Long Multiplication Calculator
Multiply two numbers with a full column-by-column working showing every partial product.
About Long Multiplication Calculator
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
Worked example
With the default values below, Long Multiplication Calculator returns Product of 7,981. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Multiplicand (top number)
- 347
- Multiplier (bottom number)
- 23
Results
- Product
- 7,981
- Partial Products
- 1041, 6940
Step by step
- 1SetupMultiply by each digit of the multiplier from right to left, shifting one place left each time.
- 2Multiply 347 by 3 (3 × 10^0 = 3)= 1041
- 3Multiply 347 by 2 (2 × 10^1 = 20)= 6940
- 4Sum all partial products= 7981
- 5Final product= 7981
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.