Summation Calculator

Evaluate a sigma summation of an expression in k from a lower to an upper index — the terms are expanded and added for you.

Sum —
Number of terms —

How to Evaluate a Summation

Enter the term expression in k and the index range.

1

Write the term

Use k as the index variable, for example k², 2k+1 or 1/k. Press the up arrow to raise an exponent; functions like sqrt also work.

2

Set the bounds

Enter the lower and upper values of k. The calculator adds one term for each whole value from the lower to the upper bound.

3

Read the sum

The total appears with the terms expanded in the steps so you can check the series.

Frequently Asked Questions

What is summation (sigma) notation?
Sigma notation, written with Σ, is a compact way to write a sum. The variable below Σ starts at the lower bound and increases by one up to the upper bound, and the terms are added. For example, Σ (k=1 to 4) k² means 1² + 2² + 3² + 4² = 30.
Which variable should I use?
Use the letter k for the index — for example k². The calculator substitutes each whole-number value of k into the expression and adds the results. You can set the lower and upper bounds independently, and the index always increases by exactly one between them.
Can it sum things like 1/k or sqrt(k)?
Yes — any expression the calculator can evaluate works, including fractions and roots. A term that is undefined (such as 1/k at k = 0) is flagged instead. The calculator does not silently skip it.
Is my data sent anywhere?
No — the calculation runs in your browser with JavaScript; nothing is uploaded or stored. The summation calculator keeps working without an internet connection. No data ever leaves your device.