Long Multiplication Calculator

Long multiplication is the written method for multiplying numbers with two or more digits. You multiply the top number, the multiplicand, by each digit of the bottom number, the multiplier, one row at a time. Each row is shifted one place to the left, which is why placeholder zeros appear. Adding all the rows gives the product.

The rows are called partial products because each one covers only part of the bottom number. In 47 × 36, the first row is 47 × 6 = 282 and the second is 47 × 30 = 1410. Their sum, 1692, is the answer. The method works for any number of digits, since it only ever needs single-digit multiplication.

Type the two numbers you want to multiply and press Calculate. The number with more digits goes on top by default, and the Swap button lets you choose the order your teacher prefers. Decimals and minus signs are accepted in either field. Spaces between digit groups are ignored, so 1 234 567 is read as 1234567.

The layout shows carries in small digits above each column and places a placeholder zero at the start of every shifted row. Turn on Show Steps to read each single-digit product and carry in words. A copy button next to the answer copies the exact product with no rounding.

Start with the ones digit of the bottom number and multiply it by each digit of the top number, from right to left. When a product reaches 10 or more, write the ones digit and carry the tens digit to the next column. Move to the tens digit of the bottom number, write one placeholder zero, and repeat. Each new digit of the bottom number adds one more placeholder zero.

When every row is done, add the partial products column by column with ordinary addition and carrying. For decimals, the calculator first ignores the decimal points and multiplies whole numbers. It then counts the decimal places in both inputs and places the point that many places from the right. The sign is decided last: two negatives or two positives give a positive product.

These examples run from a single carry to a product with 18 digits. Each shows the input, the partial products where they help, and what the answer means.

Type any example into the tool above to see the same layout with every carry drawn in. The partial products in the explanations match the rows the tool prints.

JavaScript stores regular numbers as IEEE 754 doubles, which hold integers exactly only up to 9007199254740991. Past that limit, products like 123456789 × 987654321 lose their last digits without any warning. BigInt fixes this for whole numbers by storing every digit, at the cost of a separate number type.

Python integers grow as large as memory allows, so the same product is exact by default. For decimals, Python's Decimal type keeps every decimal place, which is why 18.5 × 12.2 prints 225.70. This tool uses the BigInt approach internally, then places the decimal point the same way you would on paper.

// Regular numbers lose digits above 2^53
console.log(123456789 * 987654321);   // 121932631112635260 (wrong)
console.log(Number.isSafeInteger(123456789 * 987654321)); // false

// BigInt keeps every digit
console.log(123456789n * 987654321n); // 121932631112635269n

// Decimals still need care
console.log(0.1 * 3);                 // 0.30000000000000004

print(123456789 * 987654321)  # 121932631112635269, Python ints are exact

from decimal import Decimal
print(Decimal("18.5") * Decimal("12.2"))  # 225.70, decimal places add up
print(Decimal("3.25") * Decimal("1.4"))   # 4.550

Each input can have up to 30 digits, including decimal places, and the product is always exact. There is no rounding at any stage, so a 60-digit result shows every digit. Very long products scroll sideways in the layout rather than wrapping onto a new line.

The multiplication runs in your browser, and your numbers are never uploaded, logged or saved. No account is needed, and the page behaves the same in all five languages. The same privacy approach applies to every tool listed with the math calculators.

Most mistakes happen when a carry is forgotten or a placeholder zero is left out. Others come from misaligned columns in the final addition or a decimal point in the wrong place. The table lists each problem with a quick fix, plus the messages the tool shows for invalid input.

A fast sanity check is to round both numbers and multiply mentally. For 47 × 36, think 50 × 36 = 1800, so an answer near 1700 is plausible. If your product is far from the estimate, recheck the carries first. A result about ten times too small almost always means a missing placeholder zero.

The column method is the standard algorithm named in Common Core State Standards 5.NBT.B.5, though schools also teach other approaches. The grid or box method splits each number into tens and ones and multiplies every pair. The lattice method writes products in diagonal cells, and short multiplication handles one-digit multipliers in a single row.

This long multiplication calculator uses the column method because it is compact and matches most homework. The other written methods reach the same product. If you do not need the working, the one-line arithmetic keypad is faster; the table shows when each written method helps. To reverse a product and check it, use the long division calculator.