Average True Range (ATR): Formula, Stops and ATR Percent

J. Welles Wilder published average true range in 1978, in his book New Concepts in Technical Trading Systems, and he built it for commodity traders whose markets jumped from one session’s close to the next session’s open. Stocks gap too, so the measure carried straight over to equity charts.

True range counts the gap

A bar’s plain range is its high minus its low. That misses gaps. If a stock closes at $48 and opens the next morning at $50, the $2 jump happened overnight and never shows inside the second bar. True range takes the largest of three distances:

• High minus low.
• The distance from the high to the previous close.
• The distance from the low to the previous close.

Both distances are absolute values, so the sign drops out. A gap down counts the same as a gap up.

The bar itself was $1.50 tall. The gap doubled it.

The ATR formula and Wilder’s smoothing

ATR averages true range, usually over 14 bars. The first value is a simple average of the first 14 true ranges. After that, each new ATR keeps thirteen parts of the old one and adds one part of today’s true range: ATR = (prior ATR x 13 + today’s true range) / 14.

One wide day barely moves it.

A plain 14-day simple average of true range behaves differently: it gives the wide day full weight for exactly 14 bars and then drops it all at once, so the line jumps when the shock arrives and jumps again two weeks later when the shock falls out of the window, a second move that has nothing to do with what the stock is doing that day. Wilder’s version never drops anything. Each old bar fades by 13/14 a day.

That weight of 1/14 also explains the lag. An exponential average gives the newest bar a weight of 2 / (N + 1), and solving for N shows which exponential line ATR matches.

So “ATR (14)” reacts about as slowly as a 27-bar exponential line. Expect it to trail a fresh burst of volatility for several bars. Some charts let you switch the smoothing to a simple or exponential average, and the readings will differ a little from Wilder’s; pick one and keep it, because a stop rule tested on one version lands in a slightly different place on another.

Reading ATR on a chart

ATR sits in its own panel under price. It is a single line labeled something like “ATR (14)”, with the current value in dollars at the right edge. There is no zero-to-100 scale and no overbought line. A rising line means the bars are getting wider. A falling line means they are getting narrower.

Long stretches of low ATR tend to show up in tight consolidations, the coiled range before a breakout, while a sharp spike usually arrives with a panic or a news gap, earnings included. Spikes rarely last. Bars that wide tend to shrink back, and the slow smoothing keeps ATR reading high for a while after the chart has calmed.

ATR percent: comparing stocks at different prices

Raw ATR is in dollars. That makes it useless for comparing a $20 stock with a $400 one. Divide ATR by the closing price and multiply by 100, and the result is ATR percent: the typical one-bar move as a share of the price.

Stock A is the one that shakes you out. Its typical bar covers 5% of the price, two and a half times Stock B’s, even though its dollar figure is half as large.

Percent also fixes a slower problem. A stock that doubles over a year will usually see its dollar ATR roughly double with it, with no change in how jumpy the stock really is, so a stop rule written in dollars quietly loosens as the price climbs and a screen sorted by dollar ATR keeps promoting whatever has the highest share price. Percent stays comparable across years and across tickers.

Use it on funds as well. A -3x fund from the inverse ETF list is built to move about three times its index’s daily percentage, so its ATR percent runs far above the index’s. A stop copied from the index chart sits much too close. Sort a watchlist by ATR percent and match each name to the stop you are willing to hold.

Stops measured in ATRs

Put the stop a fixed number of ATRs from entry. Two is a common middle choice. One gets clipped by ordinary noise; three gives the trade plenty of room and shrinks the position. Either way the stop fits the stock: tight on a quiet name, wide on a wild one.

For a trailing stop, measure down from the highest close since entry. If that close is $60 and ATR is $2, a 3-ATR trail sits at $54. Let it ratchet up only. Never lower it when ATR widens.

Option sellers can use the same yardstick. Before writing a covered call, check how many ATRs separate the share price from the strike. A strike less than one ATR above the price can be reached in a single ordinary session.

Position size from the ATR stop

Once the stop is set, it decides the share count. Pick the dollar loss you accept if the stop is hit. Divide it by the stop distance.

Double the ATR and you buy half the shares for the same dollar risk. The position size calculator runs this for any account and stop distance.

Across a portfolio, the same rule gives every holding an equal dollar risk, which means the jumpy names end up as small positions and the quiet ones as large positions, and that shifts the answer to how many stocks you should own, because equal dollar amounts in stocks of very different ATR percent can leave one volatile holding driving most of the account’s daily swings.

Choosing the period

Fourteen is Wilder’s default. Most charts load it. A shorter setting, somewhere from 5 to 10 bars, tracks the latest bursts and jumps around. A longer one, 20 to 50 bars, describes the stock’s normal stride and barely reacts to a single rough week.

Match the bar to the hold. An intraday trade needs ATR from intraday bars, since a daily ATR includes overnight gaps that a position closed by the bell never faces.

Where ATR falls short

It lags. With smoothing equal to a 27-bar exponential line, a stock can change character after earnings or a buyout rumor, and ATR needs weeks to catch up. If the last few true ranges are double the ATR, trust the true ranges and widen the stop or cut the size.

It cannot forecast. All it holds is the past few weeks of bars.

Thin stocks fool it. A name that trades few shares can post wide true ranges from a handful of sloppy prints, and a single halt or news gap can swamp a short-period ATR for days.

A frequent error is reading it as a signal. A rising line gets taken as bullish. It only says the bars are wider.

Related terms

Bollinger Bands also measure volatility, from the standard deviation of closes, so a bar’s high and low never enter the sum. ATR appears among the swing trading indicators worth keeping for the jobs above: stop distance and position size.