Density altitude explained: how to calculate it and why it matters
Work it out with your own numbersDensity altitude calculator: Pressure and density altitude from elevation, pressure and temperature, with humidity and air density.Open the calculator →Density altitude is the height in the International Standard Atmosphere (ISA) where the air would be as thin as the air at your airfield right now. You get it by working out the pressure altitude, then correcting it for temperature (and, if you want, humidity). On a hot day it can be thousands of feet above the field: an airfield at 5,000 ft with 29.92 inHg set and 30 °C has a density altitude of about 7,800 ft, so the aircraft performs as if it were nearly 2,800 ft higher.
This guide covers pressure altitude, the ISA temperature, the exact formula and the quick rule, humidity, and what thin air does to take-off and climb. To work it out with today's numbers, use the density altitude calculator.
What is density altitude and why does it matter?
Engines, propellers and wings all depend on how much air they have to work with. When the air is thinner, engines make less power, propellers and wings work less well, and take-off and climb get longer and slower. Density altitude puts a single number on that: it is the altitude your aircraft will perform at, whatever the altimeter says.
Three things raise it:
- Height. The higher the airfield, the thinner the air to start with.
- Low pressure. A low altimeter setting raises the pressure altitude.
- Heat. Warm air is less dense.
Humidity adds a little more on top. Cold, high-pressure days do the opposite: the air is denser than standard and the aircraft performs as if the field were lower.
Step 1: what is pressure altitude?
Pressure altitude is what your altimeter reads with standard pressure set: 29.92 inHg or 1013.25 hPa. It is your height in the standard atmosphere worked out from pressure alone. Pilots use it for flight levels and for reading performance charts, and it is the starting point for density altitude.
The exact way to get it from the field elevation and the altimeter setting (QNH) is:
pressure altitude = elevation + 145,442 × (1 − (altimeter setting in hPa ÷ 1013.25)^0.190263) ft
1 inHg = 33.8639 hPa
The quick rules are 1,000 ft for every inch below 29.92, or about 30 ft for every hectopascal below 1013 (27 ft per hPa is closer near sea level). Above standard, you take the height off instead.
For example, a 5,000 ft airfield with 29.82 inHg is 0.10 inHg below standard. The quick rule gives 5,000 + 0.10 × 1,000 = 5,100 ft. The exact formula gives 5,094 ft. The pressure altitude calculator shows the exact answer and each quick rule side by side. Different tools turn the altimeter setting into pressure altitude in slightly different ways, so their answers can differ by a few feet at a high airfield.
Step 2: what is the ISA temperature at my airfield?
The standard atmosphere is 15 °C and 1013.25 hPa at sea level, cooling at a fixed rate as you climb: 6.5 °C per 1,000 m, which is 1.98 °C per 1,000 ft, up to the tropopause at 36,089 ft. Above that it stays at −56.5 °C up to 65,617 ft.
ISA temperature = 15 − 1.98 × pressure altitude in thousands of feet (°C)
ISA deviation = outside air temperature − ISA temperature
The quick mental rule is 2 °C per 1,000 ft, the one in the FAA Pilot's Handbook of Aeronautical Knowledge, chapter 4. At 5,000 ft the exact ISA temperature is 5.1 °C and the quick rule gives 5 °C. If the outside air is 30 °C, the day is 24.9 °C warmer than standard, or ISA+25. The ISA deviation calculator gives the ISA temperature and deviation at any altitude or flight level.
Step 3: how is density altitude calculated?
Density altitude is the standard-atmosphere height with the same air density as yours. The calculator finds the pressure at the field, divides by how warm the air is compared with standard to get the density ratio σ (sigma), and then finds the ISA height with that same ratio:
station pressure = QNH × (1 − elevation ÷ 145,442)^5.2559 hPa
density ratio σ = (station pressure ÷ 1013.25) ÷ (temperature in kelvin ÷ 288.15)
density altitude = 145,442 × (1 − σ^0.234969) ft
Temperature in kelvin is °C + 273.15. Sea-level standard air has σ = 1, or a density of 1.225 kg/m³.
