FinanceCalcs
Long Multiplication Calculator
Enter any two numbers and see every step of long multiplication shown clearly using the partial products method. Great for checking your homework or understanding how long multiplication works.
Step-by-Step Working
Add the Partial Products
"Long multiplication is just adding up partial products. Each row is what you get when you multiply by one digit at a time — then you add them all together."
How long multiplication works
Long multiplication breaks a big multiplication problem into smaller, easier steps. Here’s how it works:
1. Multiply by each digit — Take each digit of the bottom number (right to left) and multiply it by the entire top number. Each result is called a partial product.
2. Shift each row left — Each partial product is shifted one place to the left because of its place value. The ones digit stays put, the tens digit shifts one place, hundreds shifts two, and so on.
3. Add the partial products — Add all the rows together to get the final answer.
Quick Questions
What is a partial product?
A partial product is the result of multiplying the top number by just one digit of the bottom number. For example, in 347 × 26, you first multiply 347 × 6 = 2082, then 347 × 20 = 6940. These two results are the partial products, and you add them to get the final answer: 2082 + 6940 = 9022.
Why do we shift rows to the left?
Because of place value! When you multiply by the tens digit, you’re really multiplying by 10 times that digit. Shifting one place left is the same as multiplying by 10. A zero is often written as a placeholder to show this shift.
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