Maps for Math

How do you calculate density altitude exactly, including humidity?

Use the standard atmosphere: find the air pressure at your pressure altitude, correct for temperature and for water vapor from the dew point, and get the density ratio σ. Density altitude is 145,442 × (1 − σ^0.235) feet. Humid air is lighter than dry air, so on muggy days density altitude runs higher still.

altitude (ft)field 0 ftpressure altitude -100 ftdensity altitude 784 ft22 °C, dew point 2 °C: 27% humidityhumidity adds 89 ft; air is 97.7% as dense
Density altitude
784 ft
Pressure altitude
-100 ft
Standard temperature there
15.2 °C
Air density vs. sea-level standard
97.7%
Added by humidity
89.3 ft

E6B: Training aid only, not for navigation or flight. Verify with your POH/AFM and approved sources.

From ATIS or the METAR, like 30.12 (or switch to hPa).
The second temperature in the METAR (e.g. 30/18). Leave blank to assume 50% relative humidity.

Need a quick number? The 120-feet-per-degree rule of thumb gets within a few hundred feet. E6B density altitude: the 120-feet-per-degree rule →

Play

Keep the temperature hot and raise the dew point. Watch humidity push density altitude up.

Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”

Understand

DA=145,442(1−σ0.235)\text{DA} = 145{,}442\left(1 - \sigma^{0.235}\right)

Air density depends on pressure, temperature, and humidity. The standard atmosphere turns pressure altitude into a pressure ratio with an exponent, and temperature into a simple ratio:

σ=(1−6.8756×10−6 PA)5.2559⋅288.15Tv\sigma = \left(1 - 6.8756\times10^{-6}\,\text{PA}\right)^{5.2559}\cdot\frac{288.15}{T_v}

Humidity enters through the virtual temperature TvT_v: the temperature dry air would need to have the same density as your moist air. More water vapor, higher TvT_v, thinner air.

Finally, density altitude is the standard altitude with that same density, 145,442 (1−σ0.235)145{,}442\,(1 - \sigma^{0.235}) ft.

Use

Every input has a unit menu, so you can type values in the units you already have. Results follow your units.

Show the work

  1. Pressure altitude\text{PA} = 0 + (29.92 - 30.02) \times 1000 = -100\ \text{ft}
  2. Vapor pressure at the dew point (Magnus)e = 6.1094\,e^{17.625\,T_d/(T_d + 243.04)},\quad T_d = 2\ ^\circ\mathrm{C}
  3. Virtual temperature: moist air acts warmerT_v = \frac{T}{1 - 0.378\,e/p} = 22.78\ ^\circ\mathrm{C}
  4. Density ratio\sigma = (1 - 6.8756\times10^{-6}\,\text{PA})^{5.2559} \cdot \frac{288.15}{T_v + 273.15} = 0.9772
  5. Density altitude\text{DA} = 145{,}442\,(1 - \sigma^{0.235}) = 784.4\ \text{ft}
  6. Compare: dry air, and the 120 ft/°C rule of thumb\text{dry: } 695.2\ \text{ft},\quad \text{rule: } 716.2\ \text{ft}

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Enter field elevation, the altimeter setting, temperature, and the dew point from the METAR. Leave the dew point blank to assume 50% humidity.

  • Take pressure altitude and temperature to your POH performance charts for takeoff and climb numbers.
  • Above about 36,000 ft the standard atmosphere changes shape. This tool stops there.

For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.

Cheat card

σ=(1−6.8756×10−6 PA)5.2559⋅288.15Tv\sigma = \left(1 - 6.8756\times10^{-6}\,\text{PA}\right)^{5.2559}\cdot\frac{288.15}{T_v}
Tv=T1−0.378 e/pT_v = \frac{T}{1 - 0.378\,e/p}
DA=145,442(1−σ0.235)\text{DA} = 145{,}442\left(1 - \sigma^{0.235}\right)
SymbolMeaningUnit
σ\sigmaair density ÷ sea-level standard density
TvT_vvirtual temperature (humid air acts warmer)K
e,pe, pvapor pressure at the dew point, and air pressurehPa
  • The METAR gives temperature and dew point together, like 30/18.
  • Humidity usually adds a few hundred feet. It matters most on hot, muggy days.
  • For a quick in-your-head number, use the 120 ft/°C rule of thumb.

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Where it’s used

  • Aerospace
    Flight planning software and weather services compute density altitude this way, including humidity.
  • Physics
    Water vapor molecules (18 g/mol) are lighter than nitrogen and oxygen (about 29 g/mol), so moist air is less dense.

Questions people ask

Does humidity affect density altitude?

Yes. Water vapor is lighter than dry air, so humid air is less dense. On a hot, humid day it can add 200 to 500 ft to density altitude. It also reduces engine power a little more than density alone suggests.

What if I don't know the dew point?

Leave it blank and the tool assumes 50% relative humidity, and says so under the results. The METAR's second temperature is the dew point. Use it for a better answer.

How is this different from the rule of thumb?

The rule adds 120 ft per °C in a straight line and ignores humidity. This tool uses the full standard-atmosphere formula with humidity. They usually agree within a few hundred feet.

Updated : Becomes the exact tool: adds an optional dew point (humidity via virtual temperature). A blank dew point assumes 50% relative humidity, with a note. Links to the new rule-of-thumb tool LIN-0008, now the suite's main density altitude tool.

Change history (2 revisions)
  1. · rev 2: Becomes the exact tool: adds an optional dew point (humidity via virtual temperature). A blank dew point assumes 50% relative humidity, with a note. Links to the new rule-of-thumb tool LIN-0008, now the suite's main density altitude tool.
  2. · rev 1: First published.

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