Long multiplication turns a big product into several small ones. Each digit of the bottom number multiplies the whole top number, and the shifted partial products are added. Decimals are handled by counting decimal places at the end.
How to use the Long Multiplication Calculator
- First number (A)
- Second number (B)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The calculator multiplies the top number by each digit of the bottom number from right to left, adds trailing zeros for the place value and adds the partial products with exact integer arithmetic.
Formula
A × B = Σ A × (digit of B) × 10^(position)
Worked example
Inputs — First number (A): 123; Second number (B): 45.
Results — Product = 5535; Long multiplication = 123
× 45
──────
615
+ 4920
──────
5535; Number of partial products = 2.
Key terms
- Partial product
- The product of the top number and one digit of the bottom number.
Frequently asked questions
How do I multiply 123 by 45?
123 × 5 = 615 and 123 × 40 = 4,920; adding gives 5,535.
Why are the partial products shifted?
Each digit of the second number is worth ten times the digit to its right.
How do I place the decimal point?
Count the decimal places in both numbers and put that many in the answer.
What is the lattice method?
A grid-based layout of the same partial products.