About the Geometric Series Calculator
Calculate the sum of a finite geometric series, and whether it converges as n → ∞ (|r| < 1).
Also known as: sum of geometric series, geometric sum, sum of gp.
How to use this calculator
- Enter first term, common ratio, terms.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
Sₙ = a₁(1 − rⁿ)/(1 − r) · S∞ = a₁/(1 − r) for |r| < 1
Worked example
Using the values pre-filled in the calculator above:
- First term = 100
- Common ratio = 0.5
- Terms = 10
the calculator returns:
- Sum of 10 terms: 199.8047
- Infinite sum: 200