Multiplication Calculator
Whole numbers or decimals, up to 12 digits each. Negative numbers work too.
Long multiplication breaks a big product into one small row per digit. Type two numbers to see them multiplied the way it's taught in school, with every partial product, every carry and the final sum, or switch to the box method to see the same answer built from place values.
One row for every digit of the bottom number, then add
Long Multiplication in Three Steps
Write the number with more digits on top and line the digits up on the right. Here is 478 × 36.
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Multiply by the Ones Digit
Work right to left: 8 × 6 = 48, write 8 and carry 4. 7 × 6 + 4 = 46, write 6 and carry 4. 4 × 6 + 4 = 28. First row: 2,868.
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Multiply by the Tens Digit
Write a 0 on the right first, because the 3 means 30. Then 478 × 3 = 1,434, so the second row is 14,340.
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Add the Rows
2,868 + 14,340 = 17,208. A three-digit bottom number gives three rows, the last starting with two zeros.
Don't Forget the Placeholder Zero
The second row multiplies by 30, not 3. Leaving out the zero shifts the whole row one place and the answer comes out far too small.
The Box (Grid) Method
Split each number into place values, multiply every pair, then add all the boxes. Here is 23 × 14, with 23 = 20 + 3 and 14 = 10 + 4.
| × | 20 | 3 | Total |
|---|---|---|---|
| 10 | 200 | 30 | 230 |
| 4 | 80 | 12 | 92 |
Each box is a piece of the full rectangle, so the boxes add up to the whole product. The rows of long multiplication are the same row totals, just written more compactly. Switch the calculator above to Box method to see any product split this way.
Count the Places, Then the Signs
You don't line up decimal points when multiplying. Multiply as whole numbers and fix the point and the sign at the end.
Decimal Places
4.78 has 2 places and 3.6 has 1, so the answer has 3. Multiply 478 × 36 = 17,208, then place the point.
One Negative
If exactly one number is negative, the product is negative.
Two Negatives
If both numbers are negative, the signs cancel and the product is positive.
Estimate and Check on a 4 Function Calculator
Round each number to one non-zero digit for a quick estimate, then divide to check the exact answer on a basic calculator.
The Product
Estimate
Check by Dividing
Practise carrying, placeholder zeros and decimals in How to Do Long Multiplication: Steps and Examples, or brush up on the facts with the multiplication table.
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Frequently Asked Questions
How do you do long multiplication?
Multiply the top number by each digit of the bottom number, one row per digit, then add the rows. For 478 × 36: 478 × 6 = 2,868 and 478 × 30 = 14,340, so the answer is 2,868 + 14,340 = 17,208.
Why do you add a zero in long multiplication?
The zero keeps the place value right. In 478 × 36 the 3 is really 30, so the second row is 478 × 30 = 14,340, not 1,434. A digit in the hundreds place needs two zeros.
What is the box method of multiplication?
Split each number into place values and multiply every pair in a grid. For 23 × 14: 20 × 10 = 200, 3 × 10 = 30, 20 × 4 = 80, 3 × 4 = 12. The four boxes add up to 322. It's also called the grid or area method.
How do you multiply decimals?
Multiply as whole numbers, then put back as many decimal places as both numbers had together. For 4.78 × 3.6: 478 × 36 = 17,208, with 2 + 1 = 3 places, so 4.78 × 3.6 = 17.208.
How do you multiply negative numbers?
Multiply without the signs, then decide the sign. Exactly one negative gives a negative answer; two negatives give a positive one. −12 × 15 = −180 and −12 × −15 = 180.
How can I check a multiplication answer?
Estimate first, then divide. 478 × 36 is about 500 × 40 = 20,000, so 17,208 is reasonable. For an exact check, 17,208 ÷ 36 = 478.