The cell where a row meets a column holds their product, so 7 down and 8 across gives 56. Because multiplication works in either order, the chart is symmetrical about its diagonal, and every fact appears twice.
How the multiplication chart works
The formula for each cell is simply row × column. The chart runs every pair from the first number to the last, so 1 to 12 gives 12 × 12 = 144 cells. The diagonal holds the squares, n × n, and a highlighted times table is the row for that number written out in full.
First example. A 1 to 12 chart has 144 products, the largest being 12 × 12 = 144, and the squares 1, 4, 9 and so on down to 144 on the diagonal.
Second example. A 13 to 20 chart is an 8 × 8 grid that starts at 13 × 13 = 169 and ends at 20 × 20 = 400, handy for learning the teens facts.
How many different facts are in a 12 × 12 chart? Of the 144 cells, the 12 on the diagonal are unique and the other 132 pair up, so there are 12 + 66 = 78 different facts.
Multiplication chart from 1 to 20
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | 38 | 40 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 | 48 | 51 | 54 | 57 | 60 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 | 64 | 68 | 72 | 76 | 80 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | 80 | 85 | 90 | 95 | 100 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 | 78 | 84 | 90 | 96 | 102 | 108 | 114 | 120 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 | 91 | 98 | 105 | 112 | 119 | 126 | 133 | 140 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | 112 | 120 | 128 | 136 | 144 | 152 | 160 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 | 117 | 126 | 135 | 144 | 153 | 162 | 171 | 180 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | 190 | 200 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 | 143 | 154 | 165 | 176 | 187 | 198 | 209 | 220 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 | 156 | 168 | 180 | 192 | 204 | 216 | 228 | 240 |
| 13 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 | 143 | 156 | 169 | 182 | 195 | 208 | 221 | 234 | 247 | 260 |
| 14 | 14 | 28 | 42 | 56 | 70 | 84 | 98 | 112 | 126 | 140 | 154 | 168 | 182 | 196 | 210 | 224 | 238 | 252 | 266 | 280 |
| 15 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 | 195 | 210 | 225 | 240 | 255 | 270 | 285 | 300 |
| 16 | 16 | 32 | 48 | 64 | 80 | 96 | 112 | 128 | 144 | 160 | 176 | 192 | 208 | 224 | 240 | 256 | 272 | 288 | 304 | 320 |
| 17 | 17 | 34 | 51 | 68 | 85 | 102 | 119 | 136 | 153 | 170 | 187 | 204 | 221 | 238 | 255 | 272 | 289 | 306 | 323 | 340 |
| 18 | 18 | 36 | 54 | 72 | 90 | 108 | 126 | 144 | 162 | 180 | 198 | 216 | 234 | 252 | 270 | 288 | 306 | 324 | 342 | 360 |
| 19 | 19 | 38 | 57 | 76 | 95 | 114 | 133 | 152 | 171 | 190 | 209 | 228 | 247 | 266 | 285 | 304 | 323 | 342 | 361 | 380 |
| 20 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 | 220 | 240 | 260 | 280 | 300 | 320 | 340 | 360 | 380 | 400 |
Tips
- Use the diagonal. Every fact above the diagonal is mirrored below it, which halves the work.
- Spot patterns. The 9s digits add to 9, and the 5s end in 0 or 5.
- Test, don't stare. Once the chart looks familiar, switch to timed practice.
FAQ
What is on a standard multiplication chart?
A standard chart runs from 1 to 12 in both directions, giving 144 products from 1 up to 144. Some older charts stop at 10, and some schools use 1 to 20 for extension work. Change the first and last numbers to build any of them.
How do you read a multiplication chart?
Find the first number down the left-hand column and the second along the top row. Follow the row across and the column down until they meet; the number in that cell is the product. For 6 × 9, go to row 6 and column 9 to find 54.
Why is the multiplication chart symmetrical?
Multiplication is commutative, which means the order does not change the answer: 4 × 7 and 7 × 4 are both 28. Every product therefore appears on both sides of the diagonal, and only the square numbers along it appear once.
Can I print the multiplication chart?
Yes. Build the range you want, then use your browser's print command; the chart prints as a plain table. The Copy button copies the results, and the table can be selected and pasted straight into a spreadsheet or a document.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
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