Trend & direction

Wilders Moving Average · RMA

J. Welles Wilder's own smoothing method — an EMA-like average with a gentler weighting that underpins RSI, ATR and ADX.

Works best in trending marketsEngine-computed on a fixed sample series
14512096Price above EMA 12 = strengthPrice below EMA 12 = weaknessEMA 12 acts as support / resistance
EMA 12EMA 26How to read RMA on the chart — the callouts mark what to look for.

The formula

Each bar moves the previous average toward the new price by just 1/N of the gap — gentler than the EMA's 2/(N+1). That extra smoothing makes a Wilder average of length N behave almost like an EMA of length 2N−1, so a Wilder 14 is roughly as smooth as a 27-period EMA.

RMAₜ = RMAₜ₋₁ + ( Priceₜ − RMAₜ₋₁ ) ÷ N
Worked example
InputValue
Previous RMA50.00
New price57.00
Length N14
Step = (57 − 50) ÷ 140.50

New RMA = 50.00 + 0.50 = 50.50 — half the 0.93 an EMA-14 would move

What it is

Wilder's Moving Average is the personal smoothing method invented by J. Welles Wilder, the engineer-turned-trader who created the Relative Strength Index, the Average True Range, and the Directional Movement system. It is an exponential-style average, meaning it weights recent data more heavily and keeps a memory of all prior data, but it fades that memory far more gently than a standard exponential moving average. It goes by several names, including the Wilder's smoothing, the smoothed moving average, and the running moving average, and is abbreviated RMA or SMMA. Its real importance is that it is the hidden engine inside Wilder's famous indicators, so understanding it explains why those tools feel calmer than their stated periods suggest. For a beginner, it is simply a slow-and-steady moving average designed to filter noise more aggressively than an ordinary exponential average of the same length.

How it is calculated

Wilder's smoothing takes the previous average, multiplies it by the length minus one, adds the newest value, and divides the whole sum by the length. That is equivalent to applying a smoothing factor of one divided by N to the newest value, in contrast to the standard exponential moving average, which uses a heavier factor of two divided by N plus one. Because Wilder's factor is smaller, each new bar nudges the average less, so the line moves more slowly and smooths more. The first value is usually seeded with a simple average of the first N bars to get the recursion started. A crucial equivalence follows from the math: a Wilder average of length N behaves almost exactly like a standard exponential moving average of length two N minus one, so a Wilder fourteen tracks roughly like a twenty-seven-period exponential average. This is precisely why Wilder's indicators, all built on fourteen-period smoothing, feel smoother than a casual glance at the number fourteen would imply.

Reading it, step by step

You read a Wilder average like any moving average, watching its slope for direction and price's position relative to the line for bias, but you must calibrate your expectations to its extra smoothness. Because it reacts more slowly than a like-numbered exponential average, its turns come later, so a change of slope is a more deliberate, higher-conviction signal when it finally arrives. Price crossing above or below the line marks trend shifts, and the line often serves as dynamic support or resistance that trends respect. The single most important thing to internalize is that a Wilder fourteen is not comparable to an exponential fourteen; it is comparable to an exponential twenty-seven, so do not expect them to line up. When you see it embedded inside the Relative Strength Index or the Average True Range, the same gentle smoothing is what keeps those readings from jumping around on every bar.

Reading the signals on the chart

14512096
EMA 12EMA 26The ▲/▼ marks flag where price most recently crossed the line — the cues a trend-follower would act on.

Best timeframes

  • Scalping1m – 5m
  • Day trading5m – 1h
  • Swing4h – daily
  • Positiondaily – weekly

Remember a Wilder N smooths like an EMA of about 2N−1 — match lengths to other averages on the chart accordingly.

Wilder smoothing vs other averages

Wilder (RMA)EMASMA
New-bar weight1 ÷ N2 ÷ (N+1)Equal
Smoothness at length NHighestLowestMedium
Equivalent EMA≈ 2N−1N
Used insideRSI, ATR, ADXMACDBollinger

Common price-action setups

How the signal typically plays out on the chart.

Reclaim of the RMA

Price closes back above a rising RMA after a dip; enter long on the cross with a stop below the average, using its calm slope to stay with the trend.

Buy above RMA
Uptrend resumes
Dynamic-support bounce

In an uptrend the rising RMA acts as a smooth dynamic support; buy dips that hold it with a stop just below, and stay long while price closes above it.

Buy the hold
Trend continuation
Loss of the RMA

Price closing decisively below the RMA after an uptrend warns the trend is turning; exit longs or short with a stop above the average.

