SMA vs EMA: the formula difference

Two averages, two different stories

A moving average smooths a chart. Instead of staring at every tick, you look at an average of the last few closes and follow that line. There are two main versions: the simple moving average (SMA) and the exponential moving average (EMA). They look similar on a chart, but the math underneath is very different — and that difference changes how you should use them.

The SMA is the easy one. Add up the last N closing prices, divide by N. That's it. A 20-period SMA on a daily chart is the sum of the last 20 daily closes divided by 20. Every candle in that window counts the same — the close from 20 days ago has the same weight as yesterday's close.

The EMA is recursive. Today's EMA = (today's close × multiplier) + (yesterday's EMA × (1 − multiplier)). The multiplier is 2 / (N + 1). For a 20-period EMA, the multiplier is 2 / 21, which is about 0.0952. So today's close gets about 9.5% of the weight, and the rest of the line carries memory of every prior close — but that memory fades fast. Closes from a few weeks ago barely move the line.

Practical consequence: the EMA reacts faster. When price reverses, the EMA bends sooner than the SMA. That sounds purely good, but the flip side is that the EMA also reacts to noise — small wiggles that an SMA would have smoothed away can pull the EMA around. Neither version is 'better.' They're tools for different jobs.

Recap: SMA is a plain average — every candle weighted equally. EMA weights recent candles more, using a multiplier of 2/(N+1). Same period setting, different lines, different speeds.