Density Altitude Formula and ISA Standard Atmosphere
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Full bio →The ISA Standard Atmosphere
The International Standard Atmosphere (ISA) defines standard conditions used as the reference for all aviation performance calculations:
| Parameter | Sea Level Value | Lapse Rate |
|---|---|---|
| Temperature | 15°C (59°F) | −2°C per 1,000 ft (up to 36,089 ft) |
| Pressure | 29.92 inHg / 1013.25 hPa | Decreases with altitude |
| Density | 1.225 kg/m³ | Decreases with altitude |
Step 1 — Pressure Altitude
Pressure altitude is the altitude corresponding to a given atmospheric pressure, referenced to the standard sea-level pressure of 29.92 inHg:
PA (ft) = Field Elevation + (29.92 − QNH) × 1,000Where QNH is the altimeter setting in inHg. Each 0.1 inHg deviation from standard corresponds to approximately 100 ft of altitude change.
Precise formula using the barometric formula:
PA = 145,366 × [1 − (QNH / 29.921)^0.190284]The simplified linear formula (PA = field elev + (29.92 - QNH) × 1000) is accurate within ±50 ft for typical altimeter settings (28.50–31.00 inHg).
Step 2 — ISA Temperature at Pressure Altitude
ISA Temp (°C) = 15 − (2 × PA / 1,000)This applies from sea level to 36,089 ft (tropopause), where temperature stabilizes at −56.5°C.
Step 3 — Density Altitude
DA = PA + 120 × (OAT − ISA_Temp)The factor 120 ft/°C is the standard aviation approximation (some sources use 118.8 or 100). For each degree Celsius the OAT exceeds ISA temperature, density altitude increases by 120 feet.
Humidity Effect
The FAA standard formula uses dry air only. In reality, water vapor reduces air density because H₂O molecules (molecular weight 18) displace heavier N₂ (28) and O₂ (32) molecules.
For the virtual temperature correction:
Tv = T × (1 + 0.609 × e/P)Where e = actual vapor pressure, P = station pressure.
Practical rule: When dew point spread (OAT − dewpoint) is less than 5°C, add 200–400 ft to the calculated density altitude for planning purposes.
Summary Table
| Condition | Effect on DA |
|---|---|
| Temperature +1°C above ISA | +120 ft DA |
| Altimeter −0.1 inHg | +100 ft PA and DA |
| Elevation +1,000 ft | +1,000 ft DA (base) |
| High humidity (spread under 5°C) | +200–400 ft DA |
For reference data on density altitude at specific high-elevation US airports, see the High-Elevation Airport DA Reference. For how these numbers translate to engine power output, see Engine Performance at Density Altitude.