6/30/00- Updated 12:54 PM ET Understanding density altitude The idea of density altitude begins with the standard atmosphere, a table of air temperature, pressure and density at various altitudes. The actual values of all of these change with the weather. But, the standard atmosphere figures can be used to calculate for various altitudes how much lift a wing should produce, how much power will come from the engine or engines and how much thrust will push the aircraft along and how much drag should be poroduced. Pilots need to adjust these theoretical values of lift, power and thrust to take account of differences between the standard atmosphere and the real atmosphere at a particular time and place. They use charts or aviation computers to say that the real atmosphere at a particular time has the density of the standard atmosphere at a certain altitude, which is likely to be different from the true altitude. The aircraft performs as though it were at the density altitude. To see how this works, look at our standard atmosphere table. Imagine that you have some kind of device that directly measures the air's density. Imagine that this device tells you the air's density is 0.001812 slugs per cubic foot. You'd find that figure on the chart and then see that it's the density at 9,000 feet in the standard atmosphere. We'd say that the aircraft was at a density altitude of 9,000 feet, no matter what true altitude it's at. In the U.S., such a density altitude is described as a "high density altitude." This can be confusing because you might assume that the word "high" modifies "density." That is, you might thank that the air has a high density as it does at low altitudes. But, "high" really describes the altitude. In other words, the air has a "high-altitude" density, which means the thin air decreases aircraft performance. Most density altitude charts and calculators account for the air pressure and temperature, but not for humidity. Humid air is less dense than dry air, which means performance will suffer on a humid day. But these effects are not as great as temperature and air pressure. Our air density explained text has more on the effects of humidity, along with the other factors that determine density. Air density calculations Air pressure measurements How weather works index The following links are not part of USATODAY.com, but should help you understand density altitude. If you are a pilot or student pilot, they should help you fly safely by being aware of the effects on performance of high density altitude. Use your browser's ''Back button'' to return to this page. National Weahter Service, El Paso office: Density altitude calculator Federal Aviation Administraion: Density altitude information The formula for density altitude Tim Brice of the El Paso NWS office supplied us with the formula. He also has the raw perl script files for the various programs on the El Paso Weather Calculator, including the formula for density altitude, if you want to program a computer to do the calculations. Click here to go to his index to files with the scrips. In the formula, / means to divide, * means to multiply, ** means the following term is an exponent(i.e. X**0.235 means X to the 0.235 power), - means to subtract, + means to add. The standard rules of algebra apply. Density altitude = 145,366[1 - (X** 0.235 ) ] where X = 17.326(Psta) / Temperature in Rankin degrees Psta is the air pressure in inches of mercury. Use the actual peressure (the station pressure) at the elevation (true altitude) that you are interested in. The Temperature in Rankin is: Fahrenheit + 459.69 Brice notes that the temperature in the denominator should be virtual temperature in degrees Rankin, which makes the calculation a little more complicated than most want to deal with. Virtual temperature takes humidity into account. If you do want to be this precise, and do the extra math, go to the USATODAY.com Virtual temperature page for the formula. 09/22/00- Updated 07:23 PM ET The standard atmosphere The standard atmosphere can be thought of as the average pressure, temperature and air density for various altitudes. It is useful for engineering calculations for aircraft. It also shows in a general way the pressures and temperatures to be expected at various altitudes. The standard atmosphere is based on mathematical formulas that reduce temperature and pressure by certain amounts as altitude is gained. But, the results are close to averages of balloon and airplane measurements at various altitudes. The table below uses metric units, which scientists use. Click here for a version using feet, fahrenheit temperatures and pressures in inches of mercury. Height Temperature Pressure Density (m) (C) (hPa) (kg/m3) 0000 15.0 1013 1.2 1000 8.5 900 1.1 2000 2.0 800 1.0 3000 -4.5 700 0.91 4000 -11.0 620 0.82 5000 -17.5 540 0.74 6000 -24.0 470 0.66 7000 -30.5 410 0.59 8000 -37.0 360 0.53 9000 -43.5 310 0.47 10000 -50.0 260 0.41 11000 -56.5 230 0.36 12000 -56.5 190 0.31 13000 -56.5 170 0.27 14000 -56.5 140 0.23 15000 -56.5 120 0.19 16000 -56.5 100 0.17 17000 -56.5 90 0.14 18000 -56.5 75 0.12 19000 -56.5 65 0.10 20000 -56.5 55 0.088 21000 -55.5 47 0.075 22000 -54.5 40 0.064 23000 -53.5 34 