The 120 ft rule of thumb
The common shortcut is:
density altitude ≈ pressure altitude + 120 × (OAT − ISA temperature)
It is within a few hundred feet in most conditions. In examples 1 and 2 below it reads a little high compared with the exact dry-air answer, and it leaves humidity out altogether. The examples work it with 120 ft per degree. Our density altitude calculator uses 118.8 ft per degree for the same check (30 ft less at ISA+25) and shows it next to the exact answer. Use the rule to catch a mistake, not in place of the formula or your performance charts.
Does humidity affect density altitude?
Yes. Water vapour is lighter than dry air, so humid air is less dense and the density altitude is higher. The calculator works this in using the virtual temperature: the temperature dry air would need to be as light as your humid air. It finds the vapour pressure from the dew point with the Magnus formula used by the US National Weather Service:
vapour pressure e = 6.1078 × 10^(7.5 × dew point ÷ (237.3 + dew point)) hPa
virtual temperature = temperature (K) ÷ (1 − (e ÷ station pressure) × 0.378)
Density altitude then uses the virtual temperature in place of the real one. On a hot, humid day it can add 300–600 ft or more. The dew point is in the METAR straight after the temperature: in 30/20, 30 °C is the temperature and 20 °C the dew point.
Density altitude table
These are density altitudes in dry air with 29.92 inHg set, so the pressure altitude is about the same as the field elevation. The ISA temperature at each elevation is in brackets. Each value was run through the calculator's formula and rounded to the nearest 10 ft.
| Field elevation | 0 °C | 15 °C | 30 °C | 40 °C |
|---|---|---|---|---|
| Sea level (ISA 15.0 °C) | −1,840 ft | 0 ft | 1,730 ft | 2,820 ft |
| 2,000 ft (ISA 11.0 °C) | 660 ft | 2,470 ft | 4,160 ft | 5,240 ft |
| 4,000 ft (ISA 7.1 °C) | 3,150 ft | 4,930 ft | 6,590 ft | 7,650 ft |
| 6,000 ft (ISA 3.1 °C) | 5,630 ft | 7,370 ft | 9,010 ft | 10,050 ft |
| 8,000 ft (ISA −0.8 °C) | 8,100 ft | 9,820 ft | 11,420 ft | 12,440 ft |
Read across a row and you can see the heat effect: a 6,000 ft airfield at 40 °C performs like 10,050 ft. Read down a column and you see the height effect. A low altimeter setting or humid air would push every number higher.
Worked examples
Example 1: a 5,000 ft airfield at 30 °C
The altimeter setting is 29.92 inHg (1013.21 hPa) and the temperature is 30 °C.
- Pressure altitude: the setting is standard, so it is about 5,000 ft (5,001 ft).
- ISA temperature: 15 − 1.98 × 5.0 = 5.1 °C. The air is 30 − 5.1 = 24.9 °C warmer than standard.
- Station pressure: 843.0 hPa (24.89 inHg).
- σ = (843.0 ÷ 1013.25) ÷ (303.15 ÷ 288.15) = 0.8320 ÷ 1.0521 = 0.791.
- Density altitude = 145,442 × (1 − 0.791^0.234969) = about 7,800 ft (7,802 ft), 2,800 ft above the field.
- 120 ft rule: 5,001 + 120 × 24.9 = 5,001 + 2,988 = 7,989, so about 7,990 ft, 190 ft high. (The calculator's 118.8 ft per degree gives 7,960 ft.)
Now add a dew point of 20 °C (55% humidity). The vapour pressure is 23.4 hPa and the virtual temperature 33.2 °C, so the density altitude rises to about 8,140 ft: 340 ft more than in dry air.
Example 2: hot and high, a 7,000 ft airfield at 32 °C
A summer afternoon at an airfield 7,000 ft above sea level. The altimeter setting is 29.80 inHg (1009.14 hPa) and the temperature is 32 °C.
