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Updated 3 min readTapeboard DeskEdited by Marcus Reilly

What is a Moving Average? Definition, Formula, and Example

A moving average smooths price data by averaging closes over a rolling window of N bars, producing a lagging trend line that filters noise and defines the prevailing direction.

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What is a moving average?

A moving average (MA) is a statistical line plotted on a price chart that averages the last N bars' closes (or another chosen input) and re-computes every bar. As the window slides forward in time, the oldest bar drops off and the newest bar enters, producing a smooth curve that follows — but lags — the raw price. It is the single most-used indicator in technical analysis because it answers one question precisely: over the last N sessions, is the prevailing price above or below where it has been on average?

How a moving average is calculated

The two canonical forms:

Simple Moving Average (SMA):

SMA(N) = (P₁ + P₂ + … + Pₙ) / N

Every bar contributes equally.

Exponential Moving Average (EMA):

EMA_t = α × P_t + (1 − α) × EMA_{t−1}

where α = 2 / (N + 1)

Recent bars carry exponentially more weight. A 20-period EMA has α ≈ 0.0952, so today's close contributes 9.5% of the new value and the remaining 90.5% comes from yesterday's EMA.

Other variants: Weighted (WMA) uses linearly decaying weights; Volume-Weighted (VWMA) weights each close by its bar's share volume; Hull (HMA) is a reduced-lag construction popular among short-term traders.

Worked example

On 2026-04-17, SPY closed at $547.12. The 50 prior daily closes summed to $26,750, so the 50-day SMA = $535.00. Price sits 2.26% above its 50-day — a measurable bullish tilt. The 200-day SMA on the same date was $518.40; price is 5.5% above it, and the 50-day itself is 3.2% above the 200-day — both filters align long.

An EMA(20) on the same series reacts faster than its SMA counterpart. A single gap-up day of +1.5% shifts the 20-SMA by 0.075% but the 20-EMA by 0.143%, roughly twice as sensitive — the trade-off traders accept when they want earlier turns at the cost of more whipsaws.

When traders use moving averages

  • Trend definition: price above a rising 200-day = structural uptrend (Stan Weinstein, Mark Minervini frameworks). The 50-day crossing above the 200-day is a golden cross.
  • Dynamic support/resistance: crowd-watched MAs (20, 50, 200 day) become self-fulfilling pivots where dip-buyers cluster.
  • Crossover systems: price/MA or fast/slow MA crosses trigger entries — the backbone of trend-following CTAs.
  • Regime filters: mechanical systems often require SPY above its 200-day before taking any long signal, cutting drawdown in bear markets substantially.

Every Tapeboard chart ships SMA and EMA overlays with adjustable periods (add them from the indicators menu), and the anatomy of a price chart guide walks through reading price, averages, and volume together.

Limitations and common misconceptions

Moving averages lag by construction. A 50-day SMA lags price by roughly N/2 bars — about 25 sessions — so in a sharp reversal the MA confirms the new trend only after much of the move has passed. In ranging or choppy markets, MA systems whipsaw: every breakout reverses, the system buys high and sells low. The "right" period (50? 89? 200?) is usually curve-fit to the backtest window and degrades out of sample. Finally, an MA is only a function of closes — it ignores intrabar volatility, volume, and gaps. Traders treating a 200-day touch as a hard bounce line rather than a probability tilt are confusing a descriptive statistic with a support level.