Average True Range (ATR) Calculator

This page builds an ATR from scratch. You give it raw price bars and it returns a plain average of their true ranges, which is what you need on day one when there is no previous figure to roll forward. Once you have that first number, the ATR update calculator carries it forward one bar at a time using Wilder’s smoothing, which is the version a charting package shows.

Average True Range was developed by J. Welles Wilder Jr. and published in his 1978 book “New Concepts in Technical Trading Systems.” It remains one of the most used volatility indicators in technical analysis, not because it predicts direction, but because it tells you how much a security typically moves.

Each period’s True Range is the largest of three values:

TR = max(High - Low, |High - Prev Close|, |Low - Prev Close|)

The last two handle gaps. If a stock closes at $50 and opens the next day at $55 on news, the high-to-low range alone understates the real move. True Range captures the full distance from the previous close to wherever price went.

ATR = Average of True Range over N periods

Wilder used 14 periods as his default. This calculator uses 3, which is a quick read on current conditions and suits day traders and short-term swing traders. A charting package shows the 14-period smoothed version instead, and the update calculator linked above will produce that one from whatever seed you feed it.

Setting the stop. ATR sets stop-losses that adapt to what the market is actually doing. A stock moving $3 a day needs a far wider stop than one moving $0.40, and a stop placed inside the normal daily range is a stop that gets hit by noise before the trade has any chance to work. The usual rule is 1.5x to 2x ATR below entry on a long.

Sizing the position. Once the stop is set, the share count follows from it, and this is the part most people do backwards. Your risk per share is the distance from entry to stop, not the ATR itself. With a $5 ATR and a 2x stop you are risking $10 a share, so a $1,000 risk budget buys 100 shares. Pick the 1.5x stop instead and the risk per share drops to $7.50, which allows 133 shares. The wider your stop, the smaller your position: that relationship is the whole point, and it is why a fixed share count across trades of different volatility quietly makes your risk random.

One number to compare across securities. A $5 ATR means nothing until you know the price. On a $500 stock that is a 1% daily range, which is unremarkable. On a $20 stock it is 25%, which is a different animal entirely. The calculator reports ATR as a percentage of the closing price for exactly this reason.

Wilder’s original smoothing uses a running average rather than a simple one: ATR(today) = (ATR(yesterday) x 13 + TR(today)) / 14. Over three periods the difference is small. Over 14 it matters, because the smoothed version keeps a memory of older volatility that a simple average drops the moment a bar rolls out of the window.