Long multiplication (also called the standard algorithm) is the method taught in school for multiplying two multi-digit numbers by hand. It breaks a hard problem — multiplying two large numbers at once — into a series of easy single-digit multiplications, then combines them with place-value shifting and addition.
How long multiplication works
Write the multiplicand on top and the multiplier below it. Starting with the ones digit of the multiplier, multiply it by every digit of the multiplicand to get the first partial product, carrying digits into the next column exactly as in single-digit multiplication. Move to the tens digit of the multiplier, multiply again, and write that partial product shifted one place to the left (either by leaving the ones column blank or writing a placeholder zero). Repeat for every remaining digit of the multiplier, shifting one more place left each time. Finally, add all the partial products together — that sum is the answer.
Handling zeros and decimals
If a digit of the multiplier is 0, that partial product is 0 and can be skipped entirely — it never changes the final sum. Decimal numbers are multiplied the same way after removing the decimal points: multiply the digits as whole numbers, then count the total number of decimal places across both original numbers and move the decimal point that many places from the right in the raw product. For example, one decimal place in each factor means two decimal places in the final answer.
Limits and edge cases
Long multiplication works for any size of whole number or decimal, though very long numbers make the by-hand version tedious — that's exactly what this calculator automates while still showing every partial product. Negative numbers follow the usual sign rule (a negative times a positive is negative; two negatives make a positive) and are handled the same way once the sign is set aside. This calculator focuses purely on the arithmetic; it doesn't perform unit conversions or currency formatting.