Maps for Math

How do you calculate density altitude?

First find pressure altitude: field elevation plus (29.92 minus the altimeter setting) times 1,000. Then correct for temperature. Warmer than standard makes the air thinner, raising density altitude by roughly 120 feet per degree Celsius. The exact version uses the standard atmosphere, where density falls with a power of altitude.

altitude (ft)field 4,000 ftpressure altitude 4,120 ftdensity altitude 5,860 ft22 °C: 15.2 °C warmer than standardair is 83.9% as dense as sea level
Density altitude
5860 ft
Pressure altitude
4120 ft
Standard temperature there
6.84 °C
Air density vs. sea-level standard
83.9%

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).

Play

Heat the day up at a high airport. Watch density altitude climb thousands of feet.

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)

Two corrections turn field elevation into density altitude.

Pressure first. The altimeter setting tells you how today's pressure differs from the standard 29.92 inHg. Each 0.01 inHg is about 10 ft: PA=elev+(29.92−altimeter)×1000\text{PA} = \text{elev} + (29.92 - \text{altimeter}) \times 1000.

Then temperature. The standard atmosphere cools about 2 °C per 1,000 ft. Warmer air than that is thinner. The exact density uses exponents:

σ=(1−6.8756×10−6 PA)5.2559⋅288.15OAT+273.15\sigma = \left(1 - 6.8756\times10^{-6}\,\text{PA}\right)^{5.2559}\cdot\frac{288.15}{\text{OAT} + 273.15}

and density altitude is the standard altitude with that 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} = 4000 + (29.92 - 29.8) \times 1000 = 4120\ \text{ft}
  2. Standard temperature there (−1.98 °C per 1,000 ft)T_{\text{ISA}} = 15 - 1.98 \times \frac{4120}{1000} = 6.842\ ^\circ\mathrm{C}
  3. Density ratio\sigma = (1 - 6.8756\times10^{-6}\,\text{PA})^{5.2559} \cdot \frac{288.15}{22 + 273.15} = 0.8394
  4. Density altitude\text{DA} = 145{,}442\,(1 - \sigma^{0.235}) = 5860\ \text{ft}
  5. Rule of thumb: add 120 ft per °C above standard4120 + 120\,(22 - 6.842) = 5939\ \text{ft}

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Enter field elevation, the altimeter setting from ATIS or the METAR, and the temperature. Switch pressure to hPa or temperature to °F in the unit menus.

  • The rule of thumb (120 ft per °C) runs a little high on hot days compared with the exact formula.
  • Take the numbers to your POH performance charts. They are what determine takeoff distance.

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

Cheat card

PA=elev+(29.92−altimeter)×1000\text{PA} = \text{elev} + (29.92 - \text{altimeter}) \times 1000
TISA=15−1.98 PA1000 ∘CT_{\text{ISA}} = 15 - 1.98\,\frac{\text{PA}}{1000}\ ^\circ\mathrm{C}
DA≈PA+120 (OAT−TISA)\text{DA} \approx \text{PA} + 120\,(\text{OAT} - T_{\text{ISA}})
SymbolMeaningUnit
PA\text{PA}pressure altitudeft
OAT\text{OAT}outside air temperature°C
TISAT_{\text{ISA}}standard temperature at that altitude°C
  • Higher density altitude means longer takeoff rolls, slower climbs, and less engine power.
  • Hot, high, and humid is the worst combination. Humidity isn't in the formula but adds a little more.
  • Use the POH performance charts with pressure altitude and temperature for real takeoff numbers.

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Where it’s used

  • Aerospace
    Pilots check density altitude before summer departures from mountain airports, where it can exceed 10,000 ft.
  • Physics
    Density altitude is the altitude in the standard atmosphere that has the same air density as today.

Questions people ask

What is density altitude?

The altitude in the standard atmosphere where the air is as thin as it is right now. The wings, propeller, and engine all perform as if the airplane were at that altitude.

What's the difference between pressure altitude and density altitude?

Pressure altitude corrects field elevation for today's air pressure. Density altitude also corrects for temperature. On a standard day they're equal.

Why does density altitude matter?

Thin air means less lift, less thrust, and less engine power. A summer day at a 5,000 ft airport can perform like 8,000 ft, stretching the takeoff roll and cutting climb rate.

Sample EXP-0006 · rev 1 · model EXP-M06 · Level 4 · advanced algebra · updated 2026-09-26