A long multiplication calculator that shows every row
This long multiplication calculator with steps lays the sum out the way it is taught in school: the two numbers one above the other, one row for each digit of the bottom number, and a final addition. It works for whole numbers, for long multiplication with decimals, and for negative numbers, and it explains where the decimal point goes.
Use it to check homework, to see how a 3-digit by 2-digit product is built, or to produce a worked example for a class. Everything is computed in your browser with exact whole-number arithmetic, so even 30-digit numbers give the exact product.
How to use the Long Multiplication Calculator with Steps
- Type the first number (multiplicand) and the second number (multiplier). Decimals and a leading minus sign are fine.
- Read the product in the large result box.
- Study the column working: each row is the top number times one digit of the bottom number, shifted left by that digit’s place value.
- Open “Digit-by-digit steps with carries” to see every single-digit product, the carry and the digit written down.
- Press “Copy working” to paste the layout into a document, or “Swap numbers” to check that the order does not matter.
Long Multiplication Calculator with Steps features
Partial products
One labelled row per digit of the multiplier, including zero rows, with the right number of trailing zeros.
Decimals handled
Decimal points are removed, the whole numbers multiplied, and the point restored from the total number of decimal places.
Carries explained
The optional step list shows each digit times digit plus carry.
Exact
BigInt arithmetic means no floating-point rounding, up to 30 digits per number.
How long multiplication works
Take 1234 × 56. First multiply 1234 by the ones digit, 6: that is 7404. Next multiply 1234 by the tens digit, 5, but because the 5 stands for fifty you write the answer one place to the left (or add a zero): 1234 × 5 = 6170, so the row reads 61700. Finally add the rows: 7404 + 61700 = 69104.
Inside each row you multiply digit by digit from the right. 4 × 6 = 24: write 4 and carry 2. 3 × 6 = 18, plus the carried 2 is 20: write 0, carry 2. Carry on to the left, and write down the last carry in full. This is the standard algorithm; it works because multiplication spreads over addition: 1234 × 56 = 1234 × 6 + 1234 × 50.
Multiplying decimals
Ignore the decimal points, multiply as if both numbers were whole, then count the decimal places in the two original numbers and put that many places into the answer. For 12.34 × 5.6 you multiply 1234 × 56 = 69104. The factors have 2 and 1 decimal places, so the answer has 3: 69.104. Trailing zeros after the point are dropped, so 1.5 × 2 shows 3 rather than 3.0.
Worked example in a table
| Row | Working | Value |
|---|---|---|
| Ones digit 6 | 1234 × 6 | 7404 |
| Tens digit 5 | 1234 × 5, shifted one place | 61700 |
| Sum | 7404 + 61700 | 69104 |
Common mistakes
- Forgetting the zero (or the shift) on rows after the first one.
- Dropping a carry, especially a carry that ends up as the leading digit.
- Counting decimal places in the answer wrongly: count the places in both factors, not just one.
- Treating a zero digit in the multiplier as “nothing to do” and misaligning the following rows.
Related maths tools
For the opposite operation use the long division calculator; the multiplication table generator helps with the single-digit facts, and the place value chart shows why each row is shifted.
Long Multiplication Calculator with Steps FAQ
How do you do long multiplication with steps?
Write one number above the other, multiply the top number by each digit of the bottom number from the right, shift each row one place further left, and add the rows. This calculator displays each of those rows.
How do you do long multiplication with decimals?
Remove the decimal points, multiply the whole numbers, then place the decimal point so the answer has as many decimal places as the two factors have together.
What is the long multiplication method for 3 digits?
A 3-digit multiplier gives three rows: ones, tens (shifted one place) and hundreds (shifted two places). Add the three rows to get the product.
Does the order of the numbers matter?
The product is the same either way. Putting the number with fewer digits on the bottom just means fewer rows to write.
How big a number can I enter?
Up to 30 digits each, with or without a decimal point. The result is exact because it uses integer arithmetic.
Can I use negative numbers?
Yes. The digits are multiplied as usual and the sign is negative when exactly one factor is negative.