Density Altitude Formula
Calculate density altitude from pressure altitude and outside air temperature.
Critical for aircraft performance planning at high elevations or in hot weather.
The Formula
ISA Temperature = 15 − (Pressure Altitude ÷ 1,000 × 2)
Density Altitude = Pressure Altitude + 120 × (OAT − ISA Temperature)
Density altitude is the altitude in the International Standard Atmosphere (ISA) that corresponds to the actual air density at your location. It is the altitude at which the aircraft "thinks" it is flying from a performance perspective. High density altitude means thin air — the aircraft requires longer takeoff and landing rolls, climbs more slowly, and engines produce less power.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| Field Elevation | Aerodrome elevation above sea level | feet |
| Altimeter Setting | Current QNH (local altimeter setting) | inHg |
| Pressure Altitude | Altitude assuming standard pressure (29.92 inHg) | feet |
| OAT | Outside Air Temperature at the surface | °C |
| ISA Temperature | Standard temperature at that pressure altitude | °C |
| Density Altitude | Performance equivalent altitude | feet |
| 120 | Empirical constant for the FAA standard formula | — |
Example 1
Airport elevation: 5,000 ft. Altimeter: 29.92 inHg. OAT: 30°C. What is density altitude?
Pressure Altitude = 5,000 + (29.92 − 29.92) × 1,000 = 5,000 ft
ISA Temp = 15 − (5,000 / 1,000 × 2) = 15 − 10 = 5°C
Density Altitude = 5,000 + 120 × (30 − 5) = 5,000 + 3,000
Density Altitude = 8,000 ft — aircraft performs as if at 8,000 ft
Example 2
Sea-level airport. Altimeter: 29.62 inHg. OAT: 38°C (hot summer day).
Pressure Altitude = 0 + (29.92 − 29.62) × 1,000 = 300 ft
ISA Temp = 15 − (300 / 1,000 × 2) = 15 − 0.6 ≈ 14.4°C
Density Altitude = 300 + 120 × (38 − 14.4) = 300 + 2,832
Density Altitude ≈ 3,132 ft — a sea-level airport performs like a 3,100 ft airport
When to Use It
- Pre-flight performance calculations for takeoff and landing distances
- Determining safe maximum takeoff weight in high-and-hot conditions
- Evaluating climb performance (rate of climb decreases with density altitude)
- Mountain flying where combined elevation and heat create extreme density altitudes
- Any flight where OAT significantly exceeds standard ISA temperature
Rule of thumb: Density altitude above 5,000 ft significantly degrades aircraft performance. Above 8,000 ft, single-engine aircraft may struggle to climb at all when fully loaded. Always use the aircraft's Pilot Operating Handbook (POH) performance charts — they are calibrated for density altitude, not field elevation.