The Sum Calculator adds every value in a pasted list and returns the total, along with the count of values, the mean, and the range as useful companion figures. Paste values separated by commas, spaces or line breaks, and the calculator returns the sum immediately, with the running total shown so long additions can be verified step by step.
The sum is the most basic building block of statistics: nearly every other summary measure, the mean, the variance, the standard deviation, is built from a sum calculated somewhere in its formula. This page keeps that foundational calculation front and center.
Calculate the sum of a list of numbers
The sum is the total of all values added together.
Σx = x₁ + x₂ + x₃ + ... + xₙWorked example: find the sum of 12, 15, 15, 18, 22, 24, 31.
1. Add the values in order. 12 + 15 = 27. 27 + 15 = 42. 42 + 18 = 60. 60 + 22 = 82. 82 + 24 = 106. 106 + 31 = 137.
2. Read the final total. Sum = 137.
Addition is commutative, meaning the values can be added in any order and still reach the same total, which is a useful check: re-adding the same list from the opposite end should return the identical sum of 137.
Use the sum to find the mean
Once the sum and count are both known, the mean follows immediately.
mean = sum / countWorked example: the same list has a sum of 137 and a count of 7.
137 ÷ 7 ≈ 19.571.
This relationship works in reverse too: if a mean and a count are known, multiplying them back together recovers the original sum, which is a useful check when a mean was reported without the underlying sum.
Find the running total for a growing list
For a list that grows over time, such as daily sales figures or a running expense log, tracking the running total after each new entry shows how the sum builds up rather than only revealing the final figure. Worked example: adding entries one at a time to the list above.
After 12: running total 12. After 15: running total 27. After 15: running total 42. After 18: running total 60. After 22: running total 82. After 24: running total 106. After 31: running total 137.
This running view is useful for spotting exactly when a total crosses a meaningful threshold, such as a budget limit or a sales target.
Check the sum against the range
The sum and the range (maximum minus minimum) describe different things and are not directly derived from each other, but comparing them offers a rough sanity check. For the example list, the range is 31 − 12 = 19, while the sum is 137 across 7 values.
If a sum seems implausibly large or small given the range and count of the entered numbers, that's a signal to double-check the pasted data for a duplicated or missing value.
Use the sum in weighted calculations
Some real-world sums need weighting rather than simple addition, such as a weighted grade average where different assignments count for different percentages. A weighted sum multiplies each value by its weight before adding.
weighted sum = Σ(xᵢ × wᵢ)This calculator focuses on the plain, unweighted sum; a weighted average calculation, such as the one used for course grades, applies this same idea with an extra multiplication step built in before the addition.
Work through a weighted sum example
A course has three assignments worth 20%, 30% and 50% of the grade, with scores of 80, 90 and 70. 1. Multiply each score by its weight. 80 × 0.20 = 16. 90 × 0.30 = 27. 70 × 0.50 = 35.
2. Add the weighted values. 16 + 27 + 35 = 78.
The plain average of 80, 90 and 70 would be (80 + 90 + 70) / 3 ≈ 80, noticeably higher than the weighted sum of 78, since the weighted calculation gives the lower 70 score more influence by assigning it the largest weight.
Frequently asked questions
How do you calculate the sum of a list of numbers?
Add every value together in sequence: sum = x₁ + x₂ + ... + xₙ. For 12, 15, 15, 18, 22, 24, 31, the sum is 137.
How is the sum related to the mean?
The mean equals the sum divided by the count of values. For a sum of 137 across 7 values, the mean is 137 ÷ 7 ≈ 19.571.
Does the order of addition matter for the sum?
No. Addition is commutative, so values can be summed in any order and the total will be identical, which is a useful way to double-check a running total.
What is a running total?
A running total is the cumulative sum after each new value is added to a growing list, useful for tracking progress toward a budget, target or threshold over time.
How do you calculate a weighted sum?
Multiply each value by its corresponding weight, then add all the weighted values together: weighted sum = Σ(value × weight). This differs from a plain sum, which treats every value equally.
Can the sum help catch a data entry error?
Yes. Comparing the sum against the count and range of the entered data (does the total look plausible given how many values and how spread out they are) can flag an accidentally duplicated or missing entry.
Is the sum the same as the total?
Yes. "Sum" and "total" are used interchangeably to describe the result of adding a list of values together.
Summary
The sum of a list of numbers is the running total of every value added together, giving 137 for the set 12, 15, 15, 18, 22, 24, 31, regardless of the order the values are added in.
That same sum, divided by the count of values, produces the mean, about 19.571 for this example, making the sum the foundational calculation behind most other descriptive statistics.