Long Multiplication Calculator

    Multiply whole numbers with long multiplication work, partial products, place-value shifts, optional zero rows, and a step-by-step explanation.

    Non-negative whole numbers: multiplicand up to 12 digits, multiplier up to 8 digits.

    Long multiplication with partial products

    The common English intent is not just the product but the written multiplication work. This page shows each partial product, the place-value shift for tens and hundreds, and the final sum of partial products.

    a is the multiplicand, d_i is a digit of the multiplier, and i is its place from the right.

    • Use a multiplicand up to 12 digits and a multiplier up to 8 digits for readable written work.
    • Toggle zero rows when you want the layout to match a classroom worksheet.
    • Copy the step-by-step explanation for checking homework or examples.

    Why partial products shift

    Each multiplier digit represents a place value. A tens digit creates a partial product shifted one place left, a hundreds digit shifts two places left, and so on.

    Frequently Asked Questions

    Sources and References

    Calculations are based on the listed reference sources. Links open in a new tab.

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