Series Sum Calculator
A series is the sum of the terms of a sequence. This calculator supports three types of series: arithmetic series (where terms increase by a constant difference), geometric series (where terms multiply by a constant ratio), and custom series (where you enter any values you want). For arithmetic and geometric series, enter the first term, the common difference or ratio, and the number of terms. For custom series, simply paste comma-separated values, and the calculator handles the rest. The tool instantly computes the total sum, the average value, and counts how many terms you entered, making it easy to analyze any series.
Series sum formulas
Arithmetic sum: Sₙ = n/2 * (a1 + aₙ)
Geometric sum (r ≠ 1): Sₙ = a1 * (1 - r^n) / (1 - r)
Average: A = Sₙ / n
Series sum calculator: frequently asked questions
What is a series?
A series is the sum of the terms of a sequence. If a sequence is a list of numbers, a series is the result of adding all those numbers together. For example, the arithmetic sequence 1, 2, 3, 4, 5 generates the arithmetic series 1 + 2 + 3 + 4 + 5 = 15.
What is the difference between a sequence and a series?
A sequence is a list of numbers in a specific order, like 2, 4, 6, 8. A series is the sum of those numbers: 2 + 4 + 6 + 8 = 20. Sequences describe the pattern, while series represent the accumulated total.
How is the average of a series calculated?
The average of a series is the sum divided by the count of terms. If the series has sum S and n terms, the average is S/n. For example, the series 1 + 2 + 3 + 4 + 5 = 15 with 5 terms has an average of 15/5 = 3.
Can I use this calculator with any sequence?
Yes. This calculator has three modes: arithmetic series (enter first term and common difference), geometric series (enter first term and common ratio), and custom series (enter your values as comma-separated numbers). The custom mode works for any sequence, even irregular ones.
How do I enter custom values?
In custom mode, paste or type your numbers separated by commas. For example: 1.5, 3.2, 4.8, 2.1. The calculator will sum them, find the average, and count how many terms you entered. Spaces around commas are fine.
Official sources
- Khan Academy: Series and sigma notation.
- Wolfram MathWorld: Series.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.