Sell below RMA
Trend turns down

Best timeframes and settings

Wilder built his work around a length of fourteen, and that remains the canonical setting, carried through the Relative Strength Index, the Average True Range, and the Average Directional Index. The average works on any timeframe, but because of its heavy smoothing it is most at home on daily and swing horizons where its deliberate pace matches the holding period. Shortening the length speeds it up but only modestly, given the gentle weighting, while lengthening it produces an extremely slow, structural trend line. When matching a Wilder average to other averages on a chart, remember the two-N-minus-one rule, so if you want it to align roughly with a fifty-period exponential average you would use a Wilder length near twenty-five or twenty-six. The trade-off is the same as for any average, responsiveness against smoothness, but Wilder's method is deliberately parked toward the smooth, slow end of that spectrum by design.

When and where to use it

Use a Wilder average when you want a calmer, less twitchy trend line than a same-length exponential average would give, for instance as dynamic support in a trending market or as a slow crossover reference. It is the correct choice whenever you are trying to replicate or understand Wilder's own indicators, since using a plain exponential average in their place would change their behavior. It works across all liquid asset classes and is especially suited to traders who dislike the jumpiness of faster averages. It is less useful for fast intraday scalping, where its lag would be a liability, and it is not the tool for catching sharp, sudden reversals early. In a choppy range it whipsaws less than a faster average precisely because it is so smooth, but it still should not be traded mechanically as a crossover system without a trend filter.

Strategies that use it

The most authentic use is not to trade the average directly but to trade the Wilder-smoothed indicators it powers, such as taking Relative Strength Index signals or reading trend strength from the Average Directional Index, both of which owe their steadiness to this smoothing. As a standalone line, a common strategy is the dynamic support-and-resistance pullback: in an uptrend, buy dips to a rising Wilder average and hold with a stop below it, mirroring for downtrends. A second strategy is a slow crossover system, pairing a Wilder average against a faster average of price and acting when price or the faster line crosses the Wilder line, which produces fewer but cleaner signals than an all-exponential pair. A third is simply using the Wilder average as a regime filter, trading long setups only while price holds above it and shorts only while below, letting its smoothness keep you from flip-flopping on every minor wobble.

Combining it with other indicators

Because it is the backbone of the Relative Strength Index, the Average True Range, and the Directional Movement system, a Wilder average combines seamlessly with those tools, and traders often run a Wilder price average alongside them for a consistent, calm reading across the chart. It pairs with a faster average, such as an exponential or weighted line, to build a slow-and-fast crossover where the Wilder line supplies the stable trend and the faster line supplies the trigger. Momentum oscillators confirm that a price cross of the Wilder average has force behind it. The Average True Range, itself Wilder-smoothed, is a natural companion for setting stops a volatility-scaled distance from the average. Avoid pairing a Wilder N against an exponential N and expecting them to agree, because the two-N-minus-one equivalence means they are effectively different lengths and will diverge, a mismatch that confuses many newcomers.

Where it fails

The most common failure is not a market failure at all but a misunderstanding: traders compare a Wilder fourteen to an exponential fourteen, see them behave differently, and wrongly conclude one is broken, when they simply use different weightings and effective lengths. The genuine weakness is lag, because the gentle smoothing means the average turns noticeably later than faster lines at real reversals, so it is a poor early-warning tool. In fast markets that pace can leave you well behind a sharp move. Like any average it still whipsaws in a range, just less often than a quicker line. The defenses are to internalize the two-N-minus-one relationship so you match lengths correctly, to accept its lag as the price of its smoothness rather than fighting it, and to filter its crossover signals with momentum or trend-strength tools rather than trading them blindly.

A worked example

Suppose a fourteen-period Wilder average currently reads 50.00 and the newest close comes in at 53.00. The update multiplies the prior average by thirteen, giving 650, adds the new close to get 703, and divides by fourteen for a new average of about 50.21. Now compare a standard fourteen-period exponential moving average, which uses a smoothing factor of two divided by fifteen, about 0.133: it would move to 50.00 plus 0.133 times the three-point gap, landing near 50.40. The Wilder average advanced only about 0.21 while the exponential average advanced about 0.40, roughly twice as far, which shows in one bar how much more gently Wilder's method responds. Extend that behavior over many bars and the Wilder fourteen ends up tracking like an exponential twenty-seven, exactly the smoothing that gives the Relative Strength Index and the Average True Range their characteristic steadiness.

Common mistakes

  • Comparing a Wilder average to a same-number EMA and concluding it is broken — they just weight differently.
  • Forgetting a Wilder 14 lags like a ~27-period EMA, so its signals arrive later.
  • Expecting fast crossover signals from what is deliberately a heavily smoothed line.
  • Using it in a choppy range and collecting late, whipsawed crosses.
  • Setting the length as if it were an EMA, mismatching it against other averages.
  • Trading the line in isolation without the trend or structure behind it.