Long Multiplication Calculator

Work through long multiplication with each partial product or a lattice grid, long addition with carries, long subtraction with borrows, or signed-number rules.

Product A × B888,832

Whole number or decimal. Multiplication: up to 200 digits, may be negative. Addition and subtraction: zero or positive. Lattice: whole numbers up to 20 digits.

Whole number or decimal. Multiplication: up to 40 digits (one partial product per digit).

Product A × B

888,832

  • Partial products3
  • Digits in product6
Partial products for 3,472 × 256
Digit of BPlaceMultiplyPartial product
6ones3,472 × 620,832
5tens3,472 × 5 × 10¹173,600
2hundreds3,472 × 2 × 10²694,400
Sum888,832

Each digit of B multiplies all of A; the partial product is shifted one place left for each place the digit sits from the right (a trailing zero per place). Arithmetic is exact.

How this was calculated

3,472 × 6 (ones digit of B) = 20,832

3,472 × 5 (tens digit of B), shifted 1 place = 173,600

3,472 × 2 (hundreds digit of B), shifted 2 places = 694,400

Add the partial products: 20,832 + 173,600 + 694,400 = 888,832.

Long multiplication with partial products

Multiply all of A by each digit of B, starting from the ones digit. Shift each partial product one place further left for each place the digit sits from the right, then add the partial products.

Example: 3,472 × 256. 3,472 × 6 = 20,832; 3,472 × 5 tens = 173,600; 3,472 × 2 hundreds = 694,400. The sum is 20,832 + 173,600 + 694,400 = 888,832.

Long addition and subtraction

Addition works from the ones column leftward. If a column adds to 10 or more, write its last digit and carry 1. For 478 + 356: 8 + 6 = 14, write 4 and carry 1; 7 + 5 + 1 = 13, write 3 and carry 1; 4 + 3 + 1 = 8. The answer is 834.

Subtraction borrows (regroups) when a top digit is smaller than the digit below it. For 5,003 − 1,247, the ones, tens and hundreds columns each borrow, giving 3,756. If B is larger than A, the calculator subtracts A from B and makes the answer negative.

Limits

The arithmetic is exact, with no rounding. Multiplication accepts up to 200 digits in A and 40 in B, so there is one partial product per digit of B. Addition and subtraction accept whole numbers or decimals of up to 200 digits that are zero or positive; use signed numbers mode for negative values. Lattice mode takes whole numbers of up to 20 digits each.

Decimals and lists of numbers

To add or subtract decimals, line up the decimal points, pad the shorter numbers with zeros, and work column by column as with whole numbers. For 12.5 + 7.25 + 100 + 0.375, pad to three places (12.500, 7.250, 100.000, 0.375) and add to get 120.125. Choose "A list of numbers" to add up to 50 numbers at once.

To multiply decimals, ignore the points and multiply the digits, then count the decimal places in both factors. For 3.25 × 1.4, 325 × 14 = 4,550, and 2 + 1 = 3 places gives 4.550 = 4.55.

Adding and subtracting signed numbers

Signed numbers mode first rewrites subtraction as adding the opposite: A − B = A + (−B). With the same signs, add the absolute values and keep the sign, so −4 + (−6) = −10. With different signs, subtract the smaller absolute value from the larger and keep the sign of the number farther from zero, so −8 + 5 = −3.

On a number line, start at A and move |B| units right when adding a positive number, or left when adding a negative one. For −7 − (−10) = −7 + 10, start at −7 and move 10 right to land on 3.

Lattice multiplication

Lattice (grid) multiplication writes the digits of A across the top of a grid and the digits of B down the right side. Each cell holds the product of its two digits, with the tens above a diagonal line and the units below it.

Add along each diagonal from the bottom right, carrying into the next diagonal, and read the digits around the left and bottom edges. For 23 × 45 the cells are 08, 12, 10 and 15. The diagonal sums are 5, 3 and 10 (write 0, carry 1), and then 0 + 1 = 1, so the product is 1,035.

How to use the Long Multiplication Calculator

Pick the operation and enter the numbers.

  1. Choose the operation

    Pick long multiplication, lattice multiplication, addition, subtraction or signed numbers.

  2. Enter A and B

    Type whole numbers or decimals, or a list of numbers to add. Commas are allowed as thousands separators.

  3. Follow the table

    Read each partial product, carry or borrow, column by column.

References

Frequently asked questions

Why is each partial product shifted?

A digit in the tens place stands for that digit times 10, so its partial product is 10 times bigger. That shows up as one extra zero, or a shift one place to the left.

Does the order of the numbers matter?

Not for the answer, but putting the number with fewer digits second means fewer partial products.

Can I multiply negative numbers?

Yes, in multiplication mode. The digits are multiplied as usual, and the product is negative when exactly one factor is negative.

How many decimal places does a product have?

As many as the two factors have together. 0.2 × 0.03 has 1 + 2 = 3 places: 2 × 3 = 6, so the product is 0.006.

Why does subtracting a negative number make the answer bigger?

Subtracting a number is the same as adding its opposite, so 5 − (−3) = 5 + 3 = 8. On a number line, subtracting −3 moves you 3 units to the right.

Last updated . Results are estimates for informational purposes only.