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# Calculating Density Altitude with a Pencil

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We all know that as density altitude increases, there is a corresponding decrease in the power delivered by our airplane’s engine and the effectiveness of our propeller. For a typical non-turbocharged light single-engine airplane, this can result in a takeoff roll that’s 25 percent longer for every 1,000 feet of elevation above sea level. The most dangerous combination of conditions are a heavy load, unfavorable wind, high temperature, high airport elevation and high humidity.

With so many variables to consider, how are we supposed to know when our density altitude is too great for the conditions? The answer is, we need to calculate our density altitude, which we can then compare against the performance information in our aircraft manual.

We could use an E6B computer or an iPad app to calculate density altitude, but what if we accidentally left the flight computer and iPad at home? Is there an easy way to calculate approximate density altitude without the aid of these gadgets?

There sure is, and it’s a formula we as pilots should probably commit to memory.

First off, what is density altitude? From our private pilot exam prep, we know it is “pressure altitude corrected for non-standard temperature.” That’s just a fancy way of saying it’s where the airplane “feels” like it is. For example, if the density altitude is 5,000 feet at sea level, your airplane is going to take off as though it’s already flying at 5,000 feet.

How do we calculate density altitude? There are just two pieces of information you’ll need for a rough approximation: pressure altitude and temperature. Where do you find this information? Easy: for temperature, you look at the thermometer in your airplane. For pressure altitude, set the window in your altimeter to 29.92. Whatever value it reads is pressure altitude.

Finding pressure altitude when you're not sitting in the airplane is a bit more complicated, but here’s a nifty formula:

pressure altitude = (standard pressure - your current pressure setting) x 1,000 + field elevation

That’s a pretty simple formula since two of the variables will always be the same and the other two are easy enough to find. Let’s say our current altimeter setting is 29.45 and the field elevation is 5,000 feet. That means (29.92 - 29.45) x 1,000 + 5,000 = 5,470 feet.

Easy! Now let’s move on to step two, finding density altitude. Here’s the formula:

density altitude = pressure altitude + [120 x (OAT - ISA Temp)]

Now, before your eyes glaze over, here’s how simple this formula is: We already have the value for pressure altitude from our last calculation; OAT is degrees Celsius read off our thermometer (let’s say it’s a balmy 35 °C today) and ISA Temp is always 15 °C at sea level. To find ISA standard temperature for a given altitude, here’s a rule of thumb: double the altitude, subtract 15 and place a - sign in front of it. (For example, to find ISA Temp at 10,000 feet, we multiply the altitude by 2 to get 20; we then subtract 15 to get 5; finally, we add a - sign to get -5.)

So, in the example above:

density altitude = 5,470 + [120 x (35 - 5)]

Working out the math, our density altitude is 9,070 feet.

This is a rough estimate, but it will be pretty close to the actual value. Try this formula the next few times you go flying (or, just for fun, run some scenarios using Microsoft Flight Simulator) and before you know it you’ll be able find your ballpark density altitude without digging in your flight bag for that E6B.

If you're going to ignore the humidity (dew point) in the calculation to get a rough, albeit accurate enough, answer, why even bother with Pressure Altitude. Just use field elevation. As your calculation shows on a fairly extreme low pressure day of 29.45 the difference between PA and actual elevation is less than 500'. On a day with a pressure of 30.50, you're subtracting just over 500' from your altitude. Days with pressure extremes like that aren't all that often - and we're only doing a rough calculation here.

Humidity adds quite a bit more to the equation, but not enough to bother with on a quick calculation you should try to be able to do on a kneeboard or even in your head (if you're blessed with good mental math skills - I'm not).

Just drop the PA bit and use field elevation (or whatever is on your altimeter). If you really need PA for some reason, set the altimeter to 29.92. Temperature is the biggest culprit. In your example it added 3,600'.

Good point about temp. being the main culprit in density altitude changes. I'd still use PA in the calculation though since so easy to determine pressure altitude when your sitting in the airplane.

I'm trying to understand the temperature calculation. Say that the altitude is 400 ft. If I double it, I get 800 feet. Now, if I subtract 15, I get 65 after I drop the final zero in the first answer. Doesn't seem logical that the ISA temp only 400 feet ASL is -65 degrees.

Shouldn't you be finding the ISA temp at 5,000 ft instead of the 10,000 ft in your example? And we use Fahrenheit here in the US. This doesn't seem like an "easy to use" or "remember in your head" type of formula.

@electrical: if your altitude is 400 feet, that's almost sea level. At sea level ISA Temp is 15 C, which you could use. Using the formula given, it would be .4 x 2 = .8 - 15 = -14.2. Remove the - symbol (remember, two negatives make a positive) and the ISA Temp is 14.2 C.

@Dan: Using 5,000 feet the calculation is 5 x 2 = 10 - 15 = -5. Switching the symbol makes the ISA Temp 5 C. We use celsius in this formula because it uses ISA Temp, which is in C. Not coincidentally, when the FAA gives you a density altitude question on a written test with the temp in Farenheit, you'll have to convert it to celsius first to get the answer.

If you don't like this formula, consider this instead: standard temp drops 2 deg C for every 1,000-foot rise in altitude.

To convert from F to C in your head, here's the rule-of-thumb formula: (F Temp - 30) / 2 = C Temp. So for example: if the temp is 59 deg F, the conversion is (59 - 30) / 2 = 14.5 C. Which is pretty close to the actual number of 15 C.

Really, there's no need to memorize these formulas. Instead, write them down on a blank page in your logbook or a notepad.

This is the second time this week that I have seen different density altitude "quick" calculation articles from Flying, and both times the discription has been wrong, and so have the examples. The problem for Flying is in the density altitude correction for OAT compared to ISA standard temp, SO here is the correct process:

Once the pressure altitude for your airport/loaction is determined, a correction needs to be added to accomodate deviations from standard temperature lapse rates for that location (altitude) where you are . Simply put, standard ISA temperatures decrease by 2 degrees F for each 1000 ft increase in altitude (approximately). At sea level, standard temp is 15 F. At 5000 ft it should decrease by 10 F (2 deg X 5) to 5F. If the actual OAT is higher or lower than standard, the density altitude correction from standard is 120 ft per degree: + 120 ft for higher temps than standard, and - 120 ft for lower.

In the Flying example for a 5000 ft airport, the calculation would be 5470 ft (pressure altitude) plus (35 OAT-5 ISA) X 120 = 5470 + (30 X 120) = 9070 ft density altitude.

Note that at 10,000 ft. the ISA standard temp is calculated as: 15 F (sea level) minus ISA at 10,000 ft (10 X 2 deg F per 1000 = 20F) = 15 -20 = -5 F standard ISA at 10,000 ft. If the OAT is actually 35F, the density altitude correction calculation becomes 120ft(35deg - (-5deg)) = 120(40) = 4800 ft correction for non-standard temp. (If you subtract a negative number, it becomes a positive and you add it).

In Flying's simplified language, double the number of thousands of feet AGL and subtract that number FROM 15 to get standard ISA temp at your elevation, and then subtract that ISA number from the OAT and multiply by 120 for the temperature correction to density altitude. If your ISA is a positive number, subtract it from the OAT; if it is a negative (above 7500 ft), add it to the OAT - and then multiply the result by 120 ft/deg.

My reference to F is wrong! All temps referenced should have been C....

Sorry for the lousy proof reading

spope's comment: F to C conversion - helpfulhquentin's comment/explaination: better than Pope's, even with the F/C typoThey both needed a good proof reader