Sum Calculator

Q: What separators can I use between numbers?

You can use commas , spaces , semicolons , pipes (|) , or new lines to separate your numbers. The calculator treats any non-numeric character as a separator, so almost any format will work.

Q: Can I paste numbers from a spreadsheet?

Yes. Copy a column or row from Excel, Google Sheets, or any spreadsheet app and paste it straight into the text box. The calculator will read each number automatically.

Q: Is there a limit to how many numbers I can add?

In Number List mode there is no hard limit, though very large lists may slow your browser. In Series / Formula mode, finite sums allow up to 5,000,000 terms .

Q: How do I enter negative numbers?

Put a minus sign directly before the number with no space, like -8 or -3.5 . The calculator handles negatives in both Number List and Series modes.

Q: How do I enter a number in scientific notation?

Use the format 1.5e10 , where e means "times ten to the power of." For example, 3e4 equals 30,000.

Q: What does the running total table show?

It shows the cumulative sum after each number is added. Row 1 shows the first number, row 2 shows the first two numbers added together, and so on until all numbers are included.

Q: How do I sum an infinite series?

Switch to the Series / Formula tab. Enter your expression, set a starting value, and type inf , oo , or ∞ in the upper bound field. The calculator will test for convergence and give you the result if the series converges.

Q: What does it mean when the calculator says a series diverges?

It means the series does not add up to a fixed number. The partial sums keep growing or never settle, so no finite answer exists.

Q: What functions can I use in the summand expression?

You can use sqrt() , abs() , factorial() , binomial(n,k) , sin() , cos() , tan() , ln() , log() , exp() , floor() , ceil() , and sign() . Use ^ for exponents and pi or π for pi.

Q: What is the index variable and can I leave it blank?

The index variable is the letter in your formula that changes with each term, like n in 1/n^2 . If you leave the field blank, the calculator will auto-detect it for you.

Sum Calculator

Updated Jun 25, 2026 By Jehan Wadia

Introduction

This free sum calculator adds up numbers quickly and shows you the answer step by step. You can use it in two ways. In Number List mode, type or paste any set of numbers and the calculator will find their total, average, minimum, and maximum. In Series / Formula mode, enter a math expression like 1/n^2 with a start and end value, and the tool will compute the summation for you. It works with negative numbers, decimals, and even scientific notation. Whether you need to add a handful of values or evaluate a complex series, this calculator does the math and explains each step so you can follow along.

How to Use Our Sum Calculator

Enter your numbers or define a series formula below, and this calculator will give you the total sum, a step-by-step solution, a running total table, and a chart of your results.

This calculator has two modes. Use the Number List tab to add up a list of numbers. Use the Series / Formula tab to sum a math expression over a range of values.

Number List Mode

Numbers to sum: Type or paste your numbers into the text box. You can separate them with commas, spaces, semicolons, or new lines. The calculator accepts negative numbers, decimals, and scientific notation like 1.5e10.

Series / Formula Mode

Expression (summand): Type the math formula you want to sum. You can use basic operators like +, -, *, /, and ^, along with functions like sqrt(), abs(), factorial(), and binomial(n,k). For example, type 1/n^2 to sum the reciprocal of each squared number.

Index variable: Enter the single letter used in your expression that changes with each term. For example, if your expression uses n, type n here. You can leave this blank and the calculator will detect it for you.

From (lower bound): Enter the integer where the summation starts. This is the first value the index variable will take. For example, enter 1 to start summing from 1.

To (upper bound): Enter the integer where the summation ends. This is the last value the index variable will take. To sum an infinite series, type inf or ∞ instead of a number.

Press the Calculate button in either mode to see your sum, step-by-step work, and chart. Press Clear to reset the inputs.

What Is a Sum?

A sum is the result you get when you add two or more numbers together. If you have the numbers 3, 5, and 7, their sum is 15 because 3 + 5 + 7 = 15. Finding a sum is one of the most basic and important tasks in math. You use it every day — when you count money, track scores, or combine measurements.

How to Add a List of Numbers

To find the sum of a list of numbers, start with the first number. Add the second number to it. Then add the third number to that result. Keep going until you have added every number in the list. The final total is your sum. This works the same way whether the numbers are positive, negative, or have decimals. If you need to work with fractions instead of decimals, convert them first or use our dedicated tool.

What Is a Series?

A series is a sum that follows a pattern or formula. Instead of typing every number by hand, you use a rule to describe each term. For example, "add up 1/n² for every n from 1 to 100" is a series. The Greek letter sigma (Σ) is the symbol used in math to represent a series. You set a starting value, an ending value, and a formula, and then each term is calculated and added together.

