Average True Range — Technical Indicators

17 — Volatility

Average True Range#

Statistical1 min read

◆ The PatternVolatility as the typical size of a bar, gaps included, the yardstick for stops and position size

The Average True Range — Wilder's volatility measure (1978). Purely measures volatility, NOT direction.

True Range = max(H−L, |H−Prev Close|, |L−Prev Close|)
ATR = Smoothed average of TR over N periods (default 14)

Practical uses:
• Position sizing: Risk 1–2 ATR per trade → adapts to current volatility
• Stop loss: Place stops 1.5–2× ATR from entry
• Volatility filter: High ATR = trending market; low ATR = ranging

Worked example

True range looks at yesterday’s close as well as today’s high and low, so gaps count. Day 13: high 102, low 98, previous close 102, so TR = max(4, 0, 4) = 4. Five-day ATR with Wilder’s smoothing is 3.41 on day 15: the typical bar is about 3.4 points, 3.3% of the price.

The example data: 15 days, used in every indicator here

Day	High	Low	Close	Volume
1	101	99	100	50,000
2	103	100	102	62,000
3	103	100	101	48,000
4	105	101	104	70,000
5	108	104	107	85,000
6	108	105	106	60,000
7	110	106	109	90,000
8	110	107	108	72,000
9	108	104	105	80,000
10	105	102	103	66,000
11	105	102	104	55,000
12	104	101	102	75,000
13	102	98	99	95,000
14	102	99	101	64,000
15	105	101	104	71,000

Where it misleads

It measures size, not direction; a high ATR comes with rallies and crashes alike.
It is in price units. Compare it as a percentage of price across assets or long periods.
Wilder’s smoothing is slow: after a shock ATR takes several bars to reflect the new volatility, and as long to forget it.

In code

pc = df['close'].shift()
tr = pd.concat([df['high'] - df['low'], (df['high'] - pc).abs(), (df['low'] - pc).abs()], axis=1).max(axis=1)
df['atr5'] = tr.ewm(alpha=1/5, adjust=False).mean()   # Wilder smoothing

Python, in your browser — edit the code and run it again

Assumes import numpy as np, import pandas as pd, and a DataFrame df with columns high, low, close and volume — the 15 days above.

Sources

New Concepts in Technical Trading Systems, J. W. Wilder, Trend Research, 1978
C. Faith, Way of the Turtle, McGraw-Hill, 2007 — ATR (“N”) for stops and position size

Last reviewed October 2026 · How this site checks its content · Report a mistake

Check yourself

1. What does the Average True Range measure?

Show answer

B. Wilder designed it for commodities, where limit moves and gaps made the simple high–low range misleading.

2. How does the true range differ from the high minus the low?

Show answer

C. True range is the largest of: high − low, |high − previous close|, |low − previous close|.

3. Why set a stop at, say, 2 × ATR from entry?

Show answer

B. A fixed stop is too tight in volatile markets and too loose in calm ones. No stop guarantees the fill price.

Pattern bridge: Average True Range measures volatility as mean absolute deviation — a close cousin of standard deviation. In ML, gradient clipping uses a similar magnitude threshold.

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