Multiplication Calculator
A full-featured multiplication tool for everyday and classroom use. Multiply a list of numbers and see the product instantly, switch to Long Multiplication to watch partial products build up digit by digit just like pencil-and-paper, or flip to Reverse Solve to find a missing factor when you know the product.
Formula
Worked example
For 234 × 56 in long multiplication: multiply 234 by 6 (ones digit) to get 1,404; multiply 234 by 5 (tens digit) to get 1,170 with a trailing zero making it 11,700; add 1,404 + 11,700 = 13,104. For decimals like 2.3 × 4.5, temporarily ignore decimal points to multiply 23 × 45 = 1,035, then place the decimal point two places from the right to get 10.35.
How multiplication works and what these modes do
Multiplication is repeated addition: multiplying a by n means adding a to itself n times. This calculator offers three modes. "Multiply a list" handles up to any number of comma-separated factors, decimals and negatives included, and is useful when you need a quick product. "Long multiplication" shows the classic pencil-and-paper algorithm, where you multiply the top number by each digit of the bottom number in turn, shift partial products left by the appropriate place value, and then add everything up. "Reverse solve" works backward: if you know the product and one factor, dividing gives the missing factor, because division is the inverse of multiplication.
Long multiplication digit by digit
To multiply 234 by 56 by hand, write 234 on top and 56 below. Start with the ones digit of 56 (the 6): 234 × 6 = 1,404. Write that below the line. Next take the tens digit (5): 234 × 5 = 1,170, but because this digit is in the tens column, append one zero to get 11,700. Add the two partial products: 1,404 + 11,700 = 13,104. Each digit of the multiplier generates one partial product, shifted left by its place value, and the final answer is their sum. For decimals, first count the total decimal places across both numbers, multiply as integers, and then re-insert the decimal point that many places from the right.
Signs and decimals
The sign of a product depends only on how many negative factors you supply. An even count of negatives gives a positive product, while an odd count gives a negative one, because each pair of negatives cancels. With decimals, the number of decimal places in the answer equals the total decimal places across all factors before any trailing zeros are dropped: multiplying 0.2 by 0.3 yields 0.06, for instance. The calculator handles sign rules and decimal placement automatically so you can focus on the result.
Reverse solve and missing factors
If you know a product and one factor but need the other, switch to Reverse Solve. The calculator divides the product by the known factor to recover the missing one. This is useful in proportion problems (if 4 bags cost 28 dollars, how much does one bag cost?), recipe scaling, and unit-rate questions. If the result is not a whole number, the factors do not share a clean ratio, and you may want to check whether your product was rounded.
Multiplication table: 1 to 12
The standard times table covers factors 1 through 12. Each cell is simply the row number times the column number. Memorising through 12 × 12 = 144 covers the vast majority of everyday calculations and makes long multiplication faster because you can recall each single-digit product instantly rather than computing it from scratch.
Multiplication table: 1 to 12
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
Row label times column label gives the cell value. Memorising through 12 × 12 covers most everyday needs.
Frequently asked questions
Can I multiply more than two numbers at once?
Yes. In the "Multiply a list" mode, enter as many numbers as you like separated by commas, and the calculator multiplies them all together. Because multiplication is associative, chaining the factors one at a time gives the same product as any other grouping.
Does the order of the numbers matter?
No. Multiplication is commutative, so 3 × 5 × 2 gives the same product as 5 × 2 × 3 or any other arrangement. You can list your factors in whatever order is convenient.
What happens if one of the numbers is zero?
The product is zero. This is the zero property of multiplication: a single factor of zero forces the entire product to zero, regardless of how large or small the other factors are.
How does long multiplication work for decimals?
Count the total number of decimal places across both numbers. Temporarily ignore the decimal points and multiply as if the numbers were whole numbers. Once you have the integer product, place the decimal point that many positions from the right. For example, 2.3 × 4.5 has two decimal places total: multiply 23 × 45 = 1,035 and then shift two places to get 10.35.
How do I find a missing factor when I know the product?
Switch to Reverse Solve mode. Enter the product and the factor you know, and the calculator divides the product by the known factor. For example, if 4 × ? = 28, divide 28 by 4 to get 7. Division is the inverse operation of multiplication.
Why is the product of two negatives positive?
Sign rules follow a pattern: positive times positive is positive, negative times positive is negative, and negative times negative is positive. Intuitively, the first negative reverses the direction of the number line, and the second negative reverses it back. So an even number of negative factors always produces a positive product, and an odd number produces a negative product.
What are the parts of a multiplication problem called?
The number being multiplied is the multiplicand, the number you multiply by is the multiplier, and the answer is the product. In long multiplication, the intermediate results computed for each digit of the multiplier are called partial products.