Long Multiplication Calculator
Solve multi-digit multiplication problems instantly. View detailed step-by-step working out, partial products, and final answers to master the column method.
Calculate Step-by-Step
Enter your numbers below to see the traditional column method in action. The calculator breaks down the partial products and shows exactly how the final answer is reached.
Multiplication Solver
Enter two whole numbers to generate the working out
Multiplication Quick Facts
Essential rules to remember for accurate calculations
How the Column Method Works
Mastering long multiplication is about breaking a large problem into a series of smaller, manageable single-digit multiplications and additions.
Align the Numbers
Write the two numbers vertically, one above the other, ensuring the digits are aligned to the right (units under units, tens under tens, etc.).
Multiply by the Units Digit
Start with the rightmost digit of the bottom number. Multiply it by each digit of the top number, moving from right to left. Write the result below the line. Carry over any tens to the next column.
Shift and Multiply
Move to the next digit to the left in the bottom number. Before multiplying, write a ‘0’ as a placeholder in the units column of the new row. Then repeat the multiplication process.
Add the Partial Products
Once all digits of the bottom number have been used, draw a final line and add all the partial product rows together using column addition to get your final answer.
Place Value Shifts
Understanding how digits shift based on their place value is the key to accurate long multiplication.
| Multiplier Digit Position | Actual Value Represented | Placeholder Zeros Needed | Example (Multiplying by 342) |
|---|---|---|---|
| Rightmost (Units) | Ones (× 1) | 0 zeros | Multiply by 2, write normally |
| Middle (Tens) | Tens (× 10) | 1 zero | Multiply by 4, write with one ‘0’ at the end |
| Leftmost (Hundreds) | Hundreds (× 100) | 2 zeros | Multiply by 3, write with two ‘0’s at the end |
| Thousands | Thousands (× 1,000) | 3 zeros | Multiply by the digit, add three ‘0’s |
Long Multiplication FAQ
Answers to the most frequently asked questions about multi-digit multiplication.
Write the numbers one above the other, aligned to the right. Multiply the top number by each digit of the bottom number, starting from the right. Write each partial product on a new line, shifting one place to the left for each subsequent digit. Finally, add all the partial products together to get the final answer.
Yes, the calculator can handle large multi-digit numbers. For the clearest step-by-step visual breakdown, it is optimised for numbers up to 15 digits, ensuring the working out remains easy to read and understand on all devices.
Partial products are the intermediate results you get when you multiply the top number by each individual digit of the bottom number. In long multiplication, these are written on separate lines and added together to find the total product.
No, due to the commutative property of multiplication, the order does not matter (e.g., 12 × 34 is the same as 34 × 12). However, placing the number with more digits on top often makes the manual working out slightly quicker, as there are fewer rows of partial products to add.