Multiplication Calculator

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.

The number to be multiplied

The number to multiply by

Results

Product

--

Multiplicand

--

Multiplier

--

Partial Products

--

Results Table

Frequently Asked Questions

What is long multiplication?

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.

What is a partial product in long multiplication?

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.

How do I do long multiplication with decimals?

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.

How does long multiplication work with negative numbers?

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.

What is the difference between the multiplicand and the multiplier?

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.

Why is place value important in long multiplication?

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.

Can this calculator handle large numbers?

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.

What are the steps of the standard long multiplication algorithm?

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.

More Math Tools