Density Altitude Formula: How to Calculate it Correctly

Article and Photo by Ally Melick, CRJ Pilot, CFI-I, MEI

Everywhere in the country flight training is a unique experience. At the airport I trained at in Denver, low level windshear alerts were present daily from wind coming off the mountains. Winter flying started no earlier than noon when the ice finally melted off the planes, and summer flying consisted of early morning flights to avoid the afternoon thunderstorms and high density altitude. The mile high city is beautiful and colorful, but it certainly brings challenges when it comes to flying.

One of the benefits of training right next to the mountains is the gorgeous scenery and opportunity to explore the mountains and learn all the tricks to mountain flying. The most important takeaway as a mountain instructor was density altitude. By 11am, there was no chance of powering out of a downdraft over a pass so flights had to be scheduled at 5 or 6 am. When you’re already climbing up to 12,000 feet to get over a mountain ridge, the last thing you want is for the plane to be performing as if it were at 15,000 feet.

ISA

The International Standard Atmosphere (ISA) is a model that is used as a reference to standardize aircraft instruments. The standard pressure and temperature is 29.92 inches of mercury (Hg) and 15 degrees celsius. This information is used to properly calculate performance data before taking to the sky. Aircraft perform best at sea level due to the dense air. Changes in temperature or pressure will affect performance. In order to account for these changes we use what’s called the standard lapse rate. The temperature in a standard atmosphere decreases approximately 2 degrees celsius per 1000 feet. For example, at Rocky Mountain Metropolitan Airport (KBJC) the field elevation is 5,673 ft, so the standard temperature would be about 4 degrees celsius. The pressure decreases by about 1” Hg per 1000 ft. 

Defining Altitude

You’ve probably heard the book definition: density altitude is pressure altitude corrected for non-standard temperature variations. In order to understand what that means, there are a couple other altitude definitions that come into play. Indicated altitude is the altitude read directly off the altimeter. Pressure altitude is corrected for non-standard temperature. Standard atmospheric pressure is 29.92 inches of mercury (Hg). Pressure and density are directly proportional meaning that as pressure increases, air density increases. If you set the altimeter to the standard 29.92, you can read the pressure altitude off of the altimeter. For the purposes of calculating aircraft performance, pressure altitude can be calculated using the following formula: [(29.92 - altimeter setting) x 1000] + field elevation. Let’s take KBJC’s field elevation of 5,673 and say the altimeter setting was 30.10. Here’s the math:

Pressure altitude = [(29.92 - 30.10) x 1000] + 5,673

Pressure altitude = [-0.18 x 1000] + 5,673

Pressure altitude = -180 + 5,673

Pressure altitude = 5,493

When you look in the pilot’s operating handbook (POH) to calculate the performance numbers you would use 5,493 as the altitude. Now back to density altitude. Our calculations have been corrected for non-standard pressure, but temperature changes will affect aircraft performance as well. Standard temperature is 15 degrees celsius. Temperature and density are inversely proportional; as temperature increases air density decreases. The formula for Density altitude is pressure altitude + [120 x (OAT - ISA)]. Using the pressure altitude calculated above, this is what it would look like if it was 30 degrees celsius.

Density altitude = 5,493 + [120 x (35 - 15)]

Density altitude = 5,493 + [120 x 20]

Density altitude = 5,493 + 2400

Density altitude = 7,893

In terms of performance, this means that at field elevation, on the ground, your aircraft is going to perform as if it were at 7,893 feet. 

Performance

The first time I flew a plane at sea level was an entirely different experience than the high altitude flying I was used to. Even as a commercial pilot at the time I was caught off guard using full mixture to take off, and was amazed by our climb rate in that Cessna 150. If you add density altitude into the equation, calculating your performance before the flight is essential. Climbing from sea level to 3,000 feet in a Cessna 172 would take about 5 minutes at a rate of 600 feet per minute (FPM) or better, climbing from 8,000 feet to 11,000 in the same plane would take about 20 minutes at a rate of 300 FPM or less. There is a lot of danger involved with flying at high altitudes, so being aware of density altitude and understanding how it may affect your flight could save your life.

Article and Photo by Ally Melick, CRJ Pilot, CFI-I, MEI