Multiplication chart 1-30
A multiplication chart 1-30 is a 30 × 30 grid of products, from 1 × 1 = 1 to 30 × 30 = 900. Find one number down the left side and the other across the top: the square where they meet is the answer. Print it below in color, in black and white or blank, on US Letter or A4.
Print the multiplication chart 1-30
The whole chart fits on one page. On US Letter its products print at 8 points and each square is 6.1 mm wide (7.8 points and 6 mm on A4): small, but clear on a desk. The blank chart prints with the filled chart as its answer key.
| Sheet | US Letter | A4 |
|---|---|---|
| Color, one page | PDF (1 page, 64 KB) | PDF (1 page, 64 KB) |
| Black and white, one page | PDF (1 page, 63 KB) | PDF (1 page, 64 KB) |
| Blank, with answer key | PDF (2 pages, 71 KB) | PDF (2 pages, 71 KB) |
Black and white and blank charts
The black and white chart uses gray shading that copies well on a school photocopier. The blank chart keeps the numbers 1 to 30 along both edges and leaves every square empty to fill in.
How to read the 1-30 chart
- Find 23 in the colored column on the left and 17 in the colored row across the top.
- Follow row 23 across and column 17 down. They meet at 391, so 23 × 17 = 391.
- Division works backward: to find 391 ÷ 17, go down column 17 to 391 and read the number at the start of that row, 23.
The 1-30 chart in numbers
Our chart generator counted these. We count 23 × 17 and 17 × 23 as one fact, because they match on opposite sides of the diagonal.
| Chart | Squares | Different facts | Different products | Largest product |
|---|---|---|---|---|
| 1-12 | 144 | 78 | 59 | 144 |
| 1-20 | 400 | 210 | 152 | 400 |
| 1-30 | 900 | 465 | 308 | 900 |
| 1-100 | 10,000 | 5,050 | 2,906 | 10,000 |
So the 1-30 chart has 900 squares but only 308 different answers. The most repeated answers are 60 and 120, which each appear 10 times.
Square numbers from 1 to 30
The diagonal from the top left corner to the bottom right holds the square numbers, each a number times itself. They are the bold squares on the chart.
- 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
- 13 × 13 = 169
- 14 × 14 = 196
- 15 × 15 = 225
- 16 × 16 = 256
- 17 × 17 = 289
- 18 × 18 = 324
- 19 × 19 = 361
- 20 × 20 = 400
- 21 × 21 = 441
- 22 × 22 = 484
- 23 × 23 = 529
- 24 × 24 = 576
- 25 × 25 = 625
- 26 × 26 = 676
- 27 × 27 = 729
- 28 × 28 = 784
- 29 × 29 = 841
- 30 × 30 = 900
Tricks for the bigger numbers
- The 20s: Double the number, then multiply by 10. 20 × 14: double 14 is 28, and 28 × 10 = 280.
- 21 to 29: Split off the 20, multiply both parts and add. 23 × 6 = 20 × 6 + 3 × 6 = 120 + 18 = 138.
- The 30s: Multiply by 3, then by 10. 30 × 17: 3 × 17 = 51, and 51 × 10 = 510.
- Double one number, halve the other: The answer stays the same. 16 × 25 = 8 × 50 = 4 × 100 = 400.
Splitting a number this way is the distributive property, the same idea as Common Core 3.OA.B.5: "Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)"
Who needs a chart this big?
In the US, Common Core 3.OA.C.7 ends with "By the end of Grade 3, know from memory all products of two one-digit numbers." In England, Year 4 pupils should "recall multiplication and division facts for multiplication tables up to 12 × 12". Neither goes past 12 × 12, so a 1-30 chart is for looking answers up: checking long multiplication, finding factors and spotting patterns. To learn the facts themselves, start with the multiplication chart 1-12 and the times tables worksheets.
Sources
- Common Core State Standards for Mathematics, Grade 3 Operations and Algebraic Thinking: 3.OA.A.1, 3.OA.B.5, 3.OA.B.6, 3.OA.C.7, 3.OA.D.9; wording checked against the official standards PDF (page 23)
- National curriculum in England: mathematics programmes of study (Department for Education, 2013): Years 2, 3 and 4 times-table statements; Year 5 square numbers
Last checked October 25, 2026.