Math
Long Multiplication Calculator
Enter two numbers to see long multiplication exactly as it is set up on paper: the numbers stacked and right-aligned, one partial product per digit of the multiplier, each row shifted one place left, and the rows added at the bottom.
Decimals and negative numbers are handled with the standard rules, and every step is explained in words.
Goes on top. Up to 15 digits; decimals and negatives allowed.
Goes underneath. Each of its digits produces one partial-product row.
Try an example
Result
Product
—
- Partial products
- —
- Decimal places
- —
- Estimate
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the long multiplication calculator solves
Long multiplication breaks a big product into small ones you can do in your head. You multiply the top number by one digit of the bottom number at a time, write each result on its own row shifted left according to the digit's place value, and add the rows. This page draws that tableau for any two numbers and narrates each row.
Step by step
- Write the longer number on top and the other underneath, lining up the ones digits.
- Multiply the top number by the ones digit of the bottom number. Carry within the row as needed.
- Multiply by the tens digit and write that row one place to the left (or write a 0 in the ones column).
- Continue for every digit, shifting one more place each time.
- Add all the rows. That sum is the product.
- For decimals, count the total decimal places in both factors and place the point that many places from the right.
Decimals and negatives
Multiply as if there were no decimal points, then give the answer as many decimal places as the two factors have combined: 2.34 × 5.6 uses the same digits as 234 × 56 = 13104 and has 2 + 1 = 3 decimal places, so it equals 13.104. A product is negative only when exactly one factor is negative.
How to use it
- Enter the first number (it goes on top) and the second number (it goes underneath).
- Read the product and the column-method tableau with one partial product per digit.
- Open Show the work for the sentence-by-sentence explanation of each row, the shift, the addition, and decimal placement.
How to read the answer
Each partial-product row is the top number times one digit of the bottom number; the shift to the left multiplies it by the right power of ten. Adding the rows uses the distributive property. The estimate is a sanity check: if the product is not close to the estimate, look for a misaligned row.
Common mistakes and edge cases
- Forgetting to shift the second row one place left (or to write the placeholder 0).
- Dropping a carry inside a partial product, for example 6 × 4 = 24 → write 4, carry 2.
- Miscounting decimal places: multiply as whole numbers first, then count the total decimal digits in both factors.
- Giving a negative answer when both factors are negative; two negatives make a positive.
- Adding the partial products without lining up the ones column.
Worked examples
234 × 56
Two partial products: 1,404 and 11,700.
Product
13104
Decimals 2.34 × 5.6
Same digits, three decimal places.
Product
13.104
Negative factor -123 × 45
Exactly one negative, so the product is negative.
Product
-5535
Multiplying by 0
Every partial product is 0.
Product
0
Three-digit by three-digit
Three rows to add.
Product
328042
Large numbers
12 digits by 6 digits, exact.
Product
121932591494857848
Frequently asked questions
How does long multiplication work?+
Multiply the top number by each digit of the bottom number, write each answer on its own row shifted one place further left, then add the rows. 234 × 56: 234 × 6 = 1,404 and 234 × 5 = 1,170 shifted to 11,700; the sum is 13,104.
Why do you add a zero on the second line?+
The second digit of the multiplier is in the tens place, so its partial product is really the top number times a multiple of 10. Writing a 0 (or shifting left) accounts for that factor of 10.
How do I multiply decimals with long multiplication?+
Ignore the decimal points, multiply the whole numbers, then count the decimal places in both factors and put the point that many places from the right in the product.
What are partial products?+
The rows in the tableau: the top number multiplied by one digit of the bottom number. Adding them all gives the full product.
Which number goes on top?+
Either works because multiplication is commutative, but putting the number with more digits on top means fewer rows to add.
How can I check a multiplication answer?+
Divide the product by one factor and you should get the other, or estimate with rounded numbers to see if the size is right.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026