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Related Tools
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User Guide
This tool which is based on the us standard atmosphere model will calculate the air pressure at a height above or below sea level, the altitude from the atmospheric air pressure at the same level, the pressure difference between two altitudes, and the altitude difference between two atmospheric pressures.
The method and formulas used are based on the US Standard Atmosphere 1976 model for use from a height of 5000 metres below mean sea level up to a height of 84,852 metres above mean sea level. The atmospheric model assumes the air is a dry ideal gas, with an atmospheric pressure of 101325 Pa and a temperature of 288.15 K at mean sea level.
In reality the atmospheric pressure, temperature & humidity level in the air are constantly changing, therefore the accuracy in determining the true altitude is limited by this. However despite the dynamic nature of the atmosphere, standard atmosphere models serve as a way of standardising measuring instruments. If every measurement instrument is calibrated with the same atmospheric model the readings can be directly compared.
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Formulas
The formulas used by this us standard atmosphere altitude and air pressure calculator to determine each individual parameter are:
For Lb ≠ 0:
P = Pb · (Tb / (Tb + (Lb · (H – Hb))))(g · M) / (R* · Lb)
H = (((Tb / (P / Pb)(R* · Lb) / (g · M)) – Tb) / Lb) + Hb
For Lb = 0
P = Pb · e-g · M · (H – Hb) / (R* · Tb)
H = (ln(P / Pb) · (R* · Tb) / (-g · M)) + Hb
ΔP = P2 – P1
ΔH = H2 – H1
Symbols
- P = Atmospheric pressure at altitude H
- ΔP = Atmospheric pressure difference from H1 to H2 altitude
- Pb = Atmospheric pressure at interfaces between atmosphere transitional layers from b = 0 to 6
- H = Geopotential altitude relative to mean sea level
- ΔH = Geopotential altitude difference from P1 to P2 atmospheric pressure
- Hb = Geopotential altitude from mean sea level of interfaces between atmosphere transitional layers from b = 0 to 6
- Tb = Reference temperature at interface between atmosphere transitional layers from b = 0 to 6
- Lb = Standard temperature lapse rate to change reference temperature (Tb) between atmosphere transitional layers from b = 0 to 6
- g = Standard acceleration due to gravity = 9.90665 m/s2
- M = Molar mass of Earth’s atmosphere = 0.0289644 kg/mol
- R* = Universal gas constant = 8.31432 J/mol·K (* Defined by US Standard Atmosphere 1976 which differs from the current SI defined value of 8.31446261815324)
Atmospheric Layer Constants
| b | Height (m) | Pressure (Pa) | Reference Temperature (K) | Lapse Rate (K/m) |
|---|---|---|---|---|
| 0 | 0 | 101,325 | 288.15 | -0.0065 |
| 1 | 11,000 | 22,632.064 | 216.65 | 0 |
| 2 | 20,000 | 5,474.88867 | 216.65 | 0.001 |
| 3 | 32,000 | 868.018685 | 228.65 | 0.0028 |
| 4 | 47,000 | 110.906306 | 270.65 | 0 |
| 5 | 51,000 | 66.9388731 | 270.65 | -0.0028 |
| 6 | 71,000 | 3.95642043 | 214.65 | -0.002 |
Altitude (H)
This is the geopotential height above or below mean sea level.
Pressure (P)
This is the absolute pressure of air at a particular level in the atmosphere.
Altitude 1 (H1)
This is the initial altitude used in calculating the atmospheric pressure difference between two altitudes.
Altitude 2 (H2)
This is the final altitude used in calculating the atmospheric pressure difference between two altitudes.
Pressure Difference (ΔP = P2 – P1)
This is the atmospheric pressure difference when changing altitude from H1 to H2.
Pressure 1 (P1)
This is the initial atmospheric pressure used in calculating the altitude difference between two atmospheric pressures.
Pressure 2 (P2)
This is the final atmospheric pressure used in calculating the altitude difference between two atmospheric pressures.
Altitude Difference (ΔH = H2 – H1)
This is the altitude difference when changing atmospheric pressure from P1 to P2.
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