Exponential Smoothing Calculator Formula
Understand the math behind the exponential smoothing calculator. Each variable explained with a worked example.
Formulas Used
Next Forecast
forecast = alpha * actual + (1 - alpha) * forecast_prevForecast Error
error = actual - forecast_prevAdjustment (alpha * error)
adjustment = alpha * (actual - forecast_prev)Variables
| Variable | Description | Default |
|---|---|---|
actual | Latest Actual Value | 120 |
forecast_prev | Previous Forecast | 110 |
alpha | Smoothing Factor (alpha) | 0.3 |
How It Works
How to Apply Exponential Smoothing
Formula
F(t+1) = alpha * A(t) + (1 - alpha) * F(t)
Equivalently: F(t+1) = F(t) + alpha * (A(t) - F(t))
Exponential smoothing updates the forecast by adding a fraction (alpha) of the latest forecast error. Alpha near 1 means the forecast reacts quickly to changes; alpha near 0 means it changes slowly. All past data contributes, with exponentially decreasing weights.
Worked Example
Previous forecast = 110, actual = 120, alpha = 0.3.
- 01Error = 120 - 110 = 10
- 02Adjustment = 0.3 * 10 = 3
- 03New forecast = 110 + 3 = 113
- 04Or equivalently: 0.3 * 120 + 0.7 * 110 = 36 + 77 = 113
Frequently Asked Questions
How do I choose the alpha value?
Higher alpha (0.7-0.9) gives more weight to recent data, suitable for volatile series. Lower alpha (0.1-0.3) smooths more aggressively, suitable for stable series. Optimize alpha by minimizing forecast error on historical data.
What is double exponential smoothing?
Double (Holt) exponential smoothing adds a second component for trend, allowing forecasts to follow upward or downward trends rather than always lagging behind. Triple (Holt-Winters) adds a seasonal component.
How does exponential smoothing compare to moving averages?
Both smooth data, but exponential smoothing gives more weight to recent observations and requires only the latest actual value and previous forecast (not the full window of data). It is more memory-efficient and often more responsive.
Ready to run the numbers?
Open Exponential Smoothing Calculator