What does this calculator do?
Long multiplication breaks a multiplication into one partial product for each multiplier digit, then adds the shifted rows. This calculator makes those digit operations visible instead of showing only an expression value.
For a general expression use the Scientific Calculator; for fractions use the Fraction Calculator.
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Optional place value learning blocks (paid link) can make regrouping tangible. No purchase is required.
How to enter numbers and read the columns
Enter the two factors and select Calculate. Read the unsigned integer multiplication first, then the decimal-placement and sign steps. The integer working deliberately removes decimal dots before multiplication; it is not the final decimal answer.
Results start blank, clear after edits, and reappear only after a valid calculation. Reset clears both numbers and restores the default operation. Copy, Download and Print include the calculation steps and column working.
Optional squared exercise notebooks (paid link) can help keep handwritten digits aligned.
Exact method and place value
If a=A×10^(-p) and b=B×10^(-q), then ab=(A×B)×10^(-(p+q)). Multiply integer digits from right to left. At each digit, write the units digit of the product plus carry and pass the remaining tens to the next position. Shift partial products according to multiplier position.
All supported operations use integer arithmetic and decimal scaling; the tool does not evaluate user-supplied JavaScript or silently approximate an unsupported input.
Worked examples
For 23 × 14, the partial products are 92 and 230; adding gives 322. For 12.5 × 0.24, integer digits give 125 × 24 = 3000. Restore three decimal places to get 3. For -0.045 × 0.03, 45 × 3 = 135 and five decimal places give -0.00135.
Understand carries, borrowing and signs
Each partial row already includes its place-value shift, including any trailing zeros. A zero multiplier digit contributes zero. The result is exact; the full decimal scale is applied even when the displayed final answer has no trailing zeros.
Optional place value charts (paid link) can support place-value practice. For digit-by-digit division, use the existing Long Division Calculator.
Accuracy and supported input limits
Use at most 20 entered digits per number and at most 10 fractional digits. Leading zeros count toward the input limit. A leading + or - and forms such as .5 or 5. are accepted. Empty entries, commas, fractions, exponent notation and arbitrary expressions are unsupported. Very long working scrolls horizontally inside its own box; steps may be lengthy. These tools teach base-ten arithmetic, not significant-figure or measurement-uncertainty rules.
Optional arithmetic workbooks (paid link) can provide extra exercises. The Rounding Calculator handles rounding as a separate task.
Long Multiplication Calculator FAQs
Yes. Each input supports at most 20 entered digits in total, including at most 10 digits after the decimal point. Use a decimal dot, without grouping commas.
Yes. The column layout works with magnitudes; the steps explain the signs and the main answer is the signed result of the original operation.
No. These supported finite-decimal operations use exact integer arithmetic and decimal scaling. Trailing fractional zeros are removed.
The steps follow the entered digits, carries or borrows, and the selected operation. Longer inputs need more working.
No. Use ordinary whole numbers or finite decimals. Expressions, fractions, exponent notation and thousands separators are rejected.
The arithmetic runs in your browser. Copy, Download and Print are optional result actions. Changing an input clears the previous answer.
Sources and methodology
Independently implemented exact base-ten arithmetic, reviewed October 30, 2026. Column working explains place value. Sources describe the mathematics; the linked organizations do not endorse this calculator.