Geometric Series Calculator
Geometric Series Calculator sums the first n terms of a geometric series from the first term, common ratio, and term count using the closed-form partial-sum formula, rounded to four decimals.
What this calculator does
The Geometric Series Calculator estimates your result instantly from the values you enter, using standard math & conversions formulas. Geometric Series Calculator sums the first n terms of a geometric series from the first term, common ratio, and term count using the closed-form partial-sum formula, rounded to four decimals. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Geometric Series Calculator
Enter the first term a, the common ratio r, and the number of terms n, and this calculator returns the partial sum a(1 − rⁿ) ÷ (1 − r).
When the ratio equals 1 the sum reduces to a × n, which the tool handles as a special case.
Formula & Mathematical Calculation
Sum of n Terms = f(First Term (a), Common Ratio (r), Number of Terms (n))
Calculated according to standard math formulas implemented in the calculator core.
Calculation Example
For a = 2, r = 3, and n = 6, the sum is 2 × (1 − 3⁶) ÷ (1 − 3) = 2 × (1 − 729) ÷ (−2) = 2 × (−728) ÷ (−2) = 728.
Key Benefits
- Sums a geometric series in one step
- Uses the exact closed-form partial-sum formula
- Handles the ratio-equals-one case separately
- Rounds the sum to four decimal places
How to Use this Calculator
-
Enter the first term
Type the first term a into the First Term field. -
Enter the common ratio
Type the common ratio r into the Common Ratio field. -
Enter the term count
Type the number of terms n (at least 1). -
Calculate
Select Calculate and read the Sum of n Terms.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Geometric Series Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.