0.054 24000 -52.5 29 0.046 25000 -51.5 25 0.039 26000 -50.5 22 0.034 27000 -49.5 18 0.029 28000 -48.5 16 0.025 29000 -47.5 14 0.021 30000 -46.5 12 0.018 31000 -45.5 10 0.015 32000 -44.5 8.7 0.013 33000 -41.7 7.5 0.011 34000 -38.9 6.5 0.0096 35000 -36.1 5.6 0.0082 05/03/2002 - Updated 05:58 PM ET Understanding air density and its effects In simple terms, density is the mass of anything divided by the volume it occupies. As you go higher, the air's density decreases. On this page you'll find information on the effects of lower air density – such as caused by going to high altitudes – on humans, the science of air density, how humidity affects air density – you might be surprised – and the affects of air density of aircraft, Read more Related information Understanding air pressure Understanding water in the atmosphere Understanding density altitude Calculating air density Table showing the standard atmosphere Graphic How high, low air pressure affect weather Effects of lower density on humans If you go high enough, either by climbing a mountain or going up in an airplane that does not have a pressurized cabin, you will begin feeling the effects of lower air pressure and density. As air pressure decreases oxygen continues to account for about 21% of the gasses in the air as it does at seal level. But, there is less oxygen because there is less of all of the air's gasses. For instance, by the time you go to 12,000 feet the air's pressure is about 40% lower than at sea level. This means that with each breath you are getting about 40% less oxygen than at the lower altitude. These effects aren't felt in airliners because the cabins are pressurized to keep the air density inside about the same as it would be about 6,000 or 7,000 feet above sea level. The links below have more information about the effects of lower air density: Princeton U.: High Altitude: Acclimatization and Illnesses WebMD: Altitude sickness High-Altitude Medicine Guide The science of air density The air's density depends on its temperature, its pressure and how much water vapor is in the air. We'll talk about dry air first, which means we'll be concerned only with temperature and pressure. The molecules of nitrogen, oxygen and other gases that make up air are moving around at incredible speeds, colliding with each other and all other objects. The higher the temperature, the faster the molecules are moving. As the air is heated, the molecules speed up, which means they push harder against their surroundings. If the air is in a balloon, heating it will expand the balloon, cooling it will cause the balloon to shrink as the molecules slow down. If the heated air is surrounded by nothing but air, it will push the surrounding air aside. As a result, the amount of air in a particular "box" decreases when the air is heated if the air is free to escape from the box. In the free atmosphere, the air's density decreases as the air is heated. Pressure has the opposite effect on air. Increasing the pressure increases the density. Think of what happens when you press down the handle of a bicycle pump. The air is compressed. The density increases as pressure increases. Altitude and weather systems can change the air's pressure. As you go higher, the air's pressure decreases from around 1,000 millibars at sea level to 500 millibars at around 18,000 feet. At 100,000 feet above sea level the air's pressure is only about 10 millibars. Weather systems that bring higher or lower air pressure also affect the air's density, but not nearly as much as altitude. We see that the air's density is lowest at a high elevation on a hot day when the atmospheric pressure is low, say in Denver when a storm is moving in on a hot day. The air's density is highest at low elevations when the pressure is high and the temperature is low, such as on a sunny but extremely cold, winter's day in Alaska. Humidity and air density Most people who haven't studied physics or chemistry find it hard to believe that humid air is lighter, or less dense, than dry air. How can the air become lighter if we add water vapor to it? Scientists have known this for a long time. The first was Isaac Newton, who stated that humid air is less dense than dry air in 1717 in his book, Optics. But, other scientists didn't generally understand this until later in that century. To see why humid air is less dense than dry air, we need to turn to one of the laws of nature the Italian physicist Amadeo Avogadro discovered in the early 1800s. In simple terms, he found that a fixed volume of gas, say one cubic meter, at the same temperature and pressure, would always have the same number of molecules no matter what gas is in the container. Most beginning chemistry books explain how this works. Imagine a cubic foot of perfectly dry air. It contains about 78% nitrogen molecules, which each have an atomic weight of 28. Another 21% of the air is oxygen, with each molecule having an atomic weight of 32. The final one percent is a mixture of other gases, which we won't worry about. Molecules are free to move in and out of our cubic foot of air. What Avogadro discovered leads us to conclude that if we added water vapor molecules to our cubic foot of air, some