# What is Density Altitude?

I'm trying to get a deep understanding of the term: Density Altitude.

So I have read the explanations in my instruction book, and online articles. One source explained it differently then the other which confused me.

Wikipedia defines Density Altitude as:

The density altitude is the altitude relative to standard atmospheric conditions at which the air density would be equal to the indicated air density at the place of observation. In other words, the density altitude is the air density given as a height above mean sea level..".

https://en.wikipedia.org/wiki/Density_altitude

So if I would believe Wikipedia then I could look at the ISA table to find the altitude by using the pressure.

Here is an ISA table:

My instruction book (Aerodynamica, prestatieleer en vliegtuigtechniek by Bas Vrijhof on page 112, written in Dutch) claims this:

in de ISA is de dichtheidshoogte altijd gelijk aan de drukhoogte

Translated to English:

in the ISA the density altitude is equal to the pressure altitude.

So, let's say I'm flying in an aircraft, the pressure is "22.22 Hg", and the outside air temperature is -0.9°C. The altitude in the ISA would be 8000 ft. The Density Altitude would also be 8000 ft.

Skybrary defines Density Altitude as:

Density altitude is pressure altitude corrected for temperature.

This explanation contradicts with the Wikipedia explanation:

the air density would be equal to the indicated air density at the place of observation

On another wikipedia article I found this:

De relatie tussen temperatuur, hoogte en luchtdichtheid kan worden uitgedrukt in density altitude.

Translated to English:

The relationship between temperature, altitude and air density can be represented as density altitude.

So in short, each source explains Density Altitude in their own manner, some contradict the other which confuse me.

So my question is:

What is Density Altitude?

• en.wikipedia.org/wiki/Ideal_gas_law
– Sam
Feb 12, 2019 at 22:11
• Related question Feb 13, 2019 at 7:51
• I see that you've edited your question to remove the second part - there are any number of ways to verify your density altitude assumptions. I haven't tried this one but it might fit the bill. Feb 13, 2019 at 19:43
• @SteveV. While writing/updating the main question I suddenly understood the second question. So I rewrote the main question. After that, I took a look at your link and realized that Density Altitude is also affected by the dew point. So to say that The relationship between temperature, altitude and air density can be represented as density altitude is not enough, it is not wrong though. But the point is that the explanation I found and quoted here ignore the dew point. I'm just looking for a clear understanding. That's why I wrote the main question in the first place. Feb 14, 2019 at 7:49
• Density altitude is literally just the measurement of density. If you know the density $\rho$ you can convert that to density altitude and vice versa. Mar 14 at 14:15

## The concept of 'density altitude' is kind of like the concept of 'wind chill'.

Stick with me here, I'm going somewhere with this.

Cold weather is dangerous for the human body, and wind (because of increased heat loss on human skin) makes it worse. But how much worse? Is it worse to be outside in -10C temperatures with a 20 knot wind, or -15C temperatures with a 12 knot wind? The concept of 'wind chill' resolves those two values into a single easy number.

Density altitude works the same way. It's difficult and tedious to compare and contrast how an airplane will perform on a 25C day with a pressure of 29.80 at an elevation of 600 MSL, versus a 20C day with a pressure of 30.17 at an elevation of 1250 MSL. We need a way to mash all of these variables into one easy-to-use number. That number is density altitude.

So just as I can say "The wind chill is -10C" and it doesn't matter whether it's warm but windy or cold and calm, I can say "The density altitude is 2,000" and everyone will have the same idea of the expected performance of the airplane, no matter what combination of factors led to that result.

Once you start thinking of (and using!) density altitude as a simplification tool, its value becomes a lot more obvious.

