SMA and EMA moving averages: formulas and differences

A moving average is the average price over the last n periods, shifted forward with each new candle. SMA (simple moving average) = (P1 + P2 + … + Pn) / n. EMA (exponential moving average) gives more weight to recent prices: EMA today = α × price today + (1 − α) × EMA yesterday, where α = 2 / (n + 1).

Moving averages smooth out noise and help gauge the direction of a trend, but they always lag. The EMA reacts faster but gives false signals more often. Popular periods, such as 50 and 200, are a convention, and crossovers of averages (the so-called golden cross and death cross) appear with a delay. In consolidation, the averages get crossed with no meaning. They do not work on their own, only together with an assessment of context.