Long Multiplication Calculator for Multiplying Decimals, Integers, and Whole Numbers

Long Multiplication Calculator Sign

This long multiplication calculator multiplies 2 numbers (multiplicand and multiplier) and then displays the long multiplication method used to find the product of the two.

Plus, the long multiplication grid created by the calculator also serves as an interactive tutorial explaining each step of the process.

If you are looking to divide decimal numbers, please visit the Long Division Calculator.

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Long Multiplication Calculator

Multiply decimal, integer, and whole numbers and see the long multiplication method and steps used to find the product.

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Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Multiplicand:Multiplicand:Multiplicand:Multiplicand (most digits of 2 numbers):

Multiplicand:

Enter the multiplicand, which is the decimal, integer, or whole number having the greatest number of digits, up to a maximum of 99999999999 (11 digit maximum).

#
Multiplier:Multiplier:Multiplier:Multiplier (fewest number of digits):

Multiplier:

Enter the multiplier, which is the decimal, integer, or whole number having the fewest number of digits, up to a maximum of 9999999999 (10 digit maximum).

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Product:Product:Product of decimals:Product of the two decimals:

Product of the two decimals:

This is the product of the two numbers you entered. Use this number to double-check the long multiplication form in the results. Since I can't test every possible combination of numbers and/or invalid character entries, be sure to check my work before considering the result to be accurate.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

Help and Tools

Learn

How to multiply integers or decimal numbers without a calculator.

How to Multiply Decimals and Integers

To demonstrate how to multiply decimals and integers using long multiplication (without a calculator), we will use the following multiplication:

132.5 x 4.6

First I will list the steps to multiplying the numbers, then I will demonstrate each step.

  1. Write the number with the highest number of digits (multiplicand).
  2. Directly beneath the first number, write the second number (multiplier).
  3. Working from right to left, multiply by each digit of multiplicand by right-most digit of the multiplier.
  4. If a multiplication is less than 10, place the result in the first row beneath the multiplier, in the next available column cell.
  5. If a multiplication is greater than 9, place the one's portion of the result in the row beneath the multiplier, and place the ten's portion (carryover) at the top of the next column. This carryover is then added to the result of the next multiplication.
  6. For each subsequent multiplier digit, add a new row with the number of zeros indicating the power of 10 for that multiplier's digit.
  7. Repeat the multiplication for each multiplier digit.
  8. Once the multiplications are complete, you should have the same number of rows as the number of digits of the multiplier.
  9. Add up all result rows to get the product of the two numbers being multiplied.
  10. Count the number of decimal places in the multiplicand and multiplier and add them together to get the number of decimal places to create in the product.
  11. Determine if the result is positive or negative.

Here is how the above steps would play out for our example multiplication with decimals (132.5 x 4.6).

Step #1: Write and Position Numbers

Create a grid for the multiplication and enter the number with the greatest number of digits first, followed by the number with the least number of digits. Note that I have added vertical red lines to indicate where the decimal points exist.

 
 1325
x46
Step #2: Multiply One's Digit In Multiplier

Multiply the right-most digit of the multiplier (6) by each digit of the multiplicand.

  • 6 x 5 = 30, so write 0 in column #1 in the result row and write a 3 at the top of column #2.
  • 6 x 2 = 12, + carryover of 3 = 15, so write 5 in column #2 in the result row and write a 1 at the top of column #3.
  • 6 x 3 = 18, + carryover of 1 = 19, so write 9 in column #3 in the result row and write a 1 at the top of column #4.
  • 6 x 1 = 6, + carryover of 1 = 7, so write 7 in column #5 in the result row.
 113
 1325
x46
 7950
col54321
Step #3: Multiply Ten's Digit In Multiplier

Multiply the next digit of the multiplier (4, which actually represents 40) by each digit of the multiplicand.

  • Since we are now working with the tens column, write a 0 in column #1 on a new row.
  • 4 x 5 = 20, so write 0 in column #2 of the second result row and write a 2 at the top of column #3.
  • 4 x 2 = 8, + carryover of 2 = 10, so write 0 in column #3 of the second result row and write a 1 at the top of column #4.
  • 4 x 3 = 12, + carryover of 1 = 13, so write 3 in column #4 of the second result row and write a 1 at the top of column #5.
  • 4 x 1 = 4, + carryover of 1 = 5, so write 5 in column #5 of the second result row.
 112
 1325
x46
 7950
+53000
col54321
Step #4: Add Up The Result Rows

Add the two result rows together to get the product of the two numbers.

7950 + 53000 = 60950

 113
 1325
x46
 7950
+53000
=60950
Step #5: Insert Decimal Point If Applicable

Count the number of decimal places in the multiplicand (132.5 = 1 place) and in the multiplier (4.6 = 1 place) and add them together to get the number of decimal places to create in the product (1 + 1 = 2 places).

Product of 132.5 x 4.6 = 609.50 (or 609.5)

Note that if the long multiplication result does not have enough digits to create the required number of decimal places, simply add the needed number of zeros to the left side of the result.

For example, if the long multiplication result is 85091 (5 digits), but you need to add 6 decimal places, simply add a 0 to the left side of the result and insert the decimal point at the beginning, so it becomes .085901 (now has 6 decimal places).

Step #6: Determine If The Result Is Positive or Negative
  • If you multiplied 2 positive numbers, the result is positive.
  • If you multiplied a positive number by a negative number, the result is negative.
  • If you multiplied 2 negative numbers, the result is positive.

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.