Density Altitude, Air Density & Pressure Altitude

1. Density

Density is the mass per unit volume of a substance.

In atmospheric applications, density may be expressed as:

• g/m³
• kg/m³
• Percentage of standard surface density, also called relative density

Important ISA Value

• ISA Mean Sea Level density: 1225 g/m³

2. Relationship Between Pressure, Temperature and Density

Air density is governed primarily by pressure and temperature, and is also affected by humidity.

The Gas Law relationship is:

ρ ∝ P/T

Where:

• ρ = air density
• P = pressure
• T = absolute temperature

Therefore:

Key Rule

Density is directly proportional to pressure and inversely proportional to temperature.

3. Effect of Humidity on Air Density

Moist air is less dense than dry air when pressure and temperature are the same.

The reason is that water vapour (H₂O) has a lower molecular mass than the main constituents of dry air:

• Nitrogen (N₂)
• Oxygen (O₂)

When water vapour is added to air, lighter H₂O molecules replace some of the heavier N₂ and O₂ molecules. This reduces the total mass per unit volume.

Important Points

• Higher water-vapour content → lower density
• Lower water-vapour content → higher density
• Water vapour has approximately 5/8 the density of dry air
• Moist air therefore produces a higher Density Altitude for the same pressure and temperature conditions.

4. Conditions Producing Low and High Air Density

Lowest Air Density

The lowest air density occurs with the combination of:

• Low pressure
• High temperature
• High humidity

This combination is particularly important at hot, high-altitude aerodromes.

Effect on Aircraft

Low air density results in:

• Reduced lift
• Reduced engine performance
• Reduced thrust
• Increased takeoff distance
• Increased landing distance/run
• Reduced climb performance
• Reduced maximum takeoff weight capability

Highest Air Density

The highest density occurs with:

• High pressure
• Low temperature
• Lower humidity

Quick Memory Rule

High pressure + cold air = high density
Low pressure + hot, humid air = low density

5. Pressure Altitude (PA)

Pressure Altitude is the altitude in the International Standard Atmosphere (ISA) at which the atmospheric pressure is equal to the pressure at the point in question.

In Simple Terms

Pressure Altitude represents the ISA altitude corresponding to the observed pressure.

6. Density Altitude (DA)

Density Altitude is the altitude in the International Standard Atmosphere (ISA) at which the observed air density exists.

It is essentially Pressure Altitude corrected for temperature deviation from ISA.

Density Altitude is important because aircraft and engine performance depend strongly on air density.

7. Pressure Altitude vs Density Altitude

Most Important Rule

DA = PA only when OAT = ISA temperature.

8. Density Altitude Formula

The commonly used examination formula is:

DA = PA + (ISA Deviation × 120 ft)

Where:

ISA Deviation = OAT − ISA Temperature

Therefore, the complete procedure is:

1. Determine the Pressure Altitude.
2. Calculate the ISA temperature at that altitude.
3. Calculate the ISA deviation.
4. Multiply the deviation by 120 ft/°C.
5. Add the correction to the Pressure Altitude.

9. Effect of Temperature on Density Altitude

If Temperature is Higher Than ISA

• ISA deviation is positive
• Density decreases
• Density Altitude increases
• DA > PA
• Aircraft performance decreases

If Temperature is Lower Than ISA

• ISA deviation is negative
• Density increases
• Density Altitude decreases
• DA < PA
• Aircraft performance improves

If Temperature Equals ISA

• ISA deviation = 0°C
• DA = PA

10. Density Altitude Correction Factor

For examination calculations:

1°C ISA deviation = approximately 120 ft change in Density Altitude

Therefore:

• +1°C → DA increases by 120 ft
• +5°C → DA increases by 600 ft
• +7°C → DA increases by 840 ft
• −1°C → DA decreases by 120 ft
• −4°C → DA decreases by 480 ft

