A weighted moving average (WMA) smooths a time series while emphasizing certain observations. Suppose you have values and positive weights . The WMA equals so that points with larger weights influence the result more strongly. Checking “Normalize weights” rescales the inputs so the denominator equals one, which can make comparisons across windows easier.
A simple moving average (SMA) uses equal weights, which may lag behind sudden changes. By contrast, WMAs commonly assign higher weights to more recent observations. Financial analysts often combine the WMA with exponential techniques—see the exponential moving average calculator for an alternative that applies exponentially decaying weights.
Imagine daily website visits of 140, 160, 155, 170, 185, 200, and 190. To highlight the latest days, choose weights 1 through 7. The calculator evaluates and returns 234.82. Because the newest data carry the largest weights, the WMA reacts faster than an equal-weight average when visits spike.
Your weighting strategy should reflect how quickly the underlying signal changes. A linear ramp (1, 2, 3, …) emphasizes recency without completely discarding older points. Domain-specific schemes can focus on weekdays vs. weekends, emphasize quarters in financial planning, or prioritize particular sensors in engineering contexts. If you are modeling trends or building forecasts, consider comparing results with regression tools like the weighted least squares calculator.
The table below compares three weighting strategies for the same seven-day dataset. Each produces a different WMA and reacts uniquely to change.
| Weight scheme | Weights | Weight sum | WMA result |
|---|---|---|---|
| Linear ramp | 1-7 | 28 | 234.82 |
| Triangular | 1-3-3-2-1-1-1 | 12 | 209.17 |
| Uniform | 1-1-1-1-1-1-1 | 7 | 171.43 |
Regardless of the scheme, keep weights positive and aligned with your measurement goals. Experiment with different lists in the calculator and note how the summary changes.