of the nitrogen and oxygen molecules would leave — remember, the total number of molecules in our cubic foot of air stays the same. The water molecules that replace nitrogen or oxygen have an atomic weight of 18. This is lighter than both nitrogen and oxygen. In other words, replacing nitrogen and oxygen with water vapor decreases the weight of the air in the cubic foot; that is, it's density decreases. Wait a minute, you might say, "I know water's heavier than air." True, liquid water is heavier, or more dense, than air. But, the water that makes the air humid isn't liquid. It's water vapor, which is a gas that is lighter than nitrogen or oxygen. Compared to the differences made by temperature and air pressure, humidity has a small effect on the air's density. But, humid air is lighter than dry air at the same temperature and pressure. Effects of air density on airplanes, baseballs More dense, or "heavier" air will slow down objects moving through it more because the object has to, in effect, shove aside more or heavier molecules. Such air resistance is called "drag," which increases with air density. Baseball players have found that home runs travel farther in the less dense air in high-altitude Denver than in ball parks at lower elevations. The reduced drag slows the ball down at a slower rate, which means it travels farther. Aircraft pilots don't do as well as baseball players when the air's density decreases. Lower air density penalizes pilots in three ways: The lifting force on an airplane's wings or helicopter's rotor decreases, the power produced by the engine decreases, and the thrust of a propeller, rotor or jet engine decreases. These performance losses more than offset the reduced drag on the aircraft in less dense air. Pilots use charts or calculators to find out how temperature and air pressure at a particular time and place will affect the air's density and therefore aircraft performance. In general, these calculations don't take humidity into account since its affects are so much less than the others. When the air's density is low, airplanes need longer runways to take off and land and they don't climb as quickly as when the air's density is high. Air density also affects the performance of automobiles, with lower density decreasing performance in the same way it decreases the performance of aircraft engines. Turbochargers or superchargers are ways of increasing the density of the air going into an engine. The give autos more power on the ground and they allow aircraft to fly higher into thinner air than they would otherwise. Air Density and Density Altitude Calculations updated: May 31, 2002 What is density altitude? The density altitude is the altitude at which the density of the International Standard Atmosphere (ISA) is the same as the density of the air being evaluated. The Standard Atmosphere is simply a mathematical model of the atmosphere which is standardized so that predictable calculations can be made. So, the basic idea of calculating density altitude is to calculate the actual density of the air, and then find the altitude at which that same air density occurs in the Standard Atmosphere. In the following paragraphs, we'll go step by step through the process of calculating the actual density of the air, and then determining the corresponding density altitude. Density and Density Altitude: Although the concept of density altitude is commonly used to help express the effects of aircraft performance, the really important quantity is actually the air density. For example, the lift of an aircraft wing, the aerodynamic drag and the thrust of a propeller blade are all directly proportional to the air density. The downforce of a racecar spoiler is also directly proportional to the air density. Similarly, the horsepower output of an internal combustion engine is related to the air density. The correct size of a carburetor jet is related to the air density, and the pulse width command to an electronic fuel injection nozzle is also related to the air density. Density altitude has been a convenient yardstick for pilots to compare the performance of aircraft at various altitudes, but it is in fact the air density that is the fundamentally important quantity, and density altitude is simply a way to express the air density. Units: The 1976 International Standard Atmosphere is mostly described in metric SI units, and I have chosen to use those same units (in general). See ref 8 and ref 9 for conversion factors to your favorite units. Air Density Calculations: To begin to understand the calculation of air density, consider the ideal gas law: (1) P*V = n*R*T where: P = pressure V = volume n = number of moles R = gas constant T = temperature Density is simply the number of molecules of the ideal gas in a certain volume, in this case a molar volume, which may be mathematically expressed as: (2) D = n / V where: D = density n = number of molecules V = volume Then, by combining the previous two equations, the expression for the density becomes: (3) where: D = density, kg/m3 P = pressure, Pascals ( multiply mb by 100 to get Pascals) R = gas constant , J/(kg*degK) = 287.05 for dry air T = temperature, degK = deg C + 273.15 As