• Nice explanation. Perhaps it would be interesting to know how to compute the density altitude when ISA conditions are not met.
– mins
Feb 12, 2019 at 19:33
• The AOPA article covers that. Calculating Density Altitude Density altitude in feet = pressure altitude in feet + (120 x (OAT - ISA temperature)) AltimeterPressure altitude is determined by setting the altimeter to 29.92 and reading the altitude indicated on the altimeter. OAT stands for outside air temperature (in degrees Celsius). ISA stands for standard temperature (in degrees Celsius). Feb 12, 2019 at 19:39
• Every resource on density altitude provides a way to compute it when ISA conditions are not met. Almost none explain why it's valuable. I wrote this answer hoping to focus only on why density altitude exists as a concept. Feb 12, 2019 at 19:45
• There is one significant difference though: while ‘wind chill’ is a ballpark figure for comparing things with fairly vague definition, density is the variable that appears in all of lift, drag and engine power equations, and well defined. You just don't have instrument to measure it directly, so you have to calculate it from pressure and temperature. Feb 2 at 20:19
• Density altitude is literally a measure of atmospheric density. There's a one-to-one correspondence between a density altitude and the atmospheric density $\rho$ Feb 15 at 20:06

https://www.aopa.org/training-and-safety/active-pilots/safety-and-technique/weather/density-altitude

As a pilot, we like higher Pressure and Cold Temperatures - it makes the air denser so the engine can create more horsepower. High Pressure systems, where the barometer reads above 29.92, and cold air, where the temperature is below 59F (I'm in the US) mean the aircraft will get off the ground sooner and climb better. So - Winter! Ideal flying time from a performance perspective.

Summer, we may see the same increased barometer reading, but the higher temperature means the air is less dense (heat makes the air expand), so engine performance suffers. Even worse, if there is a Low Pressure system, combined with high temperatures, can make the airplane feel like it is taking off from a higher altitude.

So Density Altitude is the altitude that the airplane thinks it is - the barometer reading with temperature impact added to it.

• I never considered this could be a problem. Thanks for explaining it! Feb 12, 2019 at 13:35
• It might be important that this relation only takes take off (and landing) into account. Once airborne and cruise a 'high' density altitude does improve performance by reducing drag. Flying is a huge pile of contradicting points and piloting is about navigating amidst them. Feb 12, 2019 at 21:36

Suppose you are at a given place, with a given temperature, and the barometer shows –for example– 25.84 inches of air pressure. That's precisely the pressure at 4000 ft of altitude within the 'standard atmosphere'. Hence, you may say that the pressure altitude at that place where you are is exactly 4000 ft.

Suppose now that at the same given place the density of the air (measured or computed from pressure and temperature) is 1.121 Kg/m^3. That's precisely the density at 3000 ft of altitude within the 'standard atmosphere'. Hence, you may say that the density altitude at that same place is instead 3000ft.

• Seems pretty straightforward! Feb 13, 2019 at 12:38
• Perfect explanation-- I think. Introducing dew point doesn't alter the accuracy of this explanation, does it? (Actually I'm afraid it does-- for a given pressure, more humid air = less dense air, but no change in pressure. Aaaarggghhh.) Feb 2 at 19:51
• Aren't you describing the pressure altitude?
– fab
Feb 2 at 20:12
• @fab That doesn't matter, because the table of the standard atmosphere has a fixed correlation between pressure and density. In the example, the SA pressure at 4000 ft is 25.84 inches of mercury, with a density 88,81% that at sea level (SA). No need to know the density figure, since what matters is that the density for that pressure (25.84 inches) is the SA density for 4000 ft... Feb 3 at 7:21
• I think you are confusing pressure altitude and density altitude. The table of standard atmosphere does have a fixed correlation between pressure and density because temperature doesn't change (at a given elevation). But in real atmosphere, the temperature will affect the density, even if the pressure doesn't change
– fab
Feb 3 at 7:28

Density Altitude, in a nutshell, tells you how the plane is going to perform, in particular the climb performance for takeoffs or go-arounds.

The performance tables in your POH are based on ISA, which for practical purposes no plane ever actually flies in. That means you have to calculate the density altitude for the current conditions and look at that line in the tables to find out what the actual performance will be.

