Cumulative Sum & Running Average Calculator
Build the running total and running average of a list step by step — see how the sum and mean evolve as each value is added.
How it works
Cumulative sumₖ = x₁ + x₂ + … + xₖ · Running averageₖ = Cumulative sumₖ ÷ k
A cumulative sum (prefix sum) keeps a running total that includes every value up to the current position, and the running average divides that total by how many values have been added so far. Together they show how a series builds up and how quickly its mean stabilizes — early values swing the running average widely, while later values move it less because the divisor keeps growing.
Worked example
For 5, 10, 15, 20 the cumulative sums are 5, 15, 30, 50 and the running averages are 5, 7.5, 10, 12.5. The final total is 50 and the final running average is 50 ÷ 4 = 12.5, which equals the ordinary mean of the whole list.
Sources: Prefix sum — Wikipedia
Frequently asked questions
What is the difference between the cumulative sum and the running average?
The cumulative sum is the total so far; the running average divides that total by the number of values seen so far, so it converges toward the overall mean.
Does the order of the values change the final total?
The final cumulative sum and final running average do not depend on order, but the intermediate rows do — reordering changes the path, not the destination.
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This calculator is for educational purposes. Double-check important results before acting on them.