How this instrument works
Density altitude answers one question: how thin does the air act today, expressed as the altitude at which that same thinness would occur under a textbook standard atmosphere. It starts from pressure altitude — the reading an altimeter gives once dialed to the fixed reference setting of 29.92 inHg, which strips out the day's actual barometric pressure — and then adds a correction for how far today's outside air temperature departs from the ISA-standard temperature predicted for that altitude. Heat and low pressure both thin the air, and this formula folds both effects into one runway-length, climb-rate number.
The 1.98 inside the formula is the ISA lapse rate expressed as degrees Celsius per thousand feet — the same standard cooling rate that defines the whole ICAO standard atmosphere — so the bracket (15 − 1.98·PA/1000) simply predicts what a thermometer 'should' read at that pressure altitude on an average day. The 118.8 multiplier is not derived line by line the way a full nonlinear density calculation is; it is a straight-line engineering fit to that curve, close to exact across the pressure altitudes and temperatures most flying happens in, chosen because pilots need to work this figure out by hand or on a flight computer, not run a gas-law calculation before every takeoff.
The formula has real limits. It leaves out humidity entirely, even though moist air is measurably less dense than dry air at the same pressure and temperature, so a muggy day understates the true density altitude by a small but non-zero margin. It also assumes the pressure-altitude input is genuine — read from an altimeter set to 29.92 inHg, not simply copied from the airport's charted field elevation, which is a different number unless the local altimeter setting happens to equal standard pressure exactly. Confusing the two is the most common way this calculation goes wrong in a preflight briefing.
- Enter Pressure altitude, ft — read the altimeter after setting it to the standard 29.92 inHg (1013.25 hPa), not the field elevation off a chart.
- Enter Outside air temperature in °C, switching the unit menu to °F if that's what the weather report gives you.
- Read Density altitude, ft — the altitude at which today's air behaves like standard air, the number performance charts are keyed to.
- Compare the result against Pressure altitude, ft: the gap between the two is how many feet of 'invisible altitude' the heat has added.
Worked example — a 5,000 ft strip on a 25 °C afternoon
Pressure altitude reads 5,000 ft and the outside air temperature is 25 °C. The ISA-standard temperature predicted for 5,000 ft is 15 minus 1.98 times 5, which is 5.1 °C, so today runs 25 minus 5.1, or 19.9 °C, hotter than that standard. Multiply the deviation by 118.8: 118.8 times 19.9 equals 2,364.12. Add that to the pressure altitude and Density altitude, ft returns 5,000 plus 2,364.12, which is 7,364.12 ft.
That is 2,364 ft of performance-robbing 'altitude' added by heat alone, with the airfield's actual elevation unchanged. A takeoff and climb planned against a 5,000 ft pressure-altitude chart will fall short of what the airplane actually does that afternoon; the pilot instead needs the 7,364 ft column of the performance tables, where the same aircraft needs a longer roll and climbs more slowly, because the propeller and wings are working air that acts as thin as standard air 2,364 ft higher up.
Questions
Why isn't density altitude the same as field elevation?
Because field elevation never changes and density altitude changes with the weather. Field elevation is a fixed survey figure; density altitude depends on today's pressure altitude and outside air temperature, and it can sit thousands of feet above or a little below field elevation depending on heat and barometric pressure. A field at 2,000 ft elevation can present a density altitude over 5,000 ft on a hot summer afternoon, which is the entire reason pilots compute it separately.
Where does the 118.8 constant in the formula come from?
It is a linear approximation, not a fundamental constant like the gas constant R. Density altitude truly follows the same nonlinear relationship as air density itself, but 118.8 ft per degree Celsius of temperature deviation is a straight-line fit to that curve that tracks the exact answer closely across the pressure altitudes and temperatures most aircraft actually fly in, which is why flight computers and quick-reference charts use it instead of a full density calculation.
Does humidity change the answer?
Slightly, and this formula leaves it out. Moist air carries lighter water-vapour molecules in place of some of its nitrogen and oxygen, so it is measurably less dense than dry air at the same pressure and temperature, meaning true density altitude on a muggy day runs a little higher than this calculation shows. The effect is usually a few hundred feet at most, which is why temperature and pressure altitude, not humidity, dominate the number.
How much extra runway does a higher density altitude actually cost?
Enough to matter well before it looks dramatic. As a rough planning rule, each 1,000 ft of density altitude above field elevation lengthens takeoff roll by roughly 10 percent and trims climb rate by a comparable share, figures that come from the density-altitude column of an aircraft's own performance charts rather than from this formula itself. Stack a few thousand feet of density altitude onto a short strip and a normally comfortable margin can turn into none at all.
Can density altitude be lower than pressure altitude?
Yes — whenever the outside air temperature runs colder than the ISA-standard temperature predicted for that pressure altitude, the correction term turns negative and density altitude drops below pressure altitude. A −20 °C morning at a 5,000 ft pressure altitude, for instance, works out to a density altitude of about 2,018 ft, nearly 3,000 ft lower, so the aircraft performs better than the pressure-altitude figure alone would suggest.
Is density altitude an altitude the aircraft is actually flying at?
No — it never appears on an altimeter and it is not a height above anything. Density altitude is a performance index: the altitude in the standard atmosphere at which the surrounding air would have today's actual density. An aircraft sitting on a runway at 2,000 ft field elevation can show a density altitude of 5,500 ft without climbing an inch; the number describes how the engine, propeller and wings experience the air, not where the aircraft physically sits.