Long Addition Calculator

Created by Anna Szczepanek, PhD

Reviewed by Dominik Czernia, PhD and Jack Bowater

Last updated: Jun 05, 2023

Table of contents:

Welcome to Omni's long addition calculator! It can show you step-by-step how to solve any long addition problem, no matter whether the numbers involved are whole or have some decimal places!

If you need a quick summary of how do you do column addition or a few examples of long addition, check out the article below. Once you've mastered long addition, why not try out Omni tools dedicated to the remaining three arithmetic operations?

🙋 Want to learn how to handle complex mathematical expressions that involve more than one arithmetic operation? Check our distributive property calculator.

Long addition method

Long addition (or column addition) is a method for quickly adding together numbers with many digits. To successfully sum two natural numbers, you only need to be able to correctly add two whole numbers between 0 and 9 and remember the steps of the long addition method:

Write down the numbers one under the other and right-aligned.

In other words, the numbers have to be aligned by place value, i.e., the ones-digit of one number has to be precisely underneath the ones-digit of the other number. The same must hold for tens-digit, hundreds-digit, etc.
Calculate the sum of numbers in the far-right column.
If this sum has only one digit (in other words, it does not exceed 9), write it down in the same column, right beneath the numbers you summed.
If the sum has two digits (i.e., it is equal to 10 or more), we have to deal separately with its ones-digit and tens-digit. Place the ones-digit in the result row right beneath the column you've summed. Place the tens-digit on the top of the column to the left.

Placing the tens-digit in the next column is called carrying over and this number is called a carryover.
Repeat steps 2, 3 & 4 for the remaining columns. If there is a carryover, don't forget to include it in the sum when adding the column's numbers together!

That’s it when it comes to summing two whole numbers via long addition! To get a better grasp of this method, go through the examples in the last section of this text. You can also generate as many examples as you wish with the show steps mode of our long addition calculator!

How do you do column addition of decimal numbers?

Summing two numbers with decimal places via long addition is almost the same as the long addition of two whole numbers. The crucial step is to align the numbers correctly. As before, the numbers have to be aligned by place value.

For instance, if we want to sum 15.413 and 5437.321 using long addition, we write them down as follows:

\qquad \begin{align*} 15.413 &\\ -\ 5437.321 & \\ \end{align*}

The numbers you want to add together may have a different number of decimal places. The rule is the following: put the numbers such that the decimal places are aligned. You can then fill in the missing places with zeros.

For instance, if we want to sum 3215.41311 and 17.321 using long addition, we write them down as follows:

\qquad \begin{align*} 3215.41311 &\\ -\ \ \ \ 17.32100 & \\ \end{align*}

Once the long addition problem is correctly set up, all that's left is to add the numbers using the same column addition method that we explained in detail in the previous section. There are two things related to the decimal place that you have to remember:

When you arrive at the decimal place, rewrite it in the answer row and proceed to the next column.
If you obtain a carryover in the column after the dot, carry it to the column before the dot.

How to use this long addition calculator?

This calculator is super-easy to use! There are three major points any user should know:

Enter two positive numbers to be added together by our long addition calculator.
The calculator displays the result faster than lightning ⚡⚡ It puts the result under the numbers you've entered.
Use the show steps option whenever you want our long addition calculator to show the step-by-step solution of long addition.

Long addition examples

Here we show how to add two numbers together with the help of long addition.

Long addition example 1. Solve 15292 + 735:

Setup:

\qquad \begin{align*} 15292 &\\ +\quad\ \ 735& \\ \mathclap{\rule{1cm}{0.4pt}} \quad &\\ = \qquad \quad \end{align*}

We sum the numbers in the far-right column: 2 + 5 = 7. We put the result 7 at the very bottom of the same column:

\qquad \begin{align*} 15292 &\\ +\quad\ \ 735& \\ \mathclap{\rule{1cm}{0.4pt}} \quad &\\ = \qquad \ 7 & \end{align*}

We sum the numbers in the next column: 9 + 3 = 12. As the result 12 has two digits, we separate it into the ones-digit 2, which we put into the results row, and tens-digit 1, which we carry to the next column:

\qquad \begin{align*} 1\phantom{11} & \\ 15292 &\\ +\quad\ \ 735& \\ \mathclap{\rule{1cm}{0.4pt}} \quad &\\ = \quad \ \ \ 27 & \end{align*}

We sum the numbers in the next column, not forgetting about the digit carried from the previous column: 1 + 2 + 7 = 10. We put 0 into the result and carry 1 into the next column:

\qquad \begin{align*} 11\phantom{11} & \\ 15292 &\\ +\quad\ \ 735& \\ \mathclap{\rule{1cm}{0.4pt}} \quad &\\ = \quad \ 027 & \end{align*}

We've run out of the digits in the bottom number, but there are still digits in the upper number and the carryover from the previous column: 1 + 5 = 6. We put 6 into the result row:

\qquad \begin{align*} 11\phantom{11} & \\ 15292 &\\ +\quad\ \ 735& \\ \mathclap{\rule{1cm}{0.4pt}} \quad &\\ = \ \ \ 6027 & \end{align*}

We've run out of the digits in the bottom number, but there is one last digit in the upper number. We simply rewrite this digit 1 into the result row:

\qquad \begin{align*} 11\phantom{11} & \\ 15292 &\\ +\quad\ \ 735& \\ \mathclap{\rule{1cm}{0.4pt}} \quad &\\ = \ 16027 & \end{align*}

Long addition example 2.
Solve 4520.12 + 535.9:

Setup. We have to be careful to correctly align the numbers:

\qquad \begin{align*} 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \quad \quad \quad \ \ \ & \end{align*}

We sum the numbers in the far-right column: 2 + 0 = 2. We put the result 2 at the very bottom of the same column:

\qquad \begin{align*} 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \quad \quad \quad 2 & \end{align*}

We sum the numbers in the next column: 1 + 9 = 10. As the result 10 has two digits, we separate it into the ones-digit 0, which we put into the results, and tens-digit 1, which we carry to the column before the dot:

\qquad \begin{align*} 1\phantom{.11} & \\ 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \quad \quad \ \ 02 & \end{align*}

We've reached the decimal dot, so we put the dot in the result row as well:

\qquad \begin{align*} 1\phantom{.11} & \\ 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \quad \quad \ .02 & \end{align*}

We sum the numbers in the next column, not forgetting about the carryover: 1 + 0 + 5 = 6. We put 6 into the result row:

\qquad \begin{align*} 1\phantom{.11} & \\ 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \quad \ \ \ 6.02 & \end{align*}

We sum the numbers in the next column: 2 + 3 = 5. We put 5 into the result row:

\qquad \begin{align*} 1\phantom{.11} & \\ 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \quad \ 56.02 & \end{align*}

We sum the numbers in the next column: 5 + 5 = 10. We put 0 into the result row and carry 1 into the next column:

\qquad \begin{align*} 1\phantom{1} 1\phantom{.11} & \\ 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \ \ \ 056.02 & \end{align*}

We sum the numbers in the last column: 1 + 4 = 5. We put 5 into the result row:

\qquad \begin{align*} 1\phantom{1} 1\phantom{.11} & \\ 4520.12 &\\ +\quad 535.90& \\ \mathclap{\rule{1.5cm}{0.4pt}} \quad \ \ \ &\\ = \ \ \ 5056.02 & \end{align*}

Anna Szczepanek, PhD

Input two numbers

1st number

2nd number

Show steps?

Result of long addition:

AveragePercentagePercentage change… 29 more

Long Addition Calculator

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