How to Calculate Density Altitude: A Step by Step Guide

Out of all the atmospheric variables we get to deal with as pilots, density altitude is by far the most relevant and important. You should really have it in the back of head when you enter the cockpit for the day. Knowing how to calculate density altitude is something a lot of pilots get lazy with over the years, as technology helps us more and is often only a few taps away.

That’s why today, we’ll refresh everyone’s mind and go through a step by step guide and explanation of what it all means and how we calculate density altitude. The entire aircraft’s performance and overall behaviour hinges on whatever the density altitude is. It pretty much affects everything we do during normal day of flying. Let’s have a look!

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What is Density Altitude?

So let’s start with the basics, what is it exactly? In simple terms, Density Altitude (DA) is the pressure altitude corrected for temperature, but what does that even mean? It’s simply the altitude the aircraft ‘thinks’ it is currently flying at.

DA goes 1 step further than Pressure Altitude (PA). With the PA, we take the fact that pressure is different in real life than in the models for the “standard” atmosphere, and correct for that. It shows us our altitude above or below the 1013 HPa level. If the QNH is lower than 1013 (like in the example below), the 1013 level will be below MSL. If the QNH is higher than 1013, the 1013 level will be above MSL. This is because pressure reduces as altitude increases.

With Density Altitude however, we add a layer of realism by also taking into account that the temperature might be really high. A higher temperature reduces the ‘amount’ of air in the atmosphere i.e density. Similar to how a prevailing low pressure would reduce the amount of air we can work with.

Dense air (high pressure and low temperature) is good for aircraft performance, whether you are in a fixed wing aircraft or a helicopter. It allows the engine, propellers, or rotor system to work with more air for a similar amount of effort.

High Density Altitude Effects

Density Altitude affects so much on a normal flying day, the most important effects of a high DA are:

• A reduced engine thrust and torque
• A higher plane V1 and rotation speed
• A lower rate of climb
• A higher (autorotation) rate of descend
• A higher TAS compared to IAS for any aircraft
• Reduced Maximum Take-Off Mass
• Reduced amount of overall lift

Unfortunately, a lot of airline and helicopter pilots have to deal with high and hot conditions regularly. Knowing how bad performance is going to be affected beforehand is crucial to be fully prepared and manage the inflight risks properly.

Standard Pressure and Temperature Lapse Rates

As we know, pressure and temperature both reduce as we increase our altitude (up to a certain point). Standard temperature at Mean Sea Level (MSL) is 15ºC, and standard pressure at MSL is 1013.2 HPa (or 29.92 Hg for our American friends across the pond).

The normal lapse rate for the temperature is roughly 2ºC / 1000 ft. So let’s say we are flying at 10,000 ft, that means that on an average day (for the International Standard Atmosphere or ISA) we are experiencing a temperature of 2 x 10 = 20ºC colder than the 15ºC mentioned earlier on the surface. So 15 – 20 = -5ºC at 10,000 ft.

The atmospheric pressure on the other hand, reduces by 1 HPa every 27 ft on average (depending on other variables such as local temperature, the other value you might see elsewhere is 30 ft but this is slightly less accurate). This means that for the ISA at 10,000 ft, we experience a pressure that is 10,000 / 27 = 370 Hpa lower than pressure at MSL (1013.2 HPa). To get the figure, we just subtract 370 from 1013.2 to get 643.2 HPa at 10,000 ft.

Calculating Pressure Altitude

All good so far? Well, we can make the DA calculation easier if we know our Pressure Altitude. Let’s use the following example. The QNH at Geneva Airport is 1030 with an airport elevation of 1411 ft.

To calculate the pressure altitude, we can use the following formula:

Now before going any further, knowing that the pressure is higher than the ISA, do we expect a higher or lower pressure altitude than just the elevation of the airport? Filling in the formula gives:

This means the Pressure Altitude is 952 ft, which is lower than 1411 ft. This is of course expected, as a higher pressure will mean that our aircraft performs better as it ‘thinks’ it is lower than it actually is.

How to calculate Density Altitude

So now that we’ve compensated for a different pressure, let’s go the extra step and take the temperature into account. Let’s say it’s a really hot day in the summer, and the temperature is 24ºC.

The Density Altitude formula looks like this:

Where does the 120 come from? Don’t worry, it’s simply the accepted reduction in density altitude based on the temperature difference. So the first step is to calculate what temperature we expect at 952 ft (the PA at Geneva Airport). Remember the lapse rate?

It was 2ºC / 1000 ft, so 952 ft gives:

Subtracting this from 15ºC gives 13ºC. This is the expected temperature according to the ISA. We however have 24ºC.

So filling this in with the earlier calculated PA gives:

Tadaa, our DA is 2272 ft. Quite a bit higher than 1411 ft or 952 ft right? The sneaky thing is that if you only looked at the PA, you’d have concluded that due to high pressure, we actually expect pretty good performance. The opposite proves to be true due to the temperature that we did not take into account for PA. This, as mentioned before, will heavily influence the aircraft’s performance.

Does Humidity Affect Density Altitude?

In short, yes it definitely does. However, especially for us monkey-brained pilots, aviation regulators have accepted that for everyday calculations we can ignore its influence. As the effects are relatively small.

Water vapour however, is definitely less dense than dry air. So as the air gets more humid (assuming pressure and temperature remain the same), density reduces and therefore density altitude increases!

Unless you go to an extremely humid environment like the tropics, this change is less than 1% of the total prevailing density, so we don’t have to worry about it too much.

Conclusion

There we have it: calculating density altitude. Hopefully this provided a quick but handy refresher for those who needed it. In summary, here is the Density Altitude equation in one overview for future reference:

If you want to know more about density altitude, check out this FAA bulletin about it.

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