What density altitude actually measures
Density altitude is pressure altitude corrected for temperature and, if you want the honest answer, for humidity. It answers one question: in the standard atmosphere, at what altitude would the air be this thin? If you are sitting on a 3,000 ft strip on a 35 °C afternoon, the air around your propeller behaves like the air at roughly 6,000 ft. Every performance number in your flight manual is indexed to that figure, not to the number painted on the airport diagram.
Three things degrade together as density falls. The wing produces the same lift only at a higher true airspeed, so you accelerate for longer before rotating and touch down faster. A normally aspirated piston engine ingests fewer air molecules per stroke, so it makes less power. The propeller pushes on thinner air, so it converts that reduced power into less thrust. The three effects compound, which is why takeoff distance grows far faster than density altitude does, and why climb gradient — the number that decides whether you clear the ridge — collapses first.
Turbocharged and turbine aircraft are partly insulated from the power loss up to their critical altitude, but not from the aerodynamic half: the wing and the runway do not care what is under the cowling. Every aircraft is affected.
The formula, and why the rule of thumb drifts
Work it in three moves. First convert the altimeter setting and your elevation into station pressure — the pressure actually pushing on the aerodrome. The ICAO Standard Atmosphere makes this exact rather than approximate, because pressure raised to the power n = 0.190263 is a linear function of altitude: pn = QNHn − K·h, with h in metres and K = 8.417286×10−5. Invert that and you have the station pressure in hectopascals. Feed the same quantity into PA = 145441.6 (1 − pn/1013.25n) and you have pressure altitude in feet.
Second, get the density. The ideal gas law gives ρ = p/(Rd·T) for dry air, with T in kelvin. Moist air is lighter, not heavier, because a water molecule weighs 18 units against 29 for the dry-air average, so each molecule of vapour that displaces a molecule of air reduces density. Splitting the pressure into a dry part and a vapour part gives ρ = (p−e)/(Rd·T) + e/(Rv·T).
Third, invert the standard atmosphere's density profile. Density falls as (1 − L·h/T0)4.2559, so solving for h gives DA = 145441.6 (1 − σ0.234969). The familiar cockpit rule, add 118.8 ft per degree above ISA, is the first term of that expression expanded about sea level. It is close near sea level and increasingly generous higher up: at 5,000 ft pressure altitude and 25 °C above ISA it overstates density altitude by roughly 150 ft, which is on the safe side but not the true number.
Worked example: 5,000 ft field, QNH 1013.25 hPa, 30 °C
Take a mountain strip at 5,000 ft with a standard altimeter setting and an air temperature of 30 °C, dry air.
- Station pressure. 5,000 ft is 1,524 m. QNHn = 1013.250.190263 = 3.731238. Subtract K·h = 8.417286×10−5 × 1,524 = 0.128279, leaving pn = 3.602959, so p = 3.6029591/0.190263 = 843.07 hPa.
- Pressure altitude. 145441.6 × (1 − 3.602959/3.731238) = 145441.6 × 0.034380 = 5,000 ft. With the standard setting, pressure altitude equals field elevation exactly — that is what "standard" means.
- ISA deviation. Standard temperature at 5,000 ft is 15 − 1.9812 × 5 = 5.09 °C, so you are 30 − 5.09 = 24.9 °C above ISA.
- Density. T = 30 + 273.15 = 303.15 K. ρ = 84,307 Pa ÷ (287.053 × 303.15) = 84,307 ÷ 87,020 = 0.9688 kg/m³.
- Density ratio. σ = 0.9688 ÷ 1.225 = 0.7909, so you have 79.1% of sea-level density.
- Density altitude. σ0.234969 = 0.94636, so DA = 145441.6 × (1 − 0.94636) = 7,801 ft.
The cockpit rule of thumb would give 5,000 + 118.8 × 24.9 = 7,958 ft. Both say the same thing operationally: you are flying a 5,000 ft aeroplane out of what is effectively a 7,800 ft aerodrome. Run the numbers again with a 25 °C dew point and density altitude rises to 8,261 ft, about 460 ft more.
How to read the number you get
Density altitude is an input, not a verdict. Take it to the performance section of your takeoff distance and landing distance charts and read the answer there. What the number tells you directly is how far from book conditions you are.
