Addition Calculator
Enter up to six numbers to find their sum instantly. The calculator also shows the count, average, minimum, maximum, and range of your values, plus a full column-by-column long-addition breakdown so you can see exactly how the answer is reached. Positive numbers, negative numbers, and decimals are all supported.
How addition works
Addition is the process of combining two or more quantities into a single total. The numbers being added are called addends and the result is the sum. When you add numbers by hand, you line them up with their decimal points aligned, then work from the rightmost column to the left: add the digits in each column, write the ones digit of that column's total below the line, and carry any tens digit into the next column. This carry mechanism is what allows the sum in any column to exceed 9 without losing precision. The same process applies to decimals: align the decimal points first, then treat the calculation as if it were whole numbers.
Adding negative numbers
A negative number is simply a value below zero. Adding a negative number is the same as subtracting its absolute value: 10 + (-3) = 10 - 3 = 7. When all addends are negative, the sum is also negative: (-4) + (-6) = -10. When a mix of positive and negative values is present, the sign of the sum depends on which group has the larger absolute total. For example, 15 + (-20) + 8 = 3 because the positives (15 + 8 = 23) exceed the negatives (20) by 3.
Adding decimals
Decimal addition follows exactly the same column-by-column method as whole-number addition, but you must first align the decimal points. Pad shorter numbers with trailing zeros if needed so every number has the same number of decimal places. Then add normally, treating the decimal point as a fixed marker. For example, 37.5 + 129.44 + 48.123 becomes 37.500 + 129.440 + 48.123 once padded, and the columns add up to 215.063.
Beyond the sum: count, average, and range
This calculator also reports the count of numbers entered, their arithmetic mean (average), and the spread of the set as captured by the minimum, maximum, and range. The average is the sum divided by the count, so for 125 + 348 + 77 the average is 550 / 3 = 183.3. The range is the largest value minus the smallest, giving a rough measure of how spread out the numbers are. These secondary statistics are especially useful when you are adding a list of measurements and want a quick summary beyond the total.
Properties of addition
| Property | Rule | Example |
|---|---|---|
| Commutative | A + B = B + A | 3 + 7 = 7 + 3 = 10 |
| Associative | (A + B) + C = A + (B + C) | (2 + 3) + 4 = 2 + (3 + 4) = 9 |
| Identity | A + 0 = A | 15 + 0 = 15 |
| Additive inverse | A + (-A) = 0 | 8 + (-8) = 0 |
| Closure | Sum of two reals is a real | 1.5 + 2.7 = 4.2 (still a real) |
Core mathematical laws that govern how addition behaves for any real numbers A, B, and C.
Frequently asked questions
What is an addend?
An addend is any number being added in an addition problem. In the expression 4 + 9 + 2, all three numbers (4, 9, and 2) are addends. The result of the addition is called the sum.
Can I add more than six numbers?
This calculator supports up to six numbers at once. For longer lists, you can split the list into groups, find the sub-totals, and then add the sub-totals together. Because addition is associative, the final answer will be the same regardless of how you group the numbers.
Does the order of the numbers matter?
No. The commutative property of addition states that A + B = B + A for any real numbers. The order of the addends does not change the sum. Similarly, the associative property means you can regroup the numbers in any way and still get the same total.
How do I add a negative number?
Enter the number with a minus sign, for example -15 or -3.5. Adding a negative value is the same as subtracting: 50 + (-12) = 38. The calculator handles any mix of positive and negative addends and returns the correct signed sum.
Why does the average differ from the sum?
The average (arithmetic mean) is the sum divided by how many numbers were added. If you add 10, 20, and 30, the sum is 60 but the average is 60 / 3 = 20. The average represents the "equal share" value if the total were distributed evenly among all addends.
How is the range calculated?
The range is simply the largest number in your set minus the smallest. For the values 5, 12, 3, and 9, the range is 12 - 3 = 9. It is a basic measure of how spread out the numbers are.