What it measures
A bar’s range is its high minus its low. That misses something when a market opens away from where it last closed: the jump happened, but it is not inside the bar. The true range repairs this by measuring from the previous close whenever that gives a larger figure.
ATR is the average of the true range over a number of bars, usually 14. It was set out by J. Welles Wilder Jr. in 1978, in the same book as RSI, and uses the same smoothing.
The result is a distance in the unit of the price: ‘this market has lately been covering about 1.20 a bar’. It rises when bars get longer or gaps appear and falls when the market goes quiet. A long run upward and a long run downward can have exactly the same ATR.
How it is calculated, step by step
- 01
For each bar, work out three distances.
High − low. The high to the previous close, as a positive number. The low to the previous close, as a positive number.
- 02
The true range is the largest of the three.
TR = max(high − low, |high − previous close|, |low − previous close|). The very first bar has no previous close, so its true range is high − low.
- 03
Start the average.
First ATR = the sum of the first N true ranges ÷ N. N is usually 14.
- 04
Smooth it from then on (Wilder’s smoothing).
ATR = (previous ATR × (N − 1) + this bar’s true range) ÷ N.
Some programs average the last N true ranges plainly instead of using Wilder’s smoothing; the Rule bench on this site does that, to keep its test simple. The two methods give slightly different numbers that move in the same way.
A worked example, by hand
Five bars, written high / low / close: 10 / 8 / 9, then 11 / 9 / 10, then 13 / 10 / 12, then 12 / 11 / 11, then 15 / 14 / 14. Length 3.
- Bar 1: no previous close, so TR = 10 − 8 = 2
- Bar 2 (previous close 9): max(11 − 9, |11 − 9|, |9 − 9|) = max(2, 2, 0) = 2
- Bar 3 (previous close 10): max(13 − 10, |13 − 10|, |10 − 10|) = 3
- First ATR = (2 + 2 + 3) ÷ 3 = 2.33
- Bar 4 (previous close 12): max(12 − 11, |12 − 12|, |11 − 12|) = 1, so ATR = (2.33 × 2 + 1) ÷ 3 = 1.89
- Bar 5 (previous close 11): max(15 − 14, |15 − 11|, |14 − 11|) = 4, so ATR = (1.89 × 2 + 4) ÷ 3 = 2.59
Bar 5 is only 1 from high to low, but it opened far above the last close. Its true range is 4, and that gap is what lifted the average.
The numbers in this example were chosen to be easy to add up. They are not prices of anything.
How people read it
- As a yardstick of recent movement. A stop or a target can be described as a number of ATRs away, which scales it to how much the market has been moving instead of a fixed number of points.
- As a way to compare. ATR divided by the price gives a percentage that can be set beside another instrument’s.
- Rising or falling. A rising ATR means bars are getting longer or gaps are appearing; a falling one means the market is settling.
- In position sizing. A wider stop on the same risk means a smaller position, so a larger ATR leads, by arithmetic, to a smaller size.
What it cannot tell you
- It cannot tell you direction. It is built from distances, and every distance is positive.
- It cannot tell you how far the next bar will go. It is the average of past bars; a single bar can be several times larger, especially around scheduled news.
- It cannot make a stop safe. A stop two ATRs away is hit by an ordinary bar less often than one that is half an ATR away. It is still an instruction, not a promised price, and a gap can pass straight through it.
- It cannot be compared in raw form between instruments with different prices.
Common mistakes
- Reading a rising ATR as bullish. Markets often move fastest when they fall.
- Using yesterday’s quiet ATR to judge today’s risk before a scheduled announcement.
- Comparing the ATR of two instruments without dividing each by its price.
- Mixing time frames: a 14-bar ATR on an hourly chart and one on a daily chart are different quantities.
Questions people ask
- What is a good ATR value?
- There is no good or bad value. ATR is a distance in the unit of the price, so it depends on the instrument, its price and the time frame of the chart. It is useful only in comparison: with the same instrument’s own past, or, as a percentage of price, with another instrument.
- Why use the true range instead of high minus low?
- Because a market can jump between one bar’s close and the next bar’s open. High minus low measures only what happened inside the bar and would miss that jump. The true range measures from the previous close whenever that distance is larger, so a gap counts as movement.
- Does a high ATR mean the price will keep moving?
- No. A high ATR says that recent bars have been large. Lively periods and quiet periods both tend to last for a while, but ATR does not say when one will give way to the other, and it says nothing at all about direction.
The words on this page
An indicator is arithmetic on prices that have already happened. It describes what a price did; it does not predict what a price will do. The chart on this page is invented: a seeded random walk, not a market. This page is an explanation for study. It is not advice, a recommendation or a forecast, and nothing an indicator shows says anything certain about what a price will do next.