A partial product is one smaller multiplication created by splitting a factor into its place-value parts. Adding every partial product gives the same result as multiplying the original numbers at once.
This method is useful because it makes multiplication visible: tens multiply as tens, ones multiply as ones, and every contribution remains checkable.
For 23 × 14, the four pieces are 20×10, 20×4, 3×10, and 3×4. The calculator turns the same idea into exact digit rows for larger numbers and decimals.
Key idea
See the relationship
20×10 = 200+20×4 = 80+3×10 = 30+3×4 = 12
Quick guide
How to use this calculator
Enter a non-negative multiplicand.
Enter a non-negative multiplier.
Open the working to inspect per-digit products, carries, and shifted rows.
Calculation method
Each multiplier digit creates one shifted product
The calculator multiplies the first integer coefficient by each digit of the second, records the carries, and shifts each row according to that digit's place.
It sums those rows and restores the decimal point from the combined fractional scales. This page reuses the verified long-multiplication engine.
Worked example
Build 23 × 14 from partial products
The ones digit contributes 92 and the tens digit contributes 230; their sum is 322.
23 × 14 = (23 × 4) + (23 × 10) = 92 + 230 = 322
Supported inputs
Precision and limits
Exact decimals
Each factor may contain up to 200 digits and 100 decimal places.
Non-negative inputs
This written layout accepts zero and positive whole numbers or decimals.
Visible working
Per-digit multiplication, carries, shifts, and the final sum are exposed.
Clear syntax
Grouping separators, fractions, and scientific notation are not accepted.