If the density altitude is very high (i.e. approaching your service ceiling), it's possible that your plane won't be able to clear obstacles/terrain or, in extreme cases, even get off the runway. This happens frequently to non-turbo pistons in mountains in the summer, and it is occasionally bad enough that even airliners can't take off from airports like PHX and LAS.

Any time your planned flight will be High, Hot and Heavy (known as the three H's), you need to consider DA and check the performance tables to determine whether it will be safe. High terrain may mean a different route via mountain passes; Heavy load may mean ditching passengers/cargo or fuel, and Hot may mean waiting until night or early morning. If any of these aren't things you encounter regularly, e.g. because you live in a (relatively) cold and flat region, it would be wise to check with a CFI to refresh your knowledge and double-check your plans before you go.

Try this: Density Altitude

Defined Types of Altitude Pilots sometimes confuse the term “density altitude” with other definitions of altitude. To review, here are some types of altitude:

• Indicated Altitude is the altitude shown on the altimeter.
• True Altitude is height above mean sea level (MSL).
• Absolute Altitude is height above ground level (AGL).
• Pressure Altitude is the indicated altitude when an altimeter is set to 29.92 in Hg (1013 hPa in other parts of the world). It is primarily used in aircraft performance calculations and in high-altitude flight.
• Density Altitude is formally defined as “pressure altitude corrected for nonstandard temperature variations.

Density Altitude is basically this:

1. Compute/Measure the density at the airport site
2. Ask yourself: at what elevation do you find the same density in the Standard Atmosphere?

The answer to question 2 is the density altitude.

Steve's answer does an amazing job at describing what density altitude represents and why it's useful. But more practically, here's how you can compute it:

$$\mathrm{DA_{feet}}=\mathrm{PA_{feet}}+ 120\cdot(T_{\mathrm{OAT}}-T_{\mathrm{ISA}})\tag{1}$$

where:

• $$\mathrm{DA_{feet}}$$: Density altitude in feet
• $$\mathrm{PA_{feet}}$$: Pressure altitude in feet
• $$T_{\mathrm{OAT}}$$: Outside air temperature in Kelvin
• $$T_{\mathrm{ISA}}$$: Temperature (in Kelvin) found in the standard atmosphere at $$\mathrm{PA_{feet}}$$ feet

But if you, like me, are not quite satisfied with the above equation and you ask yourself questions like: where does that 120 come from? Or how was this equation derived? What's the non-approximated equation for density altitude? ... then look no further!

I won't provide all the steps (though I can if someone is interested), but the exact formula for computing the density altitude turns out to be:

$$\mathrm{DA}=\frac{T_0}{L}-\frac{T_{\mathrm{OAT}}}{L}\cdot\left(\frac{T_0-L\cdot\mathrm{PA}}{T_{\mathrm{OAT}}}\right)^{\frac{g}{g-R_s\cdot L}}=\frac{T_0}{L}-\frac{T_{\mathrm{OAT}}}{L}\cdot\left(\frac{T_{\mathrm{ISA}}}{T_{\mathrm{OAT}}}\right)^{\frac{g}{g-R_s\cdot L}}\tag{2}$$

where:

• $$\mathrm{DA}$$: Density altitude in meters
• $$\mathrm{PA}$$: Pressure altitude in meters
• $$T_{\mathrm{ISA}}$$: Temperature (in Kelvin) found in the standard atmosphere at $$\mathrm{PA}$$ meters (i.e. $$T_{\mathrm{ISA}}=T_0-L\cdot\mathrm{PA}$$)
• $$L$$: Temperature lapse $$=0.0065 \mathrm{~K/m}$$
• $$T_0$$: Standard temperature $$=288.15 \mathrm{~K}$$
• $$g$$: Gravitational acceleration $$\approx 9.81 \mathrm{~m/s}^2$$
• $$R_s$$: specific gas constant for dry air $$\approx 287.058 \mathrm{~J \cdot kg^{−1}K^{−1}}$$

It's worth noticing that equation 2 assumes dry air and does not account for humidity.