Memory Rule

Warm → DA goes up
Cold → DA goes down

11. ISA Temperature

For common examination calculations below approximately 36,090 ft, use:

ISA temperature at MSL = +15°C

Approximate lapse rate:

2°C per 1,000 ft

Therefore:

ISA Temperature = 15°C − (2 × altitude in thousands of feet)

For example, at 12,000 ft:

ISA Temperature = 15 − (2 × 12)

= 15 − 24

= −9°C

12. ISA Temperature Above 36,090 ft

The source states that the ISA temperature decreases up to approximately:

36,090 ft / 11 km

Above this level, up to approximately:

65,617 ft / 20 km

the temperature remains approximately constant at:

−56.5°C

Therefore:

13. Step-by-Step Density Altitude Calculation

Example 1: PA = 12,000 ft, OAT = −12°C

Step 1: Find ISA Temperature

ISA lapse rate = 2°C/1,000 ft

ISA Temp = 15 − (2 × 12)

= −9°C

Step 2: Find ISA Deviation

ISA Deviation = OAT − ISA Temp

= −12 − (−9)

= −3°C

The air is 3°C colder than ISA.

Step 3: Calculate DA

DA = PA + (ISA deviation × 120)

= 12,000 + (−3 × 120)

= 12,000 − 360

Answer

DA = 11,640 ft

Since the air is colder than ISA:

DA < PA

14. Example: PA = 22,000 ft, OAT = −22°C

ISA Temperature

ISA Temp = 15 − (2 × 22)

= −29°C

ISA Deviation

= −22 − (−29)

= +7°C

The air is 7°C warmer than ISA.

Density Altitude

DA = 22,000 + (7 × 120)

= 22,000 + 840

Answer

DA = 22,840 ft

Because the air is warmer than ISA:

DA > PA

15. Example: PA = 25,000 ft, OAT = −30°C

ISA Temperature

ISA Temp = 15 − (2 × 25)

= −35°C

ISA Deviation

= −30 − (−35)

= +5°C

Density Altitude

DA = 25,000 + (5 × 120)

= 25,000 + 600

Answer

DA = 25,600 ft

The air is warmer than ISA, so the DA is higher than the PA.

16. Example: PA = 15,000 ft, OAT = −8°C

ISA Temperature

ISA Temp = 15 − (2 × 15)

= −15°C

ISA Deviation

= −8 − (−15)

= +7°C

Density Altitude

DA = 15,000 + (7 × 120)

= 15,000 + 840

Answer

DA = 15,840 ft

17. Example: PA = 20,000 ft, OAT = −22°C

ISA Temperature

ISA Temp = 15 − (2 × 20)

= −25°C

ISA Deviation

= −22 − (−25)

= +3°C

Density Altitude

DA = 20,000 + (3 × 120)

= 20,000 + 360

Answer

DA = 20,360 ft

18. Example: PA = 40,000 ft, OAT = −60.5°C

At 40,000 ft, the source uses the ISA temperature of:

−56.5°C

ISA Deviation

= −60.5 − (−56.5)

= −4°C

The air is 4°C colder than ISA.

Density Altitude

DA = 40,000 + (−4 × 120)

= 40,000 − 480

Answer

DA = 39,520 ft

Therefore:

DA < PA

19. Density at FL 180

The source gives the following example:

Pressure

FL 180 = 18,000 ft

In ISA:

Pressure = 500 hPa

ISA Temperature

Using approximately 2°C/1,000 ft:

ISA Temp = 15 − (2 × 18)

= −21°C

Actual Temperature

OAT = −35°C

Therefore:

−35°C < −21°C

The actual air is colder than ISA.

Because density is inversely proportional to temperature:

Colder air → higher density

Conclusion

At FL 180, with the same pressure of 500 hPa, the air at −35°C has a greater density than ISA air at −21°C.