Finite vs. Infinite Series

A finite series has a set number of terms. It always has a final answer because you stop adding at some point. An infinite series keeps going forever. Some infinite series still add up to a fixed number — these are called convergent. Others grow without limit and never settle on a value — these are called divergent. A classic example of a convergent series is 1/1² + 1/2² + 1/3² + …, which equals π²/6. You can explore the behavior of these series as terms grow by examining their limits.

Common Types of Series

Arithmetic series: Each term increases by the same amount. Example: 2, 5, 8, 11, … (adding 3 each time). You can also explore these patterns with our arithmetic sequence calculator.
Geometric series: Each term is multiplied by the same number. Example: 3, 6, 12, 24, … (multiplying by 2 each time).
p-series: Each term is 1/n raised to a power p. If p is greater than 1, the infinite series converges.

Key Terms

Running total: The sum so far after each new number is added. It helps you see how the total builds up step by step.
Average (mean): The sum divided by the count of numbers. It tells you the typical value in your list. For a deeper look at averages and related measures, try our average calculator or mean median mode calculator.
Partial sum: The total of a series after adding only some of its terms. For infinite series, partial sums show whether the total is settling toward a limit.

Formulas used

Arithmetic Series Sum

S_N = \frac{N}{2}\left(a_1 + a_N\right)

Finite Geometric Series Sum

S_N = a \cdot \frac{1 - r^{N}}{1 - r}

Infinite Geometric Series Sum

S = \frac{a}{1 - r}, \quad |r| < 1

Average (Mean)

\bar{x} = \frac{S}{n}

Basel Problem (p-series, p = 2)

\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}

Ratio Test for Convergence

L = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|,\quad L < 1 \Rightarrow \text{converges}

Frequently asked questions

What separators can I use between numbers?

You can use commas, spaces, semicolons, pipes (|), or new lines to separate your numbers. The calculator treats any non-numeric character as a separator, so almost any format will work.

Can I paste numbers from a spreadsheet?

Yes. Copy a column or row from Excel, Google Sheets, or any spreadsheet app and paste it straight into the text box. The calculator will read each number automatically.

Is there a limit to how many numbers I can add?

In Number List mode there is no hard limit, though very large lists may slow your browser. In Series / Formula mode, finite sums allow up to 5,000,000 terms.

How do I enter negative numbers?

Put a minus sign directly before the number with no space, like -8 or -3.5. The calculator handles negatives in both Number List and Series modes.

How do I enter a number in scientific notation?

Use the format 1.5e10, where e means "times ten to the power of." For example, 3e4 equals 30,000.

What does the running total table show?

It shows the cumulative sum after each number is added. Row 1 shows the first number, row 2 shows the first two numbers added together, and so on until all numbers are included.

How do I sum an infinite series?

Switch to the Series / Formula tab. Enter your expression, set a starting value, and type inf, oo, or ∞ in the upper bound field. The calculator will test for convergence and give you the result if the series converges.

What does it mean when the calculator says a series diverges?

It means the series does not add up to a fixed number. The partial sums keep growing or never settle, so no finite answer exists.

What functions can I use in the summand expression?

You can use sqrt(), abs(), factorial(), binomial(n,k), sin(), cos(), tan(), ln(), log(), exp(), floor(), ceil(), and sign(). Use ^ for exponents and pi or π for pi.

What is the index variable and can I leave it blank?

The index variable is the letter in your formula that changes with each term, like n in 1/n^2. If you leave the field blank, the calculator will auto-detect it for you.

How does the calculator decide which convergence test to use?

It first checks if the series is geometric, arithmetic, constant, or a p-series. If none of those match, it tries the n-th term test and then the ratio test. If both are inconclusive, it uses numerical evaluation of partial sums.

Can I copy the result to use somewhere else?

Yes. In Number List mode, click the Copy button next to the sum. The exact value is copied to your clipboard so you can paste it into another app.

Why does my result show an approximation symbol (≈) instead of an exact answer?

The calculator shows ≈ when the answer is not a clean whole number or simple fraction. It still gives you a value accurate to about 10 significant digits.

Does the calculator show an exact fraction for the answer?

When possible, yes. If the decimal result can be written as a simple fraction with a denominator up to 10,000, the calculator displays the exact fractional form alongside the decimal.

What does the cumulative sum chart show?

The chart plots how the total grows as each number or term is added. For finite lists it shows the running total. For infinite series it shows partial sums so you can see whether the series is converging to a limit.

Can I use this calculator on my phone?

Yes. The calculator is fully responsive and works on phones, tablets, and desktop browsers. All buttons and fields are sized for easy tapping on small screens.

Is my data saved or sent to a server?

No. All calculations happen entirely in your browser. Your numbers are never uploaded or stored anywhere.