an example, using the ISA standard sea level conditions of P = 101325 Pa and T = 15 deg C, the air density at sea level, may be calculated as: D = (101325) / (287.05 * (15 + 273.15)) = 1.2250 kg/m3 This example has been derived for the dry air of the standard conditions. However, for real-world situations, it is necessary to understand how the density is affected by the moisture in the air. The density of a mixture of dry air molecules and water vapor molecules may be expressed as: (4) where: D = density, kg/m3 Pd = pressure of dry air, Pascals Pv= pressure of water vapor, Pascals Rd = gas constant for dry air, J/(kg*degK) = 287.05 Rv = gas constant for water vapor, J/(kg*degK) = 461.495 T = temperature, degK = deg C + 273.15 To determine the density of the air, it is necessary to know is the actual air pressure (also known as absolute pressure, or station pressure), the water vapor pressure, and the temperature. It is possible to obtain a rough approximation of the absolute pressure by adjusting an altimeter to read zero altitude and reading the value in the Kollsman window as the actual air pressure, but this method only gives the correct reading if the ambient air temperature happens to be the same as standard temperature at your elevation. Near the end of this page I'll discuss how to use the altimeter reading to accurately determine the actual pressure. Alternatively, there are many little electronic gadgets that can measure the actual air pressure directly, and quite accurately. The water vapor pressure can be determined from the dew point or from the relative humidity, and the ambient temperature can be measured in a well ventilated place out of the direct sunlight. In the following section, we'll calculate the portion of the total air pressure that is due to the water vapor in the air that is being measuring. Vapor Pressure: A very accurate, albeit quite odd looking, formula for determining the saturation vapor pressure is a polynomial developed by Herman Wobus (see ref 2 ) : (5) Es = eso * p-8 where: Es = saturation pressure of water vapor, mb eso=6.1078 p = (c0+T*(c1+T*(c2+T*(c3+T*(c4+T*(c5+T*(c6+T*(c7+T*(c8+T*(c9)))))))))) T = temperature, deg C c0=0.99999683 c1=-0.90826951*10-2 c2=0.78736169*10-4 c3=-0.61117958*10-6 c4=0.43884187*10-8 c5=-0.29883885*10-10 c6=0.21874425*10-12 c7=-0.17892321*10-14 c8=0.11112018*10-16 c9=-0.30994571*10-19 For situations where a slightly less accurate formula is acceptable, the following equation offers good results, especially at the higher ambient air temperatures where the saturation pressure becomes significant for the density altitude calculations. (6) where: Es = saturation pressure of water vapor, mb Tc = temperature, deg C c0 = 6.1078 c1 = 7.5 c2 = 237.3 See ref 2 and ref 11 for additional vapor pressure formulas. Here's a calculator that evaluates the saturation vapor pressure using equations 5 and 6 as given above: Saturated Vapor Press Calculator Air Temperature degrees C Sat vapor press from Eqn 5 mb Sat vapor press from Eqn 6 mb by Richard Shelquist The Smithsonian reference tables (see ref 1) give the following values of saturated vapor pressure values at specified temperatures. Entering these known temperatures into the calculator will allow you to evaluate the accuracy of the calculated results. Deg C Es, mb 30 42.430 20 23.373 10 12.272 0 6.1078 -10 2.8627 -30 0.5088 Armed with the vapor pressure equations, the next step is to determine the actual value of vapor pressure. When calculating the vapor pressure, it is often more accurate to use the dew point temperature that the relative humidity. Although relative humidity can be used to determine the vapor pressure, the value of relative humidity is strongly affected by the ambient temperature, and is therefore constantly changing during the day as the air is heated and cooled. In contrast, the value of the dew point is much more stable and is often nearly constant for a given air mass. Therefore, using the dew point as the measure of humidity allows for more stable and therefore potentially more accurate results. Actual Vapor Pressure from the Dew Point: To determine the actual vapor pressure, simply use the dew point as the value of T in equation 5 or 6. That is, at the dew point, Es = Pv. (7) Es = Pv at the dew point Actual Vapor Pressure from Relative Humidity: Relative humidity is defined as the ratio (expressed as a percentage) of the actual vapor pressure to the saturation vapor pressure at a given temperature. To find the actual vapor pressure, simply multiply the saturation vapor pressure by the percentage and the result is the actual vapor pressure. For example, if the relative humidity is 40% and the temperature is 30 deg C, then the saturation vapor pressure is 42.43 mb and the actual vapor pressure is 40% of 42.43 mb, which is 16.97 mb. Density Calculations: Now that the actual vapor pressure is known, we can calculate the density of the combination of dry air and water vapor as described in equation 4. The total measured atmospheric pressure is the sum of the pressure of the dry air and the vapor pressure: (8) P = Pd + Pv where: P = total pressure Pd = pressure due to dry air Pv = pressure due to water vapor