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Indicator Formula

Technical Details — Average True Range (ATR)

Section titled “Technical Details — Average True Range (ATR)”

Overview

Section titled “Overview”

ATR smooths the True Range to measure average volatility.

Key Concepts:

  • True Range: The largest of three range measurements (accounts for gaps)
  • RMA Smoothing: Smooths TR to reduce noise
  • Normalization: Expressed as % of price for comparability
Mathematical Derivation

Step 1 — Calculate True Range

Section titled “Step 1 — Calculate True Range”

Purpose: Measure the full range including any gaps.

$$TR[t] = \max(High[t] - Low[t], |High[t] - Close[t-1]|, |Low[t] - Close[t-1]|)$$

Where:

  • The three components capture intrabar range and any gap from previous close

What This Measures: The maximum possible price movement in a single bar

Step 2 — Smooth with RMA

Section titled “Step 2 — Smooth with RMA”

Purpose: Average the true range over n periods.

$$ATR[t] = \frac{ATR[t-1] \times (n-1) + TR[t]}{n}$$

Where:

  • $$n$$ = Smoothing period

What This Measures: Smoothed average volatility

Step 3 — Normalize to Percentage

Section titled “Step 3 — Normalize to Percentage”

Purpose: Express as % of price.

$$ATR%[t] = \frac{ATR[t]}{Close[t]} \times 100$$

What This Measures: Volatility as a percentage of price

Compact Formula Summary

$$TR = \max(H-L, |H-C_{prev}|, |L-C_{prev}|)$$ $$ATR = RMA(TR, n)$$ $$ATR% = ATR / Close \times 100$$

Default: Period = 14

Complete Calculation Example

High=46, Low=44.50, PrevClose=44.00: TR = max(1.50, |46-44|, |44.50-44|) = max(1.50, 2.00, 0.50) = 2.00

The gap from previous close (44→46) created a larger true range than the intrabar range.

Key Takeaways from the Example
  1. True Range ≥ High-Low: TR always captures the full move including gaps
  2. RMA Smoothing: ATR changes gradually, reflecting sustained volatility changes
  3. Relative Measure: ATR% allows comparing volatility across different-priced assets