The difference starts with one completed day
Let H and L be the daily high and low, and Cprev the previous daily close. Daily range is H − L. True range is max(H − L, abs(H − Cprev), abs(L − Cprev)). Equivalently, it is max(H, Cprev) − min(L, Cprev). The open helps describe the gap, but it is not an additional term in either formula.
- All prices are hypothetical dollars. The second row has a $5 opening gap, but the excess of true range over daily range is $4. Adding the opening gap to H − L would double count the portion already inside the day's range.
- True range is at least daily range for valid OHLC data. It is strictly larger only when the previous close is outside [L, H]. ADR does not add a separate overnight component, although trading after a gap can widen the daily high-low range.
| Hypothetical daily OHLC | H − L | |H − Cprev| | |L − Cprev| | True range |
|---|---|---|---|---|
| Cprev 101; O 101, H 103, L 100, C 102 | 3 | 2 | 1 | 3 |
| Cprev 101; O 106, H 108, L 105, C 107 | 3 | 7 | 4 | 7 |
| Cprev 101; O 96, H 97, L 94, C 95 | 3 | 4 | 7 | 7 |
| Cprev 100; O 103, H 105, L 99, C 104 | 6 | 5 | 1 | 6 |