Exponential Smoothing Forecast Calculator (Simple, Next-Period Demand)
Next-period forecast from five periods of actual values with simple exponential smoothing, plus the average error and bias of the forecasts it would have made.
Results
What this tool does
Simple exponential smoothing makes each forecast the previous forecast corrected by a fraction α of its error: new forecast = α × latest actual + (1 − α) × previous forecast. A large α follows the latest data closely but jumps around with noise; a small α is smooth but slow to react, and α = 2 ÷ (N + 1) behaves like an N-period moving average. The method forecasts a flat line, so it lags behind a steady trend and ignores seasons. The first forecast is set equal to the first actual value, a common convention. The error figures compare periods 2 to 5.
Formula
F(t+1) = α × A(t) + (1 − α) × F(t) · average age = (1 − α) ÷ α
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a1 | Actual value, period 1 | — |
a2 | Actual value, period 2 | — |
a3 | Actual value, period 3 | — |
a4 | Actual value, period 4 | — |
a5 | Actual value, period 5 | — |
al | Smoothing constant α (0 to 1) | — |
F | Forecast for the next period (period 6) | — |
MD | Mean absolute error of the past forecasts | — |
BS | Average error (positive = forecasts too low) | — |
AG | Average age of the data used (periods) | — |
MA | Equivalent moving average length (periods) | — |
Worked example
- Actual value, period 1100
- Actual value, period 2110
- Actual value, period 3105
- Actual value, period 4120
- Actual value, period 5115
- Smoothing constant α (0 to 1)0.3
- Forecast for the next period (period 6)110.46
- Mean absolute error of the past forecasts8.72
- Average error (positive = forecasts too low)8.72
- Average age of the data used (periods)2.33
- Equivalent moving average length (periods)5.67
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.