Calculator inputs
Paste sequential numeric values, choose the smoothing span, and compute a triangular moving average for stable trend inspection.
Example data table
This example uses a period of 5 and centered alignment.
| Index | Observed Value | Centered TMA |
|---|---|---|
| 1 | 20 | Not available |
| 2 | 22 | Not available |
| 3 | 21 | 22.3333 |
| 4 | 24 | 23.6667 |
| 5 | 26 | 24.8889 |
| 6 | 25 | 26.0000 |
| 7 | 27 | 27.0000 |
| 8 | 29 | 28.0000 |
| 9 | 28 | Not available |
| 10 | 30 | Not available |
Formula used
A triangular moving average performs two layers of simple moving average smoothing. It gives more weight to middle observations than edge observations.
- First span:
m = ceil((n + 1) / 2) - Second span:
k = floor((n + 1) / 2) - First smoothing:
SMA1_t = average(x[t-m+1] ... x[t]) - Second smoothing:
TMA_t = average(SMA1[t-k+1] ... SMA1[t]) - Equivalent interpretation: the final result behaves like a triangular weighting profile across the chosen period.
For odd periods, the weights are symmetric around a single center. For even periods, the center sits between two observations, so the aligned position may appear as a half step.
How to use this calculator
- Enter a descriptive label for your sequence, such as price, demand, output, or error rate.
- Paste time-ordered values using commas, spaces, or line breaks.
- Choose a period. Larger periods smooth more noise but add more lag.
- Select centered alignment for historical analysis or trailing alignment for operational monitoring.
- Set decimal places, scale factor, and a custom starting index when needed.
- Click Calculate TMA to display summary metrics, a trend chart, and the detailed output table above the form.
- Use the export buttons to download your results as CSV or PDF.
Frequently asked questions
1. What does a triangular moving average do?
It smooths a sequence twice using simple averages. That creates a softer trend line than a single simple moving average and emphasizes middle observations within each window.
2. Why use TMA instead of a simple moving average?
TMA generally reduces random fluctuations more strongly than a single moving average. It is useful when you care more about stable direction than fast reaction speed.
3. What period should I choose?
Short periods react faster but stay noisier. Long periods create smoother curves yet delay turning points. Choose a period that matches the volatility and decision horizon of your data.
4. What is the difference between centered and trailing alignment?
Centered alignment places the smoothed value near the middle of the contributing window. Trailing alignment places it at the end, which is often easier for dashboards and rolling monitoring.
5. Why do some rows show “Not mapped” for the raw value?
With centered alignment and even periods, the smoothed point can fall between two indices. In that case, there is no single raw observation exactly at that aligned position.
6. Can I use this for machine learning features?
Yes. TMA can be used as a feature engineering step for sequential data, especially when you want to reduce noise before trend classification, anomaly analysis, or forecasting.
7. Does scaling the series change the trend direction?
A positive scale factor changes magnitude but preserves relative direction. It can help convert units or normalize inputs before comparing different sequences visually.
8. What happens if the dataset is shorter than the period?
The calculator will stop and show a validation message. You need at least as many observations as the selected period to compute a valid triangular moving average.