Exponential Smoothing Calculator Formula

Understand the math behind the exponential smoothing calculator. Each variable explained with a worked example.

Use the Exponential Smoothing Calculator

Formulas Used

Next Forecast

forecast = alpha * actual + (1 - alpha) * forecast_prev

Forecast Error

error = actual - forecast_prev

Adjustment (alpha * error)

adjustment = alpha * (actual - forecast_prev)

Variables

VariableDescriptionDefault
actualLatest Actual Value120
forecast_prevPrevious Forecast110
alphaSmoothing 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.

actual = 120forecast_prev = 110alpha = 0.3
  1. 01Error = 120 - 110 = 10
  2. 02Adjustment = 0.3 * 10 = 3
  3. 03New forecast = 110 + 3 = 113
  4. 04Or equivalently: 0.3 * 120 + 0.7 * 110 = 36 + 77 = 113

Ready to run the numbers?

Open Exponential Smoothing Calculator