- Pressure altitude: the density altitude calculator gives 7,107 ft, and the rest of this example uses that. The step 1 formula, 7,000 + 145,442 × (1 − (1009.14 ÷ 1013.25)^0.190263), gives 7,112 ft: the two calculators turn the setting into pressure altitude slightly differently. The quick rule gives 7,000 + 0.12 × 1,000 = 7,120 ft.
- ISA temperature: 15 − 1.98 × 7.107 = 0.9 °C. The air is 32 − 0.9 = 31.1 °C warmer: ISA+31.
- Station pressure: 778.7 hPa.
- σ = (778.7 ÷ 1013.25) ÷ (305.15 ÷ 288.15) = 0.7685 ÷ 1.0590 = 0.7257.
- Density altitude = 145,442 × (1 − 0.7257^0.234969) = about 10,550 ft (10,555 ft), 3,550 ft above the field.
- 120 ft rule: 7,107 + 120 × 31.08 = 7,107 + 3,730 = 10,837, so about 10,840 ft, 280 ft high. (The calculator's 118.8 ft per degree gives 10,800 ft.)
Add a dew point of 10 °C (26% humidity) and it rises to about 10,740 ft, 190 ft more. Using the Gagg–Ferrar estimate below, a non-turbo piston engine makes about 1.132 × 0.7257 − 0.132 = 69% of its sea-level power here in dry air, or 68% with that dew point.
Example 3: a hot, humid sea-level airfield
An airfield at sea level reports 1013 hPa, 40 °C and a dew point of 28 °C.
- Pressure altitude: 7 ft. ISA temperature 15.0 °C, so the air is 25.0 °C warmer: ISA+25.
- Dry air: σ = (1013 ÷ 1013.25) ÷ (313.15 ÷ 288.15) = 0.9998 ÷ 1.0868 = 0.920. Density altitude about 2,820 ft.
- Humidity: vapour pressure 37.8 hPa (51% humidity). Virtual temperature = 313.15 ÷ (1 − (37.8 ÷ 1013) × 0.378) = 317.63 K, or 44.5 °C.
- With the virtual temperature, σ = 0.9998 ÷ (317.63 ÷ 288.15) = 0.907, and the density altitude is about 3,300 ft.
Humidity adds about 475 ft here. Even at sea level, a hot, humid day makes the aircraft perform as if the field were more than 3,000 ft up.
| Example | Pressure altitude | ISA deviation | Density altitude (dry) | With humidity |
|---|---|---|---|---|
| 5,000 ft, 30 °C | 5,001 ft | +24.9 °C | 7,800 ft | 8,140 ft (dew point 20 °C) |
| 7,000 ft, 32 °C | 7,107 ft | +31.1 °C | 10,550 ft | 10,740 ft (dew point 10 °C) |
| Sea level, 40 °C | 7 ft | +25.0 °C | 2,820 ft | 3,300 ft (dew point 28 °C) |
What does high density altitude do to take-off and climb?
Thinner air means engines make less power or thrust, propellers work less well and wings make less lift. In practice you get a longer take-off run and a lower climb rate. That is why performance charts for take-off, climb and maximum altitude are read with pressure altitude and temperature, or ISA deviation. Our calculator flags a density altitude 2,000 ft or more above the field as a sign to expect a noticeably longer take-off roll and a weaker climb.
How much power does a piston engine lose?
A normally aspirated (non-turbo) piston engine's power falls with air density. A widely used estimate is the Gagg–Ferrar formula:
power ratio = 1.132 × σ − 0.132
In Example 1 that is 1.132 × 0.791 − 0.132 = 76% of sea-level power. Turbocharged and turbine engines behave differently, so this is only a rough guide. How far the take-off roll and climb change depends on the aircraft: only its approved performance charts in the flight manual (AFM or POH) can tell you that.
