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Summation Calculator

Summation Calculator

Enter any series, function, or numbers, and the tool will find their summation by displaying whether it is convergent or not.



Enter numbers separated with comma (,):

Enter Equation:

Start Value (x): (for ∞, type oo)

End Value (n): (for -∞, type -oo)

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An online summation calculator helps you to determine the sum of specified numbers, series, or functions. Additionally, the sigma notation calculator checks whether the series has converged or not. Let’s begin to understand how to calculate the summation and sum of sigma notation.

What is Summation?

In Mathematics, the summation is the addition process of any numbers called the summands or addends, which result in the sum or total. In other words, the sum of the sequence is called the series that defines the mathematical operation “+”. The symbol used to denote summation is “Σ”.

There are two types of summation of sequences known as infinite and finite sets of sequences.

The finite sequence has an upper limit and lower limit (start and end values) and the infinite sequences will infinitely continue in series. The summation calculator uses both start and end value to calculate the results.

Summation Formula:

The sum of sigma notation can be written as

Σ_{n=1}^n i

Σ_{n=1}^n i= n(n + 1) / 2

In summation equation “i” is the start value, and n is the end limit.

What is Sigma Notation?

The Sigma notation is represented by the character S, which is derived from the Greek capital letter S. The sigma notation (S) tells us the values of the added sequence. The typical value of the sequence is shown to the right of the sigma symbol and sigma math.

The sigma notation variable is represented by an index placed under the sigma symbol. The index is usually represented by i.

The index is shown as a simplified expression for i = 1. The index assumes that the values of the sequence start with the value on the right side of an equation and the end with the value above the sigma notation.

The starting value for the notation is known as the lower limit of the summation notation.

The point at which summation notation stops is called the upper limit of summation notation.

How to Calculate a Summation?

Summation notation for a series of numbers. For example, the expression is 5n + 3, the notation is given as:

Σ_{n=0}^9 5n + 3

Where n is the placeholder of an integer and summing the expression 5n + 3 with integers 0 through 9.

Since the lower limit or start value is 0 and the upper limit or end value is 9, the sequencing through 0, 1, 2, 3, 4,…, 9. We will substitute 0 into the expression, then add the result of substituting 1 into the expression, so third until we add the result of plugging in our final integer of 9 into the expression.

How Summation Calculator Works?

Use this sigma calculator to rapidly compute the summation of given expressions of numbers over a predetermined range by following these steps:


  • First, select a calculation method either the simple sum or sigma notation sum.
  • If you selected a simple sum, then enter numbers or series separated with a comma.
  • When selecting the sigma notation, then enter an equation with start and end value.
  • Hit the calculate button to see the summation of a constant and numbers.


  • The summation calculator displays the sum of the given number and the total number of entered functions or series.
  • The sigma notation calculator provides step-by-step calculations for a given equation with start and end values.


How do I do double summation?

  • First, change the Order of expression for Double Sums
  • Now, the external-sum index is holding and increases the internal index.
  • After using the internal sum index, increase the external sum index.
  • Repeat the previous steps for the entire external sum index.

What are the characteristics of summation?

When n = 0, the value of the sum is defined as 0. The value of a finite series is always well-defined, and its elements can be added in any order. If there is no limit, the series diverges; otherwise, the series will converge.


Use this online summation calculator to find the sum of a series for a particular expression over a predetermined start and end range. Mathematical formulas usually require the sum of multiple variables, the summation technique is very convenient and can accurately represent the sum of these values of the variable.