Created by Dominika Śmiałek, MD, PhD candidate
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jun 05, 2023

Do you ever have two really big numbers you need to add together and no easy-to-click calculator at hand? With this addition calculator, you will always be able to easily add two numbers together, be they positive or negative, big or small. In the article below, we explain how our summation calculator works, and provide a section for you to familiarize yourself with the addition definition.

If you'd like to round the number you obtain, be it a decimal or simply too big, then our rounding calculator might be a tool you're looking for!

Summation, also called addition, is the process of calculating the total of two (or more) addends. What is an addend? Those numbers which are being added together are called addends, which, in our calculator, are marked as A and B. The result of this process is called a sum, in this addition calculator known as C.

The addition is one of the four basic operations of arithmetic, along with:

• Subtraction;
• Multiplication; and
• Division.

The symbol of addition is a plus (➕), and we place it between the two addends. There are notations where this is not true: check our Polish notation converter!

The addition has two properties, commutativity and associativity.

Commutativity means that you can exchange the places of the addends without changing the result of the equation, A + B = B + A.

Associativity, on the other hand, becomes a thing once we try to add more than two numbers. It means it doesn't matter whether you add the first number to the second and then the third or third to the second and then the first. The result won't change, A + (B + C) = (A + B) + C.

If you keep adding +1, the process's name is counting. Also, it's good to understand that you may add 0, though this calculation doesn't change the result. In case the equation requires the addition of negative numbers, subtract the negative value from the initial figure: A + (-B) = A - B

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

## Add numbers - not so simple?

Sounds trivial. So, the addition definition math gives you is as easy as you thought it might be - add a number to the other, and you get the result. However, as you're here, we both know it might not be that simple. Sometimes, the numbers are huge. The other option is that they're negative or maybe fractions. In all of these situations, our calculator works smoothly and gives you the right answer. The addition is also useful in finding the divisibility of a number using the sum of digits calculator.

The earliest discovered evidence suggests addition was used between 20.000 and 18.000 years BC. Fortunately, now that you have our addition calculator, you don't have to do it manually anymore!

## Summation calculator - how does it add numbers?

It's effortless and intuitive. Fill in the first addend field (A) and the second addend field (B). The calculator does everything else for you and gives you the sum (C).

A + B = C

Things can become a bit complicated if, for example, you have a binary or a fraction. In case it's a fraction, there's a solution. You can either switch it to decimal, or use our adding fractions calculator.

An extended application of the summation property can be found in the segment addition postulate, which involves finding a segment length when 3 points are collinear.

So, let's practice it with an example. Imagine, one of your addends is A = 32948 and the other B = 2938546.

32948 + 2938546 = 2,971,494

What happens if B is negative?

32948 + -2938546 = -2,905,598

And that's it! 🎉

## FAQ

### Why is plus the symbol for addition?

Historians speculate that the symbol + came to represent the addition as the result of a lengthy modification of the Latin conjunction et. The introduction of the symbol + for addition is relatively recent, dating back to the XIV century. Before that, different symbols were used, including and the bidirectional glyph used by Egyptians.

### What is the result of the addition of 41,381 and 3,819?

45,200. To calculate the sum of 41,381 and 3,819:

1. Stack the numbers aligned to the right.
2. Sum the rightmost numbers: 9 + 1 = 10. Save 0 and lend 1 to the digits to the left.
3. Sum 8 and 1 and add the 1 from the step before: 8 + 1 + 1 = 10. Save 0 and carry the one.
4. Sum 3, 8, and the 1 from step 3.: 8 + 3 + 1 = 12. Save 2 and carry 1.
5. Sum 1, 3, and the 1 from above: 1 + 3 + 1 = 5.
6. Build the result: 45,200.

### What is the difference between addition and difference?

Addition and difference are substantially the same mathematical operation. However, for positive numbers:

• The result of addition is always larger than both factors; and
• The result of subtraction is always smaller than at least one of the numbers.

Introducing negative numbers in math allows generalizing the sum to a single operation, the algebraic sum.

### How do you sum more than two numbers quickly?

To sum more than two numbers quickly, follow these easy steps:

1. Don't sum the numbers pairwise.
2. Stack the numbers vertically, and align them to the right.
3. Compute the **sum of each column of digits((, starting from the right.
4. Proceed until you reach the last digit of the longest number.

That's it!

Dominika Śmiałek, MD, PhD candidate
A +B = C
First number (A)
Second number (B)
Result
Sum (C)
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