Long Multiplication Calculator — Step-by-Step Partial Products
See how long multiplication works: enter two whole numbers and get a full breakdown — one partial product for each digit of the multiplier, then their sum.
47 × 36
47 × 6 (ones digit of multiplier)
47 × 3 × 10^1 (tens digit of multiplier)
Add partial products
- 1
Multiplicand
47 - 2
Multiplier
36 - 3
Product
47 × 36 = 1,692
How does this calculator work?
Long multiplication computes A × B by multiplying A by each digit of B separately, shifting the result left according to that digit's place value (ones, tens, hundreds, …), then summing all partial products. Enter two whole numbers up to 9,999 to see every partial product.
Formula
How this is calculated
Long multiplication breaks the multiplier into its individual digits and multiplies each by the entire multiplicand, placing the result in the correct position (ones, tens, hundreds, …). Each such product is called a partial product. Because the ones digit of B contributes directly, the tens digit contributes multiplied by 10, the hundreds digit by 100, and so on, the positional shift is automatic.
The partial products are then added together — this addition itself follows the standard column-addition algorithm (with carrying). For a two-digit multiplier there are two partial products; for a three-digit multiplier there are three, and so on. The step-by-step display names each digit's position so the connection between the written algorithm and the place-value logic is clear.
This calculator supports whole numbers up to 9,999 to keep the step list readable. For larger numbers the algorithm is identical but produces more rows.
Frequently asked questions
A digit in the tens position represents 10 times its face value, so the partial product it generates is 10 times larger than the ones partial product. This is why the tens row is written one column to the left — or equivalently, multiplied by 10 — and the hundreds row two columns, and so on.
Not for the result — multiplication is commutative (A × B = B × A). However, choosing the number with fewer digits as the multiplier produces fewer partial products and keeps the working shorter.
When multiplying a digit of B by a multi-digit multiplicand A, carries arise within the partial product itself (e.g., 7 × 8 = 56: write 6, carry 5 to the next column of the partial product). This calculator shows the partial products as single completed numbers rather than digit-by-digit to keep the display at a readable length.
Also known as
TG we-Calculate Editorial Team. (2026). Long Multiplication Calculator — Step-by-Step Partial Products [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/long-multiplication-calculator
TG we-Calculate Editorial Team. "Long Multiplication Calculator — Step-by-Step Partial Products." TG we-Calculate. 2026. https://we-calculate.com/calculator/long-multiplication-calculator.
TG we-Calculate Editorial Team, "Long Multiplication Calculator — Step-by-Step Partial Products," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/long-multiplication-calculator
@misc{wecalculate_long_multiplication_calculator, title = {Long Multiplication Calculator — Step-by-Step Partial Products}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/long-multiplication-calculator}}, year = {2026}, note = {TG we-Calculate} }
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