Long Multiplication Calculator
Multiply two numbers with a full column-by-column working showing every partial product.
Inputs
Product
7,981
Partial Products
1041, 6940
Step by step
Setup
347 × 23
Multiply by each digit of the multiplier from right to left, shifting one place left each time.
Multiply 347 by 3 (3 × 10^0 = 3)
347 × 3 = 1041, shifted 0 places → 1041
= 1041
Multiply 347 by 2 (2 × 10^1 = 20)
347 × 2 = 694, shifted 1 place → 6940
= 6940
Sum all partial products
1041 + 6940
= 7981
Final product
= 7981
How it works
Long multiplication breaks a multiplication into partial products — one for each digit of the multiplier. Each partial product is the multiplicand times one digit, shifted left by the digit's place value. The final answer is the sum of all partial products.
Formula
Long Multiplication
Product = sum of (multiplicand × each digit of multiplier × place value of that digit)
- multiplicand
- The top number
- multiplier
- The bottom number
Frequently Asked Questions
Why shift left for each digit?
Each digit in the multiplier represents a different place value (ones, tens, hundreds…). Shifting left is equivalent to multiplying by 10, 100, etc.
Does this work for negative numbers?
Yes — compute the product of the absolute values, then apply the sign rule: negative × positive = negative, negative × negative = positive.