Summation Calculator

You can use this summation calculator to rapidly compute the sum of a series for certain expression over a predetermined range.

How to use the summation calculator

  • Input the expression of the sum
  • Input the upper and lower limits
  • Provide the details of the variable used in the expression
  • Generate the results by clicking on the "Calculate" button.
Summation (Sigma, ∑) Notation Calculator
k =
n =

Supported operators, constants and functions

  • Arithmetic Operators: add "+", subtract "-", divide "/", multiply "*", exponent "^", factorial "!"
  • Comparison Operators: greater than ">", less than "<", greater than or equal ">=", less than or equal "<=", equal "=="
  • Constants: e (2.7182818284..), pi (3.1415926535..)
  • Grouping Symbols: "()" parentheses group symbols to indicate order of operations
  • Trigonometric Functions: sin(x), cos(x), tan(x), cot(x), sec(x), csc(x), asin(x), acos(x), atan(x), acot(x), asec(x), acsc(x)
  • Hyperbolic Trigonometric Functions: sinh(x), cosh(x), tanh(x), coth(x), sech(x), csch(x)
  • Inverse Hyperbolic Functions: asinh(x), acosh(x), atanh(x), acoth(x), asech(x), acsch(x)
  • Min / Max Functions: min(exp1, exp2,...), max(exp1, exp2,...)
  • Misc. Functions: log(x), log10, exp(x), sqrt(x), abs(x), ceil(x), round(x), floor(x), fact(x), dfactorial(x), mod(exp1, exp2), sign(x)

Summation Notation

Summation notation represents an accurate and useful method of representing long sums. For example, you may wish to sum a series of terms in which the numbers involved exhibit a clear pattern, as follows:

1 + 2 + 3 + 4 + 5 + 6 + 7


1 + 4 + 9 + 16 + 25 + 36 + 49

The first of the examples provided above is the sum of seven whole numbers, while the latter is the sum of the first seven square numbers. On a higher level, if we assess a succession of numbers, x1, x2, x3, . . . , xk, we can record the sum of these numbers in the following way:

x1 + x2 + x3 + . . . + xk.

A simpler method of representing this is to use the term xn to denote the general term of the sequence, as follows:

x n
n = 1

In this case, the symbol is the Greek capital letter, Sigma, that corresponds to the letter 'S', and denotes to the first letter in the word 'Sum.' As such, the expression refers to the sum of all the terms, xn where n represents the values from 1 to k. We can also represent this as follows:

x n
n = a

This representation refers to all the terms xn, where n assumes the values from a to b. In this case, a represents the lower limit, while b represents the upper limit.

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