Long Multiplication Calculator
Long multiplication is the traditional method of multiplying large numbers by hand. This calculator takes two numbers and displays the product, along with the partial products used in the standard long multiplication algorithm. Partial products are obtained by multiplying each digit of one number by each digit of the other, then shifted according to place value. Long multiplication teaches fundamental mathematical principles including place value, the distributive property, and mental arithmetic. It remains an important skill for understanding how multiplication works, beyond just using a calculator.
Long multiplication algorithm
Multiply each digit of the first number by each digit of the second
Shift partial products by place value (multiply by 10, 100, etc.)
Add all partial products to get the final result
Example: 23 × 45 = (23 × 5) + (23 × 40) = 115 + 920 = 1,035
Long multiplication examples
| First | Second | Product | Method |
|---|---|---|---|
| 23 | 45 | 1,035 | (23×5) + (23×40) |
| 12 | 34 | 408 | (12×4) + (12×30) |
| 99 | 99 | 9,801 | (99×9) + (99×90) |
| 100 | 50 | 5,000 | 100 × 50 |
Long multiplication calculator: frequently asked questions
What is long multiplication?
Long multiplication is a method of multiplying large numbers by hand. It breaks the multiplication into smaller steps using partial products, then adds them together to find the final result.
What are partial products?
Partial products are the products you get by multiplying each digit of one number by each digit of the other. For example, 23 × 45: 23 × 5 = 115 (one partial product), 23 × 40 = 920 (another partial product).
How do you align partial products?
Each partial product is shifted one place to the left for each digit position. This accounts for the place value of the digit being multiplied. The partial products are then added to get the final result.
Why is long multiplication still taught?
Long multiplication teaches place value, the distributive property, and develops mental arithmetic skills. It helps students understand the underlying principles of multiplication, not just how to get an answer.
Can long multiplication handle decimals?
Yes, long multiplication works with decimals. Count the total decimal places in both numbers, perform the multiplication ignoring decimals, then place the decimal point in the result.
Official sources
- Multiplication algorithm: NIST Special Publication 330.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.