Summation Calculator

Use this summation calculator to easily calculate the sum of a set of numbers also known as Sigma.

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How to calculate a sum?

Summation is the sequential addition on a set of numbers. Addition is one of the four basic arithmetic operations, the others being subtraction, multiplication and division. It is simple to do for a few numbers, especially integers, but can get more complex with fractions and real numbers, which is where our summation calculator can help. You can simply copy/paste the numbers, or enter them manually, separated by any non-numerical symbol - minus and dot excluded. Shortcuts exist for calculating sums of specific sequences.

Since addition is associative, the sum does not depend on how the additions are grouped, therefore, parentheses are usually omitted in summation. Addition is commutative, so permuting (changing the order of) the terms of a finite sequence does not change the result from its summation: summing 1 + 2 + 3 + 4 is the same as 1 + 4 + 3 + 2, as can be confirmed using our sum calculator. Summation can be performed on negative numbers as well, and when one wants to explicitly denote that the sign is taken during the operation, it is called an "algebraic sum".

If you are adding all numbers from a set together, you can refer to the result as "sum total", unlike if you add together only a part of the sequence.

Using the summation calculator

Our summation calculator can easily calculate the sum of any numbers you input. You can enter any real number, positive and negative alike, by separating them using commas, spaces, news lines, tabs, or a combination of the above. Just make sure to use dot (.) as a decimal notation, e.g. 1.5 instead of 1,5 since the latter will be interpreted as two separate numbers, one and five, by our sum calculator.

Summation formula and notations

Using this sigma notation the summation operation is written as summation The summation symbol Σ is the Greek upper-case letter "sigma", hence the above tool is often referred to as a sigma calculator. This is not to be confused with the sigma calculator referring to the Greek lower-case letter "sigma" (σ), meaning standard deviation. We also have a six sigma calculator for those interested in industrial process control.

As you can see, one does not need to perform all the summation operations as there exist mathematically shortcuts for many cases, the example above covers all natural numbers. For more complex series, for example summation of squares, instead of "i" one would write i2 after the sigma notation (the indexed variable).

Other notations include [1, 2, 3, 4] for the sum of all integers between 1 and 4, as well as shorthand notations such as 1, 2, ... 99, 100 referring to the sum of all integers from 1 to 100.

The notation only matters if you want to communicate summation to others. For the purpose of using this sum calculator we should say that we use the standard formula for summing up the numbers you input.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:
Georgiev G.Z., "Summation Calculator", [online] Available at: URL [Accessed Date: 30 Nov, 2020].