Track changing dispersion across time series with confidence. Use custom windows, decimals, and deviation methods. Download clean reports for audits, forecasting, and model checks.
Example dataset: 10, 12, 13, 12, 15, 18, 17, 19. Window size: 3. Method: sample.
| Window # | Window Values | Mean | Rolling Std Dev |
|---|---|---|---|
| 1 | 10, 12, 13 | 11.6667 | 1.5275 |
| 2 | 12, 13, 12 | 12.3333 | 0.5774 |
| 3 | 13, 12, 15 | 13.3333 | 1.5275 |
| 4 | 12, 15, 18 | 15.0000 | 3.0000 |
| 5 | 15, 18, 17 | 16.6667 | 1.5275 |
| 6 | 18, 17, 19 | 18.0000 | 1.0000 |
Rolling mean: mean = (sum of values in the current window) / n
Population rolling standard deviation: sqrt( sum((x - mean)^2) / n )
Sample rolling standard deviation: sqrt( sum((x - mean)^2) / (n - 1) )
Here, x is each value in the active window and n is the number of observations inside that window.
Rolling standard deviation measures changing spread in ordered data. It uses a moving window. Each new window creates a fresh deviation value. This helps you study local variability instead of one global summary. It is useful for mathematics, statistics, and time based analysis.
A single standard deviation can hide short bursts of instability. Rolling analysis solves that problem. It shows whether dispersion is rising, falling, or staying stable. This is valuable when you review time series, experimental results, process samples, or classroom datasets with sequential behavior.
The window size controls how many values enter each calculation. Small windows react quickly. Large windows smooth sudden changes. The calculator also supports minimum periods. That option allows early estimates before the full window becomes available. Step size lets you skip positions for faster review.
Use sample standard deviation when the window acts like a sample from a larger process. Use population standard deviation when the window contains the full set you want to measure. This choice changes the divisor in the variance step. That can slightly change every rolling result.
Lower rolling values mean the points inside that window stay close to the mean. Higher values mean the values spread out more. Compare the minimum, maximum, and average rolling deviation to understand stability. A sudden jump can signal noise, outliers, volatility, or a shift in behavior.
This rolling standard deviation calculator supports many tasks. Students can test formulas. Analysts can review moving variability. Researchers can inspect repeated measurements. Financial users can monitor volatility. Engineers can track process stability. Quality teams can spot inconsistent batches. It is a practical tool for clear statistical decision making.
It is a moving measure of spread. The calculator takes a window of consecutive values, computes standard deviation, then slides forward and repeats the calculation.
Use a small window when you want faster reaction to local changes. It highlights short term swings, but it can also make the output more sensitive to noise.
A larger window is better when you want smoother results. It reduces sensitivity to sudden spikes and helps reveal broader patterns in variability.
Sample deviation divides by n - 1. Population deviation divides by n. Sample is common for estimation. Population is used when the full window is the full group of interest.
Minimum periods sets the smallest number of values required before a rolling result appears. This helps you produce early values before the window fills completely.
Yes. The calculator accepts negative values, positive values, integers, and decimals. Keep the input numeric and separate entries with commas, spaces, or new lines.
High rolling deviation means the values in those windows are spread far from their local mean. That often suggests instability, volatility, or unusual observations.
They export the calculated result table and summary values. This makes it easier to save your rolling statistics for reports, assignments, or audits.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.