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Key Features
Instant Calculation
Get accurate results in real time with our optimized algorithm.
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Long multiplication breaks down multiplying two multi-digit numbers into a series of simpler partial products, one per digit of the second number, which are then added together. This tool shows every partial product and the final sum.
How it works
The first number is multiplied by each digit of the second number in turn (starting from the rightmost digit), with each partial product shifted left according to that digit's place value, then all partial products are added together.
- Enter first number.
- Enter second number.
- Click Calculate to see your results.
Examples
Multiplying a 3-digit by a 2-digit number
473 × 86: 473 × 6 = 2838, and 473 × 8 (shifted one place left) = 37840. Adding these partial products, 2838 + 37840 = 40678.
Who should use it
- Elementary and middle school long multiplication homework.
- Verifying manual long-multiplication work step by step.
Industry applications
- Education (arithmetic instruction)
Advantages
- Shows every partial product individually before the final sum.
- Clearly demonstrates why each partial product is shifted.
Limitations
- Limited to numbers up to 9 digits each to keep the working readable.
Common mistakes to avoid
- Forgetting to shift a partial product left by the correct number of places before adding it to the others.
Best practices
- Write out each partial product on its own line, correctly shifted, before adding — trying to combine steps mentally is where most manual errors creep in.
Tips
- If your manual total is off, check each partial product individually first — a single misplaced shift is the most common source of error.