Cumulative Moving Average Calculator

Enter Series Data

Example Data Table

Example sequence: 12, 15, 18, 20, 25, 30

Observation	Value	Cumulative Sum	Cumulative Moving Average	Change in CMA
Obs 1	12	12	12.0000	—
Obs 2	15	27	13.5000	1.5000
Obs 3	18	45	15.0000	1.5000
Obs 4	20	65	16.2500	1.2500
Obs 5	25	90	18.0000	1.7500
Obs 6	30	120	20.0000	2.0000

Formula Used

The calculator uses both the direct definition and the recursive update form.

Cumulative Sum at step n = x₁ + x₂ + ... + xₙ

CMAₙ = (x₁ + x₂ + ... + xₙ) / n

CMAₙ = CMAₙ₋₁ + (xₙ - CMAₙ₋₁) / n

The direct formula divides the running total by the number of observations. The recursive form is useful for streaming data because it updates the mean without recalculating every earlier sum from scratch.

How to Use This Calculator

Enter a name for the dataset.

Choose an observation prefix such as Obs, Day, or Batch.

Set decimal places and the starting observation number.

Paste the numeric sequence into the data field.

Click Calculate CMA to show the result above the form.

Review the summary metrics and the full running table.

Use Download CSV or Download PDF for reporting.

Frequently Asked Questions

1. What is a cumulative moving average?

A cumulative moving average is the mean of all values up to the current observation. It keeps the entire history instead of using a fixed window.

2. How is it different from a simple moving average?

A simple moving average uses only a chosen window, such as 5 or 20 points. A cumulative moving average uses every point from the beginning.

3. When should I use cumulative moving average?

Use it for streaming metrics, gradual process monitoring, experiments, quality tracking, and long-term signals where you want a stable running mean.

4. Can this calculator handle decimals and negative values?

Yes. It accepts integers, decimals, negative values, and scientific notation. Separate entries with commas, spaces, semicolons, tabs, or line breaks.

5. Why does the cumulative average move less over time?

Each new value is divided across a larger observation count. That lowers the influence of a single point, so the running average becomes smoother.

6. Does the order of the data matter?

Yes. The final overall mean is unchanged for the same values, but each intermediate cumulative average depends on sequence order.

7. What does change in CMA mean?

It shows how much the running mean moved after adding the newest value. Small changes usually indicate a more stable long-run average.

8. Why export results as CSV or PDF?

CSV works well for spreadsheets and scripts. PDF is better for sharing a clean summary report with detailed running-average results.