So, rearranging that equation, we see that Pd = P-Pv. Now we have all of the information that is required to calculate the air density. Calculate the air density: Now armed with those equations and the actual air pressure, the vapor pressure and the temperature, the density of the air can be calculated.. Here's a calculator that determines the air density from the actual pressure, dew point and air temperature using equations 4, 6, 7 and 8 as defined above: Air Density Calculator Air Temperature degrees C Actual Air Pressure mb Dew Point degrees C Air Density kg/m3 by Richard Shelquist Some examples of calculations using air density: Example 1) The lift of an aircraft wing may be described mathematically (see ref 8) as: L = c1 * d * v2/2 * a where: L = lift c1 = lift coefficient d = air density v = velocity a = wing area From the lift equation, we see that the lift of a wing is directly proportional to the air density. So if a certain wing can lift, for example, 3000 pounds at sea level standard conditions where the density is 1.2250 kg/m3, then how much can the wing lift on a warm summer day in Denver when the air temperature is 95 deg (35 deg C), the actual pressure is 24.45 in-Hg (828 mb) and the dew point is 67 deg F (19.4 deg C)? The answer is about 2268 pounds. Example 2) The engine manufacturer Rotax advises that their carburetor main jet should be adjusted according to the air density (see ref 6). Specifically, if the engine is jetted properly at air density d1, then for operation at air density d2 the new jet diameter j2 is given mathematically as (Note: in some equations, where the exponent may not be obvious, the symbol ** is used to denote exponentiation.): j2 = j1 * (d2/d1)**(1/4) where: j2 = diameter of new jet j1 = diameter of jet that was proper at density d1 d1 = density at which the original jet j1 was correct d2 = the new air density That is, Rotax says that the correct jet diameter should be sized according to the fourth root of the ratio of the air densities (i.e. take the square root twice). For example, if the correct jet at sea level standard conditions is a number 160 and the jet number is a measure of the jet diameter, then what jet should be used for operations on the warm summer day in Denver described above? The ideal answer is a jet number 149, and in practice the closest available jet size is then selected. Example 3) In the same service bulletin mentioned above, Rotax says that their engine horsepower will decrease in proportion to the air density. hp2 = hp1 * (d2/d1) where: hp2 = the new horsepower at density d2 hp1 = the old horsepower at density d1 If a Rotax engine was rated at 38 horsepower at sea level standard conditions, what is the available horsepower according to that formula when the engine is operated at a temperature of 30 deg C, a pressure of 925 mb and a dew point of 25 deg C? The answer is approximately 32 horsepower. (Click this link for details on the SAE method of correcting horsepower.) Back on the trail of Density Altitude... The definition of density altitude is the altitude at which the density of the 1976 International Standard Atmosphere is the same as the density of the air being evaluated. So, now that we know how to determine the air density, we can solve for the altitude in the International Standard Atmosphere that has the same value of density. The International Standard Atmosphere is a mathematical description of a theoretical column of air (see ref 5). To get the proper results, it is necessary to use the following constants that are specified in the 1976 International Standard Atmosphere document: Po = 101325 sea level standard pressure, Pa To = 288.15 sea level standard temperature, deg K g = 9.80665 gravitational constant, m/sec2 L = 6.5 temperature lapse rate, deg K/km R = 8.31432 gas constant, J/ mol*deg K M = 28.9644 molecular weight of dry air, gm/mol In the ISA, the lowest region is the troposphere which extends from sea level up to 11 km (about 36,000 ft). The model that will be developed here is only valid in the troposphere. The equations that define the air in the troposphere are: (9) (10) (11) where: T = ISA temperature in deg K P = ISA pressure in Pa D = ISA density in kg/m3 H = ISA geopotential altitude in km One way to determine the altitude at which a certain density occurs is to rewrite the equations and solve for the variable H, which is the geopotential altitude. So, it is now necessary to rewrite equations 9, 10, and 11 in a manner that expresses altitude H as a function of density D. After a bit of gnashing of teeth and general turmoil, the exact solution for H as a function of D, may be written as: (12) Using the numerical values of the ISA constants, that expression may be evaluated as: where H = geopotential altitude, km D = air density, kg/m3 Now that H is known as a function of D, it is easy to solve for the Density Altitude of any specified air density. It is interesting to note that equations 9, 10 and 11 could also be evaluated to find H as a function of P as follows: where H = geopotential altitude, km P = actual air pressure, Pascals Now that we can determine the altitude for a given density, it may be useful to consider some of the definitions