Long Multiplication Calculator
Multiply whole numbers or decimals using the Standard Algorithm with step-by-step work.
Multiply numbers using long multiplication with step-by-step work. Shows partial products and visual grid.
How to Use
Performing Long Multiplication
This calculator multiplies positive or negative whole numbers or decimals using the Standard Algorithm (traditional long multiplication method). Enter your multiplicand and multiplier to see the complete step-by-step solution.
How to Do Long Multiplication by Hand:
- Stack the numbers: Place the larger number on top, aligned by place value
- Multiply by ones digit: Multiply top number by the ones digit of the bottom number
- Shift and multiply: Move to tens digit, shift result one place left, multiply again
- Continue for each digit: Repeat for hundreds, thousands, etc.
- Add partial products: Sum all partial products to get the final answer
Parts of Long Multiplication:
- Multiplicand: The number being multiplied (top number)
- Multiplier: The number you multiply by (bottom number)
- Partial Products: Results from multiplying by each digit
- Product: The final answer after adding partial products
What is Long Multiplication Calculator?
Long multiplication (also called column multiplication or the Standard Algorithm) is a method for multiplying large numbers by hand. It breaks down the problem by multiplying the multiplicand by each digit of the multiplier separately, then adding all the partial products together.
This method works by leveraging place value. When you multiply by the tens digit, you're actually multiplying by that digit times 10, which is why you shift the partial product one place to the left. Similarly, hundreds mean shifting two places, and so on.
Long multiplication with decimals: Count total decimal places in both numbers, perform multiplication as if they were integers, then insert the decimal point in the product with that many decimal places from the right.
Formula
Standard Algorithm Steps:
1. Multiply top number by ones digit of bottom number
2. Write partial product, carrying digits as needed
3. Multiply by tens digit, shift result one place left
4. Continue for each digit in the multiplier
5. Add all partial products using long addition
Long Multiplication with Decimals:
1. Count total decimal places in both numbers
2. Ignore decimals, multiply as integers
3. Insert decimal point with that many places from right
Example: 45.2 x 0.21 = 9.492 (3 decimal places)
Negative Number Rules:
• Positive x Positive = Positive
• Negative x Negative = Positive
• Positive x Negative = Negative
• Negative x Positive = Negative
Examples
Example 1: 234 x 56
Step 1: 234 x 6 = 1,404
Step 2: 234 x 5 = 1,170 (shift left → 11,700)
Step 3: Add partial products: 1,404 + 11,700
Product = 13,104
Example 2: 256 x 32
Step 1: 256 x 2 = 512
Step 2: 256 x 3 = 768 (shift left → 7,680)
Step 3: Add: 512 + 7,680
Product = 8,192
Example 3: 45.2 x 0.21 (with decimals)
Total decimal places: 1 + 2 = 3
Multiply as integers: 452 x 21 = 9,492
Insert decimal with 3 places from right
Product = 9.492
Example 4: -24 x 15 (negative number)
Multiply absolute values: 24 x 15 = 360
One negative, one positive → result is negative
Product = -360