Formula
Station pressure comes from the altimeter setting and the field elevation by the ISA hydrostatic reduction. Pressure altitude is the elevation in the standard atmosphere that has that station pressure. Density comes from the ballistic page’s moist-air equation: ρ = (P − 0.378 Pv) / (Rd T), with Rd = 1,716.49 ft·lb/(slug·°R). Density altitude is the ISA altitude with that density.
P = altimeter × ((288.15 − 0.0065 h) / 288.15)^5.25588
DA = 145,442.16 × (1 − (ρ / 0.0023769)^0.234969)
rule of thumb = PA + 120 × (OAT°C − ISA°C)
ISA°C = 15 − 2 × PA / 1,000
Standard sea level in the Pilot’s Handbook is 59°F and 29.92 inHg. At those inputs and zero humidity, density altitude is about zero. The 120-foot rule is the linearization in FAA-P-8740-02. On the published 7,000 ft, 18°C, standard-pressure example it returns 9,040 ft. The dry density inversion returns about 8,930 ft, within 150 ft of that pamphlet figure. The difference is the linearization, not a second atmosphere. At 50% relative humidity the inversion is about 9,090 ft. The ballistic calculator uses this density and does not report density altitude on its own page.
Worked examples
Sea level, 59°F, 29.92 inHg, dry. Station pressure is 29.92. Density altitude is within a few feet of zero.
7,000 ft field, altimeter 29.92, 64.4°F (18°C), dry. Station pressure is 23.09 inHg. Pressure altitude is 7,000 ft. Density altitude is about 8,928 ft. The FAA rule of thumb is 9,040 ft.
The same field at 50% relative humidity. Density altitude rises to about 9,088 ft, because the vapor term lightens the air.
Reference
ISA sea-level anchors used in the inversion: 59°F, 29.92 inHg, 0.0023769 slug/ft³.
Questions
What is density altitude at a 7,000 foot field, 18°C, standard pressure?
The FAA’s 120-foot rule of thumb gives 9,040 ft. This page inverts the moist-air density on the ISA atmosphere and gets about 8,930 ft dry, 112 ft lower. At 50% relative humidity it is about 9,090 ft. The 120-foot rule is a linearization. The density inversion is the answer this page leads with.
Does humidity raise density altitude?
Yes. Water vapor is lighter than dry air, so the same station pressure is less dense when the air is moist. The correction is the virtual-temperature term already in the ballistic atmosphere model, the 0.378 vapor-pressure subtraction.
What do I type for pressure?
The altimeter setting, the number in the Kollsman window, plus the field elevation. The page reduces that to station pressure with the ISA hydrostatic equation. At sea level the two pressures match.
Sources
- International Standard Atmosphere troposphere: the hydrostatic pressure ratio with exponent 5.25588, and the density inversion. Sea-level density 0.0023769 slug/ft³.
- FAA-P-8740-02, Density Altitude. The worked “about 9,040 ft” case is pressure altitude 7,000 ft and 18°C, using 120 ft per degree Celsius. Pilot’s Handbook of Aeronautical Knowledge, standard sea level 15°C / 59°F and 29.92 inHg.
- Humidity uses the virtual-temperature density already in the ballistic model, ρ = (P − 0.378 Pv) / (Rd T). The dry answer is about 112 ft below the pamphlet on that example. The pamphlet is a linearization. This page leads with the density inversion and prints both.