Enter two numbers to see them multiplied the way you would on paper: each digit of the bottom number gives a partial product, carries are written above, placeholder zeros shift each row, and the rows are added to give the answer. Decimals and negative numbers work too.
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Enter your values to see the result.
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How to use the Long Multiplication Calculator
Type the first number (it goes on top) and the second number.
Keep the box ticked to put the longer number on top, which means fewer rows to add.
Press Multiply to see the answer and the column working.
Read the digit-by-digit steps to follow each carry and partial product.
Compare with your own work row by row to find where a mistake crept in.
Long multiplication, step by step: 347 × 28
Set it up. Write 347 on top and 28 underneath, lining up the ones digits on the right.
Multiply by the ones digit (8). 7 × 8 = 56: write 6, carry 5. 4 × 8 = 32, plus 5 = 37: write 7, carry 3. 3 × 8 = 24, plus 3 = 27: write 27. First partial product: 2,776.
Multiply by the tens digit (2). Write a placeholder 0 in the ones column first. 7 × 2 = 14: write 4, carry 1. 4 × 2 = 8, plus 1 = 9. 3 × 2 = 6. Second partial product: 6,940.
Add the partial products. 2,776 + 6,940 = 9,716.
The same idea works for any size: a 4-digit × 3-digit problem has three partial products, with zero, one and two placeholder zeros.
Multiplying decimals and negatives
Problem
Multiply as whole numbers
Decimal places
Answer
4.25 × 1.6
425 × 16 = 6,800
2 + 1 = 3
6.800 = 6.8
0.07 × 0.3
7 × 3 = 21
2 + 1 = 3
0.021
12.5 × 8
125 × 8 = 1,000
1 + 0 = 1
100.0 = 100
3.14 × 2.5
314 × 25 = 7,850
2 + 1 = 3
7.850 = 7.85
−12 × 15
12 × 15 = 180
0
−180 (one negative factor)
−0.5 × −0.4
5 × 4 = 20
1 + 1 = 2
0.20 = 0.2 (two negatives make a positive)
Tips for fewer mistakes
Use squared paper or draw columns so every digit stays in its place-value column.
Write carries small above the next digit and cross them out once used, so they are not added twice.
Don't forget the placeholder zeros. Missing a zero is the most common error; the answer comes out about 10 times too small.
A zero digit in the bottom number (as in 805 × 309) gives a row of zeros. You can skip it, but then shift the next row by two places.
Estimate before and after. Rounding to one significant figure (805 × 309 ≈ 800 × 300 = 240,000) tells you roughly how big the answer should be.
Frequently asked questions
How do you do long multiplication?
Write the larger number on top and the other below it, aligned on the right. Multiply the top number by each digit of the bottom number, starting from the ones digit, carrying tens to the next column. Shift each new row one place left by writing a placeholder zero, then add all the rows.
Why do we add zeros in long multiplication?
Each digit of the bottom number has a place value. In 347 × 28, the 2 really means 20, so 347 × 2 is written as 694 with one zero after it: 6,940. The zeros keep every partial product in the correct column.
How do you multiply decimals using long multiplication?
Ignore the decimal points and multiply as whole numbers, then count the total number of decimal places in both factors and put that many digits after the point in the answer. 4.25 × 1.6: 425 × 16 = 6800, with 2 + 1 = 3 decimal places, gives 6.800 = 6.8.
What is a partial product?
It is the result of multiplying the top number by one digit of the bottom number, including its placeholder zeros. The final answer is the sum of all the partial products. For 347 × 28 they are 2,776 (347 × 8) and 6,940 (347 × 20), and the sum is 9,716.
Does it matter which number goes on top?
No, multiplication is commutative, so the answer is the same. Putting the number with more digits on top means fewer partial products to add, which is quicker and leaves less room for mistakes.
How can I check a long multiplication answer?
Estimate first by rounding each number: 347 × 28 is about 300 × 30 = 9,000, so 9,716 is reasonable. You can also swap the numbers and multiply again, or divide the answer by one factor to get the other.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.