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Lindy at TacPro 2004

Manual Calculation of Density Altitude

by Linden B. (Lindy) Sisk

Last Revision March 6, 2009

This article is an addition to and continuation of the method of using density altitude in computing ballistic performance, Making Ballistic Cards Using Density Altitude

Your Kestrel includes humidity in its calculation of density altitude. This method does not. However, it will get you pretty close if you don't have a Kestrel or other weather meter to do the calculation for you.

First we must calculate the pressure altitude, because barometric pressure varies, which affects the pressure altitude. The pressure altitude is the altitude an aircraft altimeter would read at our location if the reference pressure on the altimeter were set to the current sea-level barometric pressure.

Then we must compensate the pressure altitude for the temperature, which is usually different than the ICAO standard temperature at the pressure altitude.

Step 1 Calculation of Pressure Altitude

If you have the station pressure, from a watch or other instrument, we can use this formula:

The basic formula for Pressure Altitude is this:

Pressure Altitude = Physical Altitude + (29.92 - Sea Level Pressure) * 1000

But first we must calculate the sea level pressure:

Sea Level Pressure = Station Pressure + Physical Altitude / 1000

See Note (1) below.

Example: Your altitude is 7,200 feet, and the station pressure is 22.50 inches.

Sea Level Pressure = 22.50 + (7200 / 1000) = 22.50 + 7.2 = 29.7 inches

So, using 29.7 for the SLP, we have:

Pressure altitude = 7,200 + (29.92 - 29.7)*1000 = 7,200 + 220 = 7420

Or you can use the following table:


Sta. Press    Press. Alt.               Sta. Press    Press. Alt.
Inches Hg    Feet               Inches Hg    Feet
32.0    -1,870               20.5    10,092
31.5    -1,429               20.0    10,726
31.0    -983               19.5    11,374
30.5    -531               19.0    12,034
30.0    -73               18.5    12,709
29.5    392               18.0    13,399
29.0    862               17.5    14,104
28.5    1,340               17.0    14,826
28.0    1,824               16.5    15,566
27.5    2,315               16.0    16,324
27.0    2,814               15.5    17,101
26.5    3,320               15.0    17,899
26.0    3,834               14.5    18,718
25.5    4,356               14.0    19,561
25.0    4,886               13.5    20,429
24.5    5,425               13.0    21,323
24.0    5,973               12.5    22,245
23.5    6,531               12.0    23,198
23.0    7,098               11.5    24,183
22.5    7,675               11.0    25,204
22.0    8,262
21.5    8,861
21.0    9,471

If you would like to download a copy of the Excel spreadsheet upon which the table above is based, so you can print your own copy, right-click on the following link: Pressure Altitude Spreadsheet.

If you don't understand the difference between the sea-level barometric pressure and station pressure, please see this reference: Ballistic Software and Barometric Pressure.

If we know the sea-level barometric pressure, we can do one of two things.

The first thing we can do is simply to put the SLP into this formula we have already seen:

Pressure Altitude = Physical Altitude + (29.92 - Sea Level Pressure) * 1000

However, if we want to use the station pressure with the table above, then we need to know the station pressure.

An approximation for the station pressure is:

Station Pressure = Sea-level Barometric Pressure - (Physical Altitude / 1000)

You may obtain the sea-level barometric pressure from the weather service. The sea-level barometric pressure is also what is reported by radio and TV stations.

Example: Your local TV station is reporting that the barometric pressure is 30.14 inches. You're at an altitude of 4,500 feet.

Station Pressure = 30.14 - (4500 / 1000) = 30.14 - 4.5 = 25.64

Then use the table above.

But what if we have nothing to tell us the atmospheric pressure at all? Then do this:

Station Pressure = 29.92 - (Physical Altitude / 1000)

No, it's not going to be precisely accurate, as it's based upon two assumptions, one that the barometric pressure at sea level is always 29.92, and a second that atmospheric pressure declines at the rate of 1 inch of mercury per thousand feet of altitude gain - but it's better than nothing.

Step 2 Correction for Temperature

Now, using the example for pressure altitude of 7,420 feet with a temperature of 78 degrees F., we have to correct that for the difference between the ICAO temperature and the actual temperature. Why do we have to do that? Hotter air is less dense than cooler air, so, if the air temperature is warmer than the ISA temperature at our altitude, the density altitude will be correspondingly higher.

Step 2a - Calculation of ISA Temperature at Pressure Altitude

ISA Temperature = 59 - (Pressure Altitude / 1000) * 3.6

ISA Temperature = 59 - (7420 / 1000) * 3.6 = 59 - (7.4 * 3.6) = 59 - 26.64

ISA Temperature = 32.36

Step 2b - Calculation of Temperature Correction in Feet

Correction (feet) = (Actual Temperature - ISA Temperature) * 66.67

Correction (feet) = (78 - 32.36) * 66.67

Correction (feet) = 3043 feet

Step 3 Add Pressure Altitude and Temperature Correction

Density Altitude = Pressure Altitude + Temperature Correction.

Density Altitude = 7420 + 3043

Density Altitude = 10463 feet

The increase from the temperature correction results from the fact that the temperature is above the ISA temperature for that altitude. If the temperature were below the ISA Temperature, the correction would be negative, and the Density Altitude would be lower than the pressure altitude.

Or, you can use this chart to do the temperature correction. Use the Pressure Altitude obtained from Step 1.

5000 Feet DA

Chart Courtesy of Michael Field

How Accurate is this Calculation?

If we put the data from the calculation above into the Density Altitude calculator here this is what we get:

Density Altitude

So, the error is not very large.

It's not as accurate as the calculation of density altitude from a Kestrel or other weather meter.

The calculation neglects humidity - but we know that humidity is a minor factor in shooting at distances out to about 1000 yards with most small arms capable of shooting to that distance with some accuracy.

If we are not using the station pressure to calculate the pressure altitude, we are also an making an assumption that the decline of barometric pressure with altitude is linear and about one inch of mercury per thousand feet. That isn't true at higher altitudes.

So, it's not perfectly accurate at longer distances at higher altitudes. The conclusion we might reasonably draw from that is, if you're going to use a Density Altitude Table for shooting long distances under differing environmental conditions, a Kestrel or other weather meter which calculates density altitude would be a useful piece of kit.

A method which gets us close to the correct answer is better than no answer at all.

Note 1: A precise formula for pressure altitude as a function of station pressure is here. I don't recommend it for manual calculation, unless you have access to a scientific calculator. If you're going to haul around a scientific calculator in the field, you might just as well haul a PDA with an installed ballistic program.

Reference: Equations - Air Density and Density Altitude by Richard Shelquist