Sigma (Σ) Summation Calculator
Use this tool to compute finite sums quickly. Enter an expression in i, then choose the start, end, and step.
What is an online summation calculator?
An online summation calculator helps you evaluate finite sums written in sigma notation, such as Σ(i=1 to n) i or Σ(i=1 to n) i². Instead of adding terms manually, the calculator evaluates each term based on your expression and returns the total instantly.
This is useful in algebra, statistics, finance, and programming whenever you need sequence totals, arithmetic series, polynomial sums, or custom index-based formulas.
How to use this summation tool
1) Enter the expression
Type a formula using i as the index variable. Example inputs:
- i for the sum of integers
- i^2 for square numbers
- 2*i + 5 for a linear sequence
- (i+1)/i for fractional terms
2) Set start and end values
The start and end values define the summation bounds. If you set start = 1 and end = 10, the calculator evaluates terms at i = 1, 2, 3, ... 10.
3) Choose step size
Step controls how i changes each term. A step of 1 checks every integer. A step of 2 checks odd or even indices depending on your start value.
Popular summations you can compute
Sum of first n natural numbers
Use expression i with start = 1, end = n. For n = 100, result is 5050.
Sum of squares
Use expression i^2. For i from 1 to 5, the result is 55.
Sum of cubes
Use expression i^3. For i from 1 to 4, the result is 100.
Arithmetic sequence totals
If your terms follow a + d(i-1), enter it directly as an expression and sum over your chosen range.
Why this calculator is useful
- Fast checking: verify homework or spreadsheet formulas.
- Concept clarity: see how bounds and step size affect totals.
- Flexible input: evaluate custom finite sums without rewriting equations.
- Practical modeling: use it for budgeting, trend analysis, and algorithm testing.
Common mistakes to avoid
- Using a step of zero (this is undefined and will fail).
- Picking a step direction that never reaches the end value.
- Forgetting parentheses in expressions like (i+1)/2.
- Typing unsupported characters in the formula.
Quick FAQ
Does it support decimal results?
Yes. If your expression creates decimals, the final summation can be decimal as well.
Can I use negative ranges?
Absolutely. You can sum from negative to positive values, as long as the step direction is valid.
Is this for finite sums only?
Yes, this calculator is designed for finite summation with explicit start and end bounds.
Final note
If you work with sigma notation, sequence sums, or arithmetic series often, this online summation calculator gives you a fast and reliable way to compute totals and verify your math.