Exponential Smoothing Calculator
Smooth and forecast a series with exponentially decaying weights — the workhorse of short-term forecasting, with its error measures.
Each smoothed value is a blend of the newest observation and the previous smoothed value: S_t = αx_t + (1−α)S_(t−1).
How the exponential smoothing calculator works
Each smoothed value is a blend of the newest observation and the previous smoothed value: S_t = αx_t + (1−α)S_(t−1). Expanding it shows every past point still contributes, with weight decaying geometrically.
α controls the trade-off: near 1 the series tracks every wiggle, near 0 it barely moves. The next-period forecast from simple exponential smoothing is just the last smoothed value — it carries no trend, which is what Holt's method adds.
Formula: S_t = αx_t + (1 − α)S_(t−1)
Worked examples
| Inputs | Forecast for the next period | Note |
|---|---|---|
| α = 0.3 on a rising series | 18.64635 | the forecast lags the trend |
| α = 1 | 22 | the forecast is just the last value |
| α = 0.05 | 12.505738 | very smooth, very slow |
FAQFrequently asked questions
What does α control?
How fast the smoothing forgets. Near 1 it tracks the latest point; near 0 it barely moves.
How do I choose α?
Minimise the forecast error on your own data — try a range and pick the lowest RMSE. Values between 0.1 and 0.3 are common for stable series.
How does it compare to a moving average?
A moving average drops points entirely once they leave the window; exponential smoothing keeps every point with a decaying weight. An α of 0.2 behaves roughly like a 9-period average.
Can it handle a trend?
Not on its own — simple exponential smoothing always forecasts a flat line and lags a trending series. Holt's method adds a trend term; Holt-Winters adds seasonality.
What is MAPE for?
Percentage error, which makes accuracy comparable across series of different scales. It breaks down when values approach zero.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.