of altitude. Different Flavors of Altitude: There are three commonly used varieties of altitude (see ref 4). They are: Geometric altitude, Geopotential altitude and Pressure altitude. Geometric altitude is what you would measure with a tape measure, while the Geopotential altitude is a mathematical description based on the potential energy of an object in the earth's gravity. Pressure altitude is what an altimeter displays when set to 29.92. The ISA equations use geopotential altitude, because that makes the equations much simpler and more manageable. To convert the result from the geopotential altitude H to the geometric altitude Z, the following formula may be used: (13) where E = 6356 km, the radius of the earth (for 1976 ISA) H = geopotential altitude, km Z = geometric altitude, km Density Altitude Calculator: The following calculator uses equation 12 to convert an input value of air density to the corresponding altitude in the 1976 International Standard Atmosphere. Then, the results are displayed as both geopotential altitude and geometric altitude, which are very nearly identical at lower altitudes. Note that since these equations are designed to model the troposphere, this calculator will give an error message if the calculated value of altitude is beyond the bounds of the troposphere, which extends from sea level up to a geopotential altitude of 11 km. Density Altitude Calculator 1 Air Density kg/m3 Geopotential altitude H m Geometric altitude Z m by Richard Shelquist Here's a calculator that uses the actual pressure, air temperature and dew point to calculate the air density as well as the corresponding density altitude: Density Altitude Calculator 2 Air Temperature degrees C Actual Air Pressure mb Dew Point degrees C Air Density kg/m3 Geopotential altitude H m Geometric altitude Z m by Richard Shelquist Density Altitude calculations using Virtual Temperature: As an alternative to the use of equations which describe an atmosphere made up up the combination of air and water vapor, it is possible to define a virtual temperature and then consider the atmosphere to be only dry air. The virtual temperature is the temperature that dry air would have if its pressure and specific volume were equal to those of a given sample of moist air. It's often easier to use virtual temperature in place of the actual temperature to account for the effect of water vapor while continuing to use the gas constant for dry air. The results should be exactly the same as in the previous method, this is just an alternative method. There are two steps in this scheme: first calculate the virtual temperature and then use that temperature in the corresponding altitude equation. The equation for virtual temperature may be derived by manipulation of the density equation that was presented earlier as equation 4: Recalling that P = Pd + Pv, which means that Pd = P - Pv, the equation may be rewritten as Finally, a new temperature Tv, the virtual temperature, is defined such that By evaluating the numerical values of the constants, setting Pv = E, noting that Rd = R*1000/Md and that Rv=R*1000/Mv, then the virtual temperature may be expressed as: (14) where Tv = virtual temperature, deg K T = ambient temperature, deg K c1 = ( 1 - (Mv / Md ) ) = 0.37800 E = vapor pressure, kg/m3 P = actual (station) pressure, mb where Md is molecular weight of dry air = 28.9644 Mv is molecular weight of water = 18.016 (Note that for convenience, the units in Equation 14 are not purely SI units, but rather are customary units for the vapor pressure and station pressure.) The following calculator uses equation 6 to find the vapor pressure, then calculates the virtual temperature using equation 14: Virtual Temperature Calculator Air Temperature degrees C Actual Air Pressure mb Dew Point degrees C Virtual Temperature degrees C by Richard Shelquist The virtual temperature Tv may used in the following formula to calculate the density altitude. This formula is simply a rearrangement of equations 9, 10 and 11: (15) Using the numerical values of the ISA constants, equation 15 may be rewritten using the virtual temperature as: where H = geopotential density altitude, km Tv = virtual temperature, deg K P = actual (station) pressure, Pascals Using the Altimeter Setting: When the actual pressure is not known, the altimeter reading may be used to determine the actual pressure. The altimeter setting is the value in the Kollsman window of an altimeter when the altimeter is adjusted to read the correct altitude. The altimeter setting is generally included in National Weather Service reports, and can be used to determine the actual pressure using the following equations: According to NWS ASOS documentation, the actual pressure Pa is related to the altimeter setting AS by the following equation: (16) By numerically evaluating the constants and converting to customary units of altitude and pressure, the equation may be written as: Pa = [ASk1 - ( k2 * H ) ]1/k1 where Pa = actual (station) pressure, mb AS = altimeter setting, mb H = geopotential station elevation, m k1 = 0.190263 k2 = 8.417286*10-5 When converted to English units, this is the relationship between station pressure and altimeter setting