Below about 2,000 ft density altitude you are in territory where sea-level figures are broadly representative. At 5,000 ft, the widely used +10% per 1,000 ft takeoff rule gives 1.105 = 1.61, so a typical normally aspirated light single needs about 60% more runway than the sea-level chart shows and climbs noticeably more slowly. Above 8,000 ft the margins get thin fast: the same rule gives 1.108 = 2.14, so ground roll can be double the sea-level figure and rate of climb can fall by half or more, and the accident record for high-density-altitude departures is dominated by aircraft that got airborne and then could not out-climb rising terrain.
Two derived numbers matter alongside it. Relative air density tells you directly what fraction of sea-level mass flow the engine is getting — 79% in the example above. ISA deviation is the number airline and turbine performance systems use, because turbine thrust is scheduled against temperature rather than density. If you fly behind a turbine, the ISA deviation figure is often the one your manual asks for.
Remember also that indicated airspeed still reads correctly, but your true airspeed at rotation and touchdown is higher than the indicator shows. At a density ratio of 0.79, true airspeed is 1/√0.79 = 1.125 times indicated, so you touch down 12.5% faster over the ground and dissipate 27% more kinetic energy in the brakes.
Density altitude at standard pressure, by elevation and temperature
| Field elevation | 0 °C | 10 °C | 20 °C | 30 °C | 40 °C |
|---|---|---|---|---|---|
| Sea level | −1,840 | −600 | 590 | 1,720 | 2,820 |
| 2,000 ft | 660 | 1,870 | 3,040 | 4,160 | 5,230 |
| 4,000 ft | 3,150 | 4,350 | 5,490 | 6,590 | 7,650 |
| 6,000 ft | 5,630 | 6,810 | 7,930 | 9,010 | 10,050 |
| 8,000 ft | 8,100 | 9,260 | 10,360 | 11,420 | 12,440 |
Read your elevation row and the nearest temperature column, then interpolate. Add roughly 400-500 ft when the air is close to saturated at 30 °C.
Mistakes that make a density altitude figure wrong
- Using indicated altitude instead of field elevation. If the altimeter is set to QNH it already reads elevation, but if it is set to 29.92 it is reading pressure altitude and you must not apply the setting correction twice.
- Entering QFE as the altimeter setting. QFE makes the altimeter read zero on the ground. Feeding QFE and field elevation into this calculation produces a station pressure far too low and a density altitude several thousand feet too high.
- Reading the temperature off a sun-soaked OAT probe. A gauge in direct sun on a parked aircraft can read 8-10 °C high. Use the ATIS or a shaded thermometer.
- Ignoring humidity on a tropical morning. At 30 °C and saturated, water vapour adds roughly 400 ft. It is small relative to the temperature effect, but it arrives on exactly the days when your margins are already smallest.
- Treating density altitude as a substitute for the performance chart. The relationship between density altitude and distance is not linear, and it differs between aircraft. This figure is the chart's entry argument, not its output.
- Forgetting that runway slope, surface and weight act on top of it. A hot, high, grass, uphill, heavy departure multiplies four penalties together.
Which standard atmosphere this uses
All constants here come from the ICAO Standard Atmosphere, published as ISO 2533 and as ICAO Doc 7488: sea-level pressure 1013.25 hPa, sea-level temperature 288.15 K, sea-level density 1.225 kg/m³, and a tropospheric lapse rate of 6.5 K per kilometre up to 11,000 m. Some published pilot formulas use 145366.45 ft in place of 145441.6 ft, which comes from an older 288.0 K sea-level temperature; the difference is under 10 ft at 8,000 ft and has no operational consequence. Vapour pressure uses the Magnus form given by Buck (1981) over liquid water.
Where this sits among the other performance numbers
Density altitude is the second step in a chain. The first is pressure altitude, which depends only on elevation and the altimeter setting and is what you set 29.92 to read. The third is the performance chart itself. If your flight manual's charts are indexed to pressure altitude and temperature rather than to density altitude — many are — use the pressure altitude and ISA deviation figures from this page and skip the density altitude entirely.
Downstream, density altitude drives almost everything else you compute for the flight. True airspeed scales with 1/√σ, so cruise speed rises with density altitude even as climb performance falls. Fuel burn at a given power setting is roughly proportional to the mass of air the engine ingests. And once airborne, your ground speed depends on that true airspeed plus the wind.
For unmanned aircraft the same physics applies with sharper edges: a multirotor sized for sea level can lose so much rotor thrust at 8,000 ft density altitude that it cannot hover at maximum takeoff mass. Manufacturers publish a service ceiling in density altitude for exactly this reason.
Finally, treat this as planning information rather than certification data. Where a regulation, an operations manual or an aircraft flight manual specifies a method, that method governs.