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Trading Math
How to Calculate Average True Range by Hand
Average true range is the average of fourteen days' true ranges, and a day's true range is the largest of three distances. This paper shows you the three distances, measures them on a real pair of days, works the fourteen-day average on real days, and shows where the platform draws the same sum as a line below the chart.
A day's true range is the largest of three distances: today's high to today's low, today's high to yesterday's close, and today's low to yesterday's close. On a day that opens where yesterday closed, the first is the largest and the true range is simply the day's range. On a day that opens with a gap — above yesterday's close or below it — one of the other two is larger, because the jump from yesterday's close counts as movement even though no bar shows it. The word true is there for the gap.
The three, measured
Here are the three on a real pair of days. Friday 28 August 2026 closed at 1.15820. On Monday 31 August the euro against the dollar ran from a low of 1.15786 to a high of 1.16207 — a pip is the fourth decimal place, so 42.1 pips from high to low. From the high down to Friday's close is 38.7; from Friday's close down to the low is 3.4. The largest is 42.1, the plain range, because Friday's close sat inside Monday's bar. Had Monday opened at, say, 1.16000, the second distance would have been 38.7 and the third 21.4, and the first would still have won; the second or third wins only when the previous close sits outside the bar altogether.
