Exponential Moving Average (EMA) and exponential smoothing formula

How recursive exponential smoothing works

Unlike a simple moving average that abruptly drops old observations outside a window, an Exponential Moving Average blends today's observation with yesterday's smoothed level: EMA_t = Alpha * Actual_t + (1 - Alpha) * EMA_{t-1}, where 0 < Alpha <= 1.

In finance and operations, a common N-period EMA convention sets Alpha = 2 / (N + 1) (for a 3-period span, Alpha = 2 / 4 = 0.50). Seed the very first row directly with the first actual observation (C2 = B2).

Alpha smoothing factor and recursive EMA formulas

Lock $E$2 on the smoothing constant Alpha so you can tune responsiveness across the entire series instantly.

=$E$2 * B5 + (1 - $E$2) * C4

Convert Span N into standard EMA Alpha

Span = 3 produces Alpha = 0.5; Span = 9 produces Alpha = 0.2.

=2 / (D2 + 1)

Inputs and interpretation

Use a span of at least 1 and ordered, evenly spaced numeric observations. This example seeds with the first observation; an initial average gives a different early series. Missing periods require an explicit policy. The span-to-alpha conversion is a convention, not an automatically optimized forecast. Simple EMA here does not model trend or seasonality like FORECAST.ETS.

Further reading

• Microsoft Support — FORECAST.ETS function overview