that is used by the National Weather Service ASOS weather stations (see ref 10 ) as: Pa = [AS0.1903 - (1.313 x 10-5) x H]5.255 where Pa = actual (station) pressure, inches Hg AS = altimeter setting, inches Hg H = station elevation, feet Using these equations, the altimeter setting may be readily converted to actual pressure, then by using the actual pressure along with the temperature and dew point, the local air density may be calculated, and finally the density may be used to determine the corresponding density altitude. Given the values of the altimeter setting (the value in the Kollsman window) and the altimeter reading (the geometric altitude), the following calculator will convert the altitude to geopotential altitude, and solve equation 16 for the actual pressure at that altitude. Altimeter Setting to Actual Pressure Altimeter Setting hPa (mb) Geometric Altitude meters Geopotential Altitude meters Actual Pressure hPa (mb) by Richard Shelquist Using National Weather Service Barometric Pressure: Now you're probably wondering about converting sea-level corrected barometric pressure, as commonly reported by the National Weather Service, to actual air pressure for use in calculating density altitude. Well the good news is that yes, sea level barometric pressure can be converted to actual air pressure. The bad news is that the result may not be very accurate. If you want accurate density or density altitude calculations, you really need to know the actual air pressure. In order to compare surface pressures from various parts of the country, the National Weather Service converts the actual air pressure reading into a sea level corrected barometric pressure. In that way, the common reference to sea level pressure readings allows surface features such as pressure changes to be more easily understood. But, unfortunately, there really is no fool-proof way to convert the actual air pressure to a sea level corrected value. There are a number of such algorithms currently in use, but they all suffer from various problems that can occasionally cause inaccurate results (see ref 7). It has been estimated that the errors in the sea level pressure reading (in mb) may be on the order of 1.5 times the temperature error for a station like Denver at 1640 meters. So, if the temperature error was 10 deg C, then the sea level pressure conversion might occasionally be in error by 15 mb. At the very highest airports such as Leadville, Colorado at an elevation of 3026 meters (9927 ft), perhaps the error might be on the order of 30 mb. And further complicating matters, without knowing the details of the algorithm that was used to calculate the sea level pressure, it is likely that there will be some additional error introduced in the process of converting the sea level pressure back to the desired actual station pressure. These error estimates are probably on the extreme side, but it seems reasonable to say that the density altitude calculations made using the National Weather Service sea level pressure calculations may have an uncertainty of ±10% or more. When using pressure data from the National Weather Service, be certain to find out if the pressure is the altimeter setting or the sea-level corrected pressure. They may be quite different in some situations. Density Altitude Algorithm... Here is a list of the steps performed by my Density Altitude Calculator : 1. convert ambient temperature to deg C, 2. convert geometric (survey) altitude to geopotential altitude in meters, 3. convert dew point to deg C, 4. convert altimeter setting to mb. 5. calculate the saturation vapor pressure, given the ambient temperature 6. calculate the actual vapor pressure given the dew point temperature 7. use geopotential altitude and altimeter setting to calculate the absolute pressure in mb, 8. use absolute pressure, vapor pressure and temp to calculate air density in kg/m3, 9. use the density to find the ISA altitude in meters which has that same density, 10. convert the ISA geopotential altitude to geometric altitude in meters, 11. convert the geometric altitude into the desired units and display the results. On-Line Calculators: Click here for Density Altitude Calculator with English units only. Click here for Density Altitude Calculator with Metric units only. Click here for Density Altitude Calculator using relative humidity rather than dew point. Click here for Density Altitude Calculator with both English and Metric units. Click here for new Engine Tuner's Calculator that includes relative horsepower, air density, density altitude, virtual temperature, absolute pressure, vapor pressure, relative humidity and dyno correction factor! Simpler Methods of Calculation... If you want to know the actual density altitude, it will need to be calculated in a manner similar to what I have described above. There are many forms of simpler approximations and generalizations that have been developed over the years, but they are not really density altitude, they are just numbers that are kinda like density altitude. When the air is dry, the approximations and simplifications can be fairly accurate but in real life situations with moisture in the air they can be quite inaccurate.