It's easy to show that if $$T_{\mathrm{OAT}}=T_{\mathrm{ISA}}=T_0-L\cdot\mathrm{PA}$$, it follows that $$\mathrm{DA}=\mathrm{PA}$$, as one would expect, since density altitude is pressure altitude corrected for temperature, but if the temperature is exactly the one it would have in the standard atmosphere no correction is needed and the density altitude equals the pressure altitude. So far so good.

But equation 2 is still quite different from 1.

In order to get a nice linear relation, we need to compute the Taylor expansion of equation 2 and only keep the constant and the linear terms. In other word we want to compute the equation of the line tangent to the function described by equation 2 and passing at $$T_{\mathrm{OAT}}=T_0-L\cdot\mathrm{PA}=T_{\mathrm{ISA}}$$

The linear approximation (see this link) is therefore given by:

$$\mathrm{DA}\approx DA(T_{\mathrm{ISA}})+\frac{DA'(T_{\mathrm{ISA}})}{1!}(T_{\mathrm{OAT}}-T_{\mathrm{ISA}})\tag{3}$$

If you run the math, you get:

$$\mathrm{DA}\approx\mathrm{PA}+(T_{\mathrm{OAT}}-T_{\mathrm{ISA}})\cdot\frac{R_s}{g-R_s\cdot L}\tag{4}$$

which finally looks similar to equation 1. The multiplicative term is:

$$\frac{R_s}{g-R_s\cdot L}= 36.13\mathrm{\frac{m}{K}}=118.55\mathrm{\frac{ft}{K}}$$

And that's where the 120 comes from

The altimeter, although used primarily to give you altitude, is a pressure gauge. Through mathematical trickery in its innards, it will take the pressure and temperature and QNH and give you an altitude reading.

When you set 29.92 in the window, then the altimeter is truly measuring pressure, albeit in odd units of "pressure altitude". The reading has a one-to-one correspondence with other units of pressure. Just an odd nonlinear conversion to go from one to the other.

Pressure altitude is important, because airfoils fly by pressure. Thinner air but higher speed gives the same pressure, gives the same indicated airspeed. Planes in 1G flight stall at the same IAS, regardless of TAS.

When you make the temperature correction to the altimeter reading, you get density altitude. The altimeter is now measuring density not altitude or pressure. Density altitude is a measure of density. Again, just weird units with a nonlinear conversion to other measures of density.

Density altitude is important, because it tells you how many atoms of oxygen are in each parcel of air, and engines ingest oxygen to generate thrust. The same pressure but higher temperature and therefore less density, and you get less oxygen atoms per gulp.

So to summarize, Density Altitude is actually a measure of density, just an odd one.

• "Airfoils fly by pressure", actually they perform based on density altitude, which is pressure corrected for temperature (and to a lesser extent humidity). Adjustments for "Standard conditions" gives us a reference point to say for example: I'm at 5000 feet, it's 30 C, based on my pressure and temperature my plane will perform as if i'm at 8000 feet under standard conditions based on my POH charts. Nothing "odd" about that. Feb 2 at 10:27
• It's important because higher TAS means a longer runway to get going, and "density altitude" tells one how close they are to the service ceiling for a given weight (to see if one can safely climb out). Feb 2 at 10:36
• In the equation $\frac{1}{2} \rho V^{2}$ there is a one-to-one mapping between the density term $\rho$ and the density altitude. That's my point. Density is also important because engine performance is critically tied to density (until we have battery powered aircraft). Feb 2 at 17:08
• @MikeY Airfoils fly by density, not pressure, as both lift and drag equations also use the $\frac12\rho v^2$ term (which is called dynamic pressure, but does not depend on static pressure but on density). Feb 2 at 20:32
• And don't forget props are airfoils too. At lower density they must spin faster to generate the same amount of thrust (or change pitch if they can). This is why aspirated fixed pitch really suffer at high density altitudes. Feb 2 at 21:00