Common mistakes
- Using the field elevation as the pressure altitude. On a low-pressure day the pressure altitude is higher. Correct for the altimeter setting first.
- Using 15 °C as the ISA temperature at every airfield. 15 °C is ISA at sea level only. At 5,000 ft it is 5.1 °C, so 20 °C there is already ISA+15.
- Trusting the 120 ft rule on a very hot day. It read about 190 ft high in Example 1 and 280 ft high in Example 2. Use it as a check.
- Forgetting humidity. Dry-air figures understate density altitude on humid days, by about 475 ft in Example 3.
- Mixing up the dew point and the temperature. In a METAR the temperature comes first: 30/20 is 30 °C with a dew point of 20 °C.
- Using the engine power estimate for a turbocharged or turbine aircraft. The Gagg–Ferrar formula is for normally aspirated piston engines.
- Planning from density altitude alone. It tells you how thin the air is, not your take-off distance. That comes from the charts for your aircraft and weight.
What should I do on a high density altitude day?
Work out the pressure altitude and temperature for your departure time, then read your aircraft's take-off and climb charts with those numbers. The density altitude calculator is useful for study, for planning and for cross-checking that the chart numbers make sense, but the flight manual, your operator's procedures and official reports always come first.
Quick summary
- Density altitude is the standard-atmosphere height with the same air density as your airfield now.
- Start with pressure altitude: about 1,000 ft per inHg (or 30 ft per hPa) below standard.
- ISA temperature = 15 − 1.98 °C per 1,000 ft of pressure altitude.
- Quick rule: add about 120 ft for every °C above ISA. The exact formula uses the density ratio σ.
- Humidity raises density altitude further, often by a few hundred feet on hot days.
- High density altitude means less power, a longer take-off roll and a weaker climb. Check your performance charts.
Work out today's numbers with the density altitude calculator, the pressure altitude calculator and the ISA deviation calculator. For the opposite problem, cold air and altimeters that over-read, see cold temperature altimeter correction explained.
Common questions
What is density altitude in simple terms?
It is the height in the standard atmosphere where the air would be as thin as the air at your airfield right now. On a hot day, or when the pressure is low, it is higher than the field elevation, so the aircraft performs as if the airfield were higher up. A 5,000 ft airfield at 30 °C with 29.92 inHg set has a density altitude of about 7,800 ft.
How do you work out density altitude?
Find the pressure altitude from the field elevation and altimeter setting, find the ISA temperature at that pressure altitude, then correct for how much warmer or colder the real air is. The quick rule is pressure altitude plus about 120 ft for every °C above ISA. The exact method uses the standard-atmosphere formula, and humidity can be added through the virtual temperature.
What is the 120 ft rule for density altitude?
Density altitude is roughly pressure altitude plus 120 ft for every degree Celsius the air is warmer than ISA. It lands within a few hundred feet of the exact answer in most conditions. At a 5,000 ft airfield at 30 °C it gives about 7,990 ft against about 7,800 ft from the formula.
Does humidity raise density altitude?
Yes. Water vapour is lighter than dry air, so humid air is less dense. On a hot, humid day it can add 300 to 600 ft or more. At sea level, 40 °C and a dew point of 28 °C, humidity adds about 475 ft: 3,300 ft instead of 2,820 ft in dry air.
Is pressure altitude the same as density altitude?
No. Pressure altitude is what the altimeter reads with 29.92 inHg (1013.25 hPa) set, so it only corrects for pressure. Density altitude also corrects for temperature, and humidity if you include it. They are equal only when the temperature is exactly ISA and the air is dry.
Can density altitude be below the field elevation?
Yes. When the air is colder than ISA it is denser than standard, and the density altitude is lower than the field. At sea level with 29.92 inHg and −10 °C it is about −3,130 ft, so the aircraft performs as if it were below sea level.
This guide explains the rules in plain English for planning. It is not legal, financial or flight-operations advice; check your contract, the official source linked above, your employer or your operator.