# Sum Of Series Calculator Sum arithmetic series, geometric series, or a custom list of terms > Canonical page: https://elysiatools.com/en/tools/sum-of-series-calculator - **Category:** Math & Numbers - **Keywords:** sum of series, series, arithmetic series, geometric series, partial sum, math ## Overview The Sum Of Series Calculator is a versatile mathematical utility designed to quickly compute the total sum of arithmetic sequences, geometric progressions, or any custom list of numbers. Whether you are solving complex algebra problems, evaluating financial growth models, or simply adding up an arbitrary dataset, this tool provides instant and accurate partial sums without the need for manual calculations or complex spreadsheet formulas. ## Inputs - **Series Type** (select) - **First Term** (number) - **Common Difference Or Ratio** (number) - **Number Of Terms** (number) - **Terms List** (textarea): 1, 3, 6, 10, 15 ## When to use - Solving math assignments that require calculating partial sums of arithmetic or geometric progressions. - Evaluating financial models, such as compound interest or cumulative returns, using geometric series. - Quickly finding the total sum of an arbitrary, comma-separated list of numerical values without opening a spreadsheet. ## How it works - Select your desired series type: Arithmetic, Geometric, or Custom List. - For arithmetic or geometric series, input the first term, the common difference or ratio, and the total number of terms (up to 200). - For a custom list, simply paste your comma-separated numbers into the provided text area. - The calculator instantly processes the parameters and outputs the exact total sum in a structured JSON format. ## Use cases - Students and educators verifying manual calculations for algebra and calculus coursework. - Financial analysts calculating the cumulative value of investments over multiple compounding periods. - Programmers and data analysts needing a quick way to sum a hardcoded array of numbers. ## Frequently asked questions ### What is the difference between an arithmetic and geometric series? An arithmetic series adds a constant value (common difference) to each consecutive term, while a geometric series multiplies each term by a constant value (common ratio). ### What is the maximum number of terms I can calculate? The calculator supports computing the sum for up to 200 terms in a single arithmetic or geometric sequence. ### Can I sum a random list of numbers? Yes, by selecting the 'Custom List' option, you can paste any comma-separated sequence of numbers to calculate their total sum. ### Can I use negative numbers or decimals? Yes, the first term, common difference, common ratio, and custom list items can all include negative numbers and decimal values. ### How is the result formatted? The tool outputs the final calculated sum as a structured JSON object, making it easy to read, copy, or integrate into other applications. ## Related tools - [RLC Admittance Calculator (Y = G + jB)](https://elysiatools.com/en/tools/admittance-calculator): Compute complex admittance Y = 1/Z = G + jB for series or parallel RLC circuits: G = R/|Z|², B = −X/|Z|². Returns conductance, susceptance, magnitude and phase angle. Supports any subset of R/L/C. - [Arithmetic Sequence Calculator](https://elysiatools.com/en/tools/arithmetic-sequence-calculator): Calculate the nth term, first terms, and finite sum of an arithmetic sequence - [Cantilever Beam Calculator](https://elysiatools.com/en/tools/cantilever-beam-calculator): Calculate the maximum bending moment M_max, maximum shear force V_max and free-end deflection δ_max of a cantilever beam under a free-end point load P or a uniformly distributed load q. Point load: δ = PL³/(3EI); UDL: δ = qL⁴/(8EI). - [Determinant Calculator](https://elysiatools.com/en/tools/determinant-calculator): Compute the determinant of a square matrix and explain the main calculation steps - [Geometric Sequence Calculator](https://elysiatools.com/en/tools/geometric-sequence-calculator): Calculate the nth term, first terms, and finite sum of a geometric sequence - [RLC Impedance & Phase Angle Calculator](https://elysiatools.com/en/tools/impedance-calculator): Compute complex impedance, magnitude |Z| and phase angle φ for series or parallel RLC circuits: X_L=2πfL, X_C=1/(2πfC), |Z|=√(R²+X²), φ=atan2(X,R). Supports any subset of R/L/C and an optional linear frequency sweep. - [Limit Calculator](https://elysiatools.com/en/tools/limit-calculator): Calculate limits of functions as x approaches a value - [Linear Equation Solver](https://elysiatools.com/en/tools/linear-equation-solver): Solve linear equations of the form ax + b = 0 using coefficients or a typed equation ## Samples - [Android Image Processing Java Samples](https://elysiatools.com/en/samples/android-image-processing-java): Android Java image processing examples including reading/saving images, scaling, and format conversion - [Android Image Processing Kotlin Samples](https://elysiatools.com/en/samples/android-image-processing-kotlin): Android Kotlin image processing examples including reading/saving images, scaling, and format conversion - [Web Image Processing Python Samples](https://elysiatools.com/en/samples/web-image-processing-python): Web Python image processing examples using PIL/Pillow including reading, saving, resizing, and format conversion - [Web Image Processing Rust Samples](https://elysiatools.com/en/samples/web-image-processing-rust): Web Rust image processing examples including image read/save, scaling, and format conversion ## Related content - [Math & Numbers Utility Tools](https://elysiatools.com/en/hubs/math-&-numbers-utility): Explore 48 math tools for &-numbers-utility workflows and compare closely related utilities quickly.