True Range

How True Range Is Different from Other Indicators

The concept of True Range and calculation of ATR (Average True Range) is confusing for many people, as you are actually comparing three values instead of applying one exact formula. This article is a detailed guide to calculation of True Range. I’ve tried to attach a few simple chart examples to better illustrate the point.

How True Range Is Different from Range

The typical way how to measure Range is to subtract the bar’s low from the high. Classical Range is fast and easy, but it has one drawback: it only measures intraday volatility and fails to look at the volatility between individual bars (sometimes there are gaps, when market opens totally outside the previous day’s range on the next day). This is where True Range is much better.

True Range Formula

True Range is the maximum of three price ranges.

  • True Range = MAX of ( H – L ; H – C.1 ; C.1 – L )
  • H = high of current bar
  • L = low of current bar
  • C.1 = close of previous bar

Note that we always take absolute values of the differences.

1) Typical Situations when True Range = High less Low

Very often True Range equals the traditional Range. This is when the distance between high and low (the traditional Range) is greater than both

  • the distance of high (H) from previous bar’s close (C.1) and
  • the distance of Low (L) from previous bar’s close.

This happens when the close of the previous bar is within the current bar’s range. See the picture.

True Range

2) Typical Situations when True Range = High less Previous Close

The second type of situation is when the previous bar’s close (C.1) is lower than current bar’s low (L). When this happens, the distance between current bar’s high and previous bar’s close is greater than the distance between current bar’s high and low. Therefore True Range equals high less previous close. This is the case any time when the new bar opens above the previous bar’s close and the price doesn’t get below it during the whole bar duration.

Calculating ATR

Previous Bar’s High or Low Are Not Important

Note that the previous bar’s high (H.1) is not important at all for True Range. In the picture above you see two different situations when True Range equals high less previous close. It doesn’t matter whether the high of the first bar (H.1) is lower or higher than current bar’s low (L). In the situation on the picture, the high of the first bar could have been even higher than the second bar’s high, but True Range at the second bar would still be the same. Neither high nor low of the previous bar enter the True Range calculations in any way.

3) Typical Situations when True Range = Previous Close less Low

Finally, let’s look at the third possible situation. When previous bar’s close (C.1) is higher than current bar’s high (H), True Range equals previous bar’s close less current bar’s low (L). An example of such situation would be a “gap down” trading day. Again, the low of the first bar (L.1) is unimportant for the second bar’s True Range.

Calculating ATR

True Range in Another (Maybe Simpler) Way

There are only three numbers you need to know for determining True Range:

  1. Previous bar’s close (C.1)
  2. Current bar’s high (H)
  3. Current bar’s low (L)

True Range is simply the greatest distance you can find between any two of these three prices.

Calculating and Using Average True Range

Most frequently the concept of True Range is used in the smoothed form of Average True Range, which is an indicator calculated as exponential moving average of True Range. The period length used in this calculation is typically 14 or 20.

Average True Range was first described by J. Welles Wilder Jr. in late 1970’s. ATR is widely used to assess volatility conditions in the market. Typical applications of ATR include risk management, determining position size, or setting stop-loss order distance as a multiple of ATR.