Enter a multiplicand and a multiplier to calculate the product using the Multiplication Calculator. You get the final result along with a step-by-step long multiplication breakdown showing each partial product — great for checking your work or learning the standard algorithm.
Product
--
Multiplicand
--
Multiplier
--
Partial Products
--
Long multiplication is a method for multiplying larger numbers by hand using the standard algorithm. You multiply each digit of the multiplier by the entire multiplicand, shift results according to place value, and then add the partial products together to get the final result.
A partial product is the result of multiplying the entire multiplicand by just one digit of the multiplier. In long multiplication, you calculate one partial product per digit in the multiplier, then sum them all to get the final product.
To multiply decimals using long multiplication, ignore the decimal points and multiply the numbers as if they were whole numbers. Count the total number of decimal places in both the multiplicand and multiplier, then place the decimal point that many places from the right in the final product.
When multiplying negative numbers, first multiply the absolute values using the standard long multiplication method. Then apply the sign rules: a positive times a positive is positive, a negative times a negative is positive, and a positive times a negative (or vice versa) is negative.
The multiplicand is the number being multiplied, and the multiplier is the number you are multiplying by. For example, in 234 × 56, the multiplicand is 234 and the multiplier is 56. The result is called the product.
Place value ensures each partial product is correctly shifted before adding. When you multiply by the tens digit of the multiplier, for instance, that partial product must be shifted one place to the left (equivalent to multiplying by 10). Without this shift, the final sum would be incorrect.
Yes, this calculator can handle large whole numbers. For very large numbers, JavaScript's number precision can handle integers accurately up to 15–16 significant digits. For extremely large values beyond that range, slight rounding may occur.
First, write the multiplicand on top and the multiplier below it. Starting with the ones digit of the multiplier, multiply it by each digit of the multiplicand from right to left, carrying when needed. Repeat for each subsequent digit of the multiplier, shifting one place left each time. Finally, add all partial products to get the result.