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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

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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