Long Multiplication Calculator

The long multiplication calculator works the standard algorithm digit by digit. For 347 × 26, multiply 347 by the ones digit 6 to get 2,082. Then multiply by the tens digit 2, which is worth 20, so write a zero first: 6,940. Add the partial products: 2,082 + 6,940 = 9,022.

How to use the long multiplication calculator

1. Type the two numbers. Whole numbers, decimals and negative numbers all work, up to 40 digits each.
2. Pick a method: Standard (columns and carries), Lattice (grid with diagonals) or Area model (box method).
3. Read the product and the written-out working. In the Standard view, the buttons above the grid show the carries for each row.
4. Look at the yellow check box: an estimate and a division check tell you the answer is the right size.

How to do long multiplication step by step

Long multiplication (the standard algorithm) breaks a big multiplication into one-digit multiplications. Each digit of the bottom number makes one row, called a partial product.

1. Write the longer number on top and line up the digits on the right.
2. Multiply the top number by the ones digit of the bottom number, from right to left. When a product is 10 or more, write the ones digit and carry the tens digit to the next column.
3. Move to the tens digit. Write one placeholder zero on the right first, because this digit is worth ten times as much. Multiply again.
4. Repeat for each digit, adding one more placeholder zero each time.
5. Add the partial products.

Worked example: 347 × 26

Worked example with a zero: 4,506 × 307

The partial products are 4,506 × 7 = 31,542, then 4,506 × 0 = 0 for the tens digit, then 4,506 × 300 = 1,351,800. The zero row can be skipped as long as the hundreds row is shifted two places. The total is 31,542 + 1,351,800 = 1,383,342.

Multiplying decimals with long multiplication

Ignore the decimal points, multiply the whole numbers, then put the point back. The answer has as many decimal places as the two factors together.

For 3.47 × 2.6, multiply 347 × 26 = 9,022. The factors have 2 + 1 = 3 decimal places, so count three digits from the right: 9.022. A quick estimate agrees: 3 × 3 = 9.

Sometimes you need extra zeros. For 0.25 × 0.04, multiply 25 × 4 = 100. The answer needs 2 + 2 = 4 decimal places, so write 100 as 0.0100, which is 0.01. Trailing zeros after the decimal point can be dropped at the end, but only after you have counted the places.

Multiplying negative numbers

Multiply as if both numbers were positive, then decide the sign:

The lattice method

The lattice method (also called the grid or Napier’s method) separates multiplying from adding, which makes carrying easier to keep straight. For 347 × 26, draw a grid of 3 columns and 2 rows, with 347 across the top and 26 down the right side. Draw a diagonal through each box.

In each box, write the product of its column and row digits, tens above the diagonal and ones below: 3 × 2 = 06, 4 × 2 = 08, 7 × 2 = 14, 3 × 6 = 18, 4 × 6 = 24 and 7 × 6 = 42. Then add along each diagonal, starting at the bottom right: 2; then 4 + 4 + 4 = 12 (write 2, carry 1); then 2 + 8 + 1 + 8 = 19, plus the carried 1 = 20 (write 0, carry 2); then 1 + 0 + 6 = 7, plus the carried 2 = 9; the last diagonal holds 0. Reading the digits from the top left gives 09022, which is 9,022.

The area model (box method)

The area model writes each number in expanded form and multiplies every pair of place values. For 347 × 26, split 347 into 300 + 40 + 7 and 26 into 20 + 6:

Adding the six boxes gives 6,000 + 800 + 140 + 1,800 + 240 + 42 = 9,022. The area model shows why the standard algorithm works: each partial product is a sum of boxes. The row for 6 adds to 2,082 and the row for 20 adds to 6,940.

How to check a long multiplication answer

• Estimate. Round each number to one significant figure: 347 × 26 is about 300 × 30 = 9,000, so 9,022 is the right size. An answer near 90,000 or 900 points to a missing or extra placeholder zero.
• Divide back. 9,022 ÷ 26 should give 347. The long division calculator shows that working step by step.
• Swap the numbers. 26 × 347 must give the same product, because multiplication is commutative.

Common long multiplication mistakes

• Forgetting the placeholder zero on the second row, which makes the answer far too small.
• Adding the carry before multiplying instead of after: in 6 × 4 with a carry of 4, the result is 24 + 4 = 28, not 6 × 8.
• Carrying from one row into the next row. Each partial product has its own carries; cross them out before starting the next row.
• Lining up decimal points as in addition. In multiplication, line up the digits on the right and count decimal places at the end.

Long Multiplication practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

Why do you add a zero in long multiplication?

The second digit of the bottom number is in the tens place, so it is worth ten times its face value. In 347 × 26, the 2 means 20, and 347 × 20 = 6,940. The zero shifts the row one place left; the third row gets two zeros, and so on.

Which number should go on top?

Either order gives the same answer. Putting the number with more digits on top means fewer partial products to add, so there is less to go wrong.

How do you multiply decimals by hand?

Multiply as whole numbers, then count the decimal places in both factors and place the point that many digits from the right of the product. For 1.2 × 0.3, 12 × 3 = 36 and there are two decimal places, so the answer is 0.36.

Is the lattice method the same as long multiplication?

It uses the same digit products and gives the same answer, but it writes every product first and does all the adding along the diagonals at the end. Many students find it easier to keep track of carries.

Related calculators

• Long division calculator: divide with every step shown
• Rounding calculator: round numbers for quick estimates
• Scientific notation converter: very large products
• Fraction, decimal and percent calculator: convert decimal answers