Multiplication Chart 1 to 20
Every product from 1 × 1 to 20 × 20. Pick a square to see how to work it out from facts you already know.
More options1–20
Chart size
Answers
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13 × 14
182
13 rows of 14, or 14 rows of 13: both make 182.
- Turned round
- 14 × 13 = 182
- As division
- 182 ÷ 13 = 14
How this works: Method, 5 sources, Checked against 1 worked example,
How this works
Method
Past 12, few people know the facts by heart, so the chart is for working them out. Split the larger number into 10 and the rest: 17 × 14 is 17 × 10 = 170 plus 17 × 4 = 68, which makes 238. Each part is a fact you already know or can double your way to. Full method
Sources
- Wikipedia, Square number
- Common Core State Standards for Mathematics, Grade 3, 3.OA.B.5 (2010)
- Department for Education, National curriculum in England: mathematics programmes of study (2013)
- Common Core State Standards for Mathematics, Grade 3 (3.OA.B.5, 3.OA.C.7) (2010)
- Standards and Testing Agency, Multiplication tables check assessment framework (updated March 2022, 2018)
How it’s tested
One worked example for this page is checked by automated tests before every release: given the inputs, the tool must show the expected answer.
Changes
- First published: the chart from 1–10 to 1–20, practice with progress for each person, printable charts and sheets, the 2 to 12 tables and check practice.
Working out the bigger squares on a 1 to 20 chart
Past 12, few people know the facts by heart, so the chart is for working them out. Split the larger number into 10 and the rest: 17 × 14 is 17 × 10 = 170 plus 17 × 4 = 68, which makes 238. Each part is a fact you already know or can double your way to.
The diagonal holds the squares up to 400. Squares of numbers ending in 5 follow a pattern: multiply the tens digit by the next number up and write 25 after it, so 15 × 15 = 225 (1 × 2 = 2, then 25).
Numbers just either side of a round number give another shortcut: 19 × 21 is 20 × 20 minus 1, which is 399, because (20 − 1)(20 + 1) = 20² − 1². The chart lets you check every such trick against the real answer.
a × b = a × 10 + a × (b − 10)
- The squares on the diagonal of a 1 to 20 chart run from 1 to 400; a square number is a number multiplied by itself. Source: Wikipedia, Square number.
- Splitting a factor into easier parts and adding the products is the distributive property, which the Common Core teaches in grade 3. Source: Common Core State Standards for Mathematics, Grade 3, 3.OA.B.5 (2010).
Squares from 11 × 11 to 20 × 20, worked out
Each square found by splitting one number into 10 and the rest.
| Square | Route | Answer |
|---|---|---|
| 11 × 11 | 11 × 10 = 110, 110 + 11 = 121 | 121 |
| 12 × 12 | 12 × 10 = 120, 12 × 2 = 24 | 144 |
| 13 × 13 | 13 × 10 = 130, 13 × 3 = 39 | 169 |
| 14 × 14 | 14 × 10 = 140, 14 × 4 = 56 | 196 |
| 15 × 15 | 15 × 10 = 150, 15 × 5 = 75 | 225 |
| 16 × 16 | 16 × 10 = 160, 16 × 6 = 96 | 256 |
| 17 × 17 | 17 × 10 = 170, 17 × 7 = 119 | 289 |
| 18 × 18 | 18 × 10 = 180, 18 × 8 = 144 | 324 |
| 19 × 19 | 19 × 10 = 190, 19 × 9 = 171 | 361 |
| 20 × 20 | 20 × 10 = 200, 20 × 10 = 200 | 400 |
Frequently Asked Questions
How many different facts are on a 1 to 20 chart?
400 squares hold 210 different facts: 20 squares on the diagonal and 190 pairs that appear twice, such as 13 × 17 and 17 × 13 (both 221).
How do I multiply two numbers between 11 and 20 in my head?
Add one number to the ones digit of the other, multiply by 10, then add the two ones digits multiplied together. For 14 × 17: 14 + 7 = 21, so 210, plus 4 × 7 = 28, makes 238.
Can I print the 1 to 20 chart on one page?
Yes. Choose Print, then Chart, and keep the size at 1–20. It fits one A4 or US Letter page in black and white, with larger squares on the 1–10 and 1–12 sizes.