20. Density and Altitude

As altitude increases:

• Weight of the overlying air decreases.
• Atmospheric pressure decreases.
• Temperature generally decreases through the troposphere.
• The decrease in pressure has a greater effect on density than the decrease in temperature.

Therefore:

Air density decreases rapidly with increasing altitude.

Important Figure

At approximately 20,000 ft, air density is about 50% of its surface value.

21. Pressure Effect vs Temperature Effect

Although colder air tends to increase density, the reduction in pressure with altitude has a much stronger effect.

The source gives the following comparison near the surface:

• 10 hPa decrease in pressure → approximately 1% reduction in density
• 1°C decrease in temperature → approximately 0.3% increase in density

Therefore, during vertical movement:

Pressure change has a much greater effect on density than the opposing temperature change.

22. Density and Latitude

At the Earth’s surface:

• The Equator is warmer → lower density.
• The Poles are colder → higher density.

Therefore, at the surface:

Density generally increases from the Equator toward the Poles.

23. Change in Density with Latitude at Altitude

The source identifies an important reversal at approximately 26,000 ft (about 8 km).

Below approximately 26,000 ft

• Density is generally lower near the Equator.
• Density generally increases toward the Poles.
• Around 26,000 ft, density tends to become approximately uniform with latitude.

Above approximately 26,000 ft

The relationship reverses:

• Density decreases with increasing latitude.
• Density becomes lower toward the Poles.
• Therefore, at high altitudes, density can be lower over the Poles than over the Equator.

Why?

Although polar air is colder, the pressure decreases more rapidly with height over the cold polar air column. The pressure effect dominates the temperature effect.

Exam Memory Point

Around 8 km / 26,000 ft: density becomes approximately equal across latitudes. Above this level, the latitude–density relationship reverses.

24. Important Tropopause Comparison

The source specifically notes the comparison between summer and winter tropopause:

Memory Point

Winter tropopause → lower and warmer than summer tropopause.

25. Anticyclonic Conditions and Density

An anticyclone is associated with relatively high pressure.

At a constant temperature:

Pressure ↑ → Density ↑

Therefore, compared with an area of lower pressure, air under anticyclonic/high-pressure conditions will have greater density, assuming temperature is the same.

Important Exam Logic

If the question compares density under different pressure conditions while temperature is constant:

Choose the higher-pressure condition for higher density.

26. Density Altitude and Aircraft Performance

Density Altitude is an important indicator of aircraft performance.

High Density Altitude

High DA means:

Lower air density

Consequently:

• Lift decreases.
• Engine performance decreases.
• Thrust decreases.
• Takeoff roll increases.
• Landing run increases.
• Climb performance decreases.
• Maximum takeoff weight capability may be reduced.

Low Density Altitude

Low DA means:

Higher air density

Consequently:

• Lift improves.
• Engine performance improves.
• Takeoff roll is reduced.
• Climb performance improves.

27. Complete Relationship Table

Density Altitude

28. Most Important Formulas

Gas Law Relationship

ρ ∝ P/T

ISA Temperature

For the common exam approximation below 36,090 ft:

ISA Temp = 15°C − (2°C × altitude in thousands of feet)

ISA Deviation

ISA Deviation = OAT − ISA Temperature

Density Altitude

DA = PA + (ISA Deviation × 120 ft)

Correction

1°C deviation = approximately 120 ft DA correction

29. Quick Exam Rules

Warm air → low density → high Density Altitude → poor aircraft performance

Cold air → high density → low Density Altitude → better aircraft performance

High pressure → high density

Low pressure → low density

High humidity → low density

Low humidity → higher density

High altitude → low pressure → low density

DA > PA → warmer than ISA

DA < PA → colder than ISA

DA = PA → OAT = ISA

1°C ISA deviation → 120 ft DA correction

Lowest density → low pressure + high temperature + high humidity

30. High-Value Exam Summary

One-Line Memory Aid

“High, Hot and Humid = High Density Altitude and Poor Performance.”