liminfoAtmosphere Model
Free reference guide: Atmosphere Model
About Atmosphere Model
The ISA Standard Atmosphere Reference is a free online tool providing comprehensive data for the International Standard Atmosphere (ISA) as defined by ICAO. It includes sea-level reference values (T0=288.15K, P0=101325Pa, rho0=1.225 kg/m3), physical constants (R=287.058 J/kg-K, gamma=1.4), atmospheric layer definitions with lapse rates from 0 to 84,852 meters across all seven ISA layers (troposphere, tropopause, stratosphere, and beyond), and complete formulas for temperature, pressure, density, and speed of sound calculations.
This reference serves aerospace engineers, pilots, meteorologists, and aviation students who need accurate ISA data for aircraft performance calculations, flight planning, and atmospheric science. It covers practical aviation applications including pressure altitude, density altitude (DA = PA + 118.8 x (OAT - ISA_temp)), TAS/CAS/EAS airspeed conversions, Mach number calculations, and dynamic pressure. Pre-computed altitude data is available for key reference points: sea level, 1000m, 3000m, 5000m, 8848m (Everest), 11000m (tropopause), and 20000m.
The reference also includes ready-to-use Python and JavaScript code examples for computing ISA values programmatically, covering both the troposphere (0-11 km) and the full 7-layer atmosphere model (0-84 km). All data is accessible offline with instant search and category filtering across ISA Constants, Core Formulas, Altitude Data, Aviation Applications, and Code Examples.
Key Features
- Complete ISA sea-level constants and atmospheric physical constants (R, gamma, molar mass)
- Seven atmospheric layer definitions with temperature lapse rates from 0 to 84,852 meters
- Core formulas: troposphere temperature/pressure, isothermal layer pressure, air density, speed of sound
- Pre-computed altitude data tables at sea level, 1000m, 3000m, 5000m, 8848m, 11000m, and 20000m
- Aviation applications: pressure altitude, density altitude, TAS/CAS/EAS conversion, Mach number, dynamic pressure
- Ready-to-use Python and JavaScript code for troposphere and full 7-layer ISA calculations
- Bilingual Korean and English with instant search and five-category filtering
- Fully offline-capable after page load with mobile-responsive design
Frequently Asked Questions
What is the International Standard Atmosphere (ISA)?
The ISA is a model of atmospheric conditions defined by ICAO, establishing standard values for temperature, pressure, density, and other properties as a function of altitude. At sea level, ISA conditions are: temperature 15 degrees C (288.15 K), pressure 101,325 Pa (1013.25 hPa or 29.92 inHg), and density 1.225 kg/m3. The ISA serves as the baseline for aircraft performance calculations, altimeter calibration, and aerospace engineering.
What is the temperature lapse rate in the troposphere?
In the ISA troposphere (0 to 11,000 meters), the temperature decreases linearly at a rate of -6.5 degrees C per kilometer (-0.0065 K/m). The formula is T(h) = 288.15 + (-0.0065) x h in Kelvin. At 11,000 meters (the tropopause), the temperature reaches -56.5 degrees C (216.65 K) and remains isothermal through the tropopause layer up to 20,000 meters.
How do I calculate pressure altitude?
Pressure altitude is the altitude corresponding to the current barometric pressure in the ISA model, without QNH correction. The formula is: h_p = (1 - (P/P0)^0.190284) x 44,330 meters. For aviation, the rule of thumb in feet is: h_p approximately equals (1013.25 - QNH) x 30 feet. For example, if QNH is 1003 hPa, the pressure altitude is approximately 307 feet.
What is density altitude and why does it matter for aviation?
Density altitude is the ISA altitude that corresponds to the actual air density at a given location. It is calculated as DA = PA + 118.8 x (OAT - ISA_temp) in feet, where PA is pressure altitude and OAT is outside air temperature. It matters because aircraft performance (lift, engine power, propeller efficiency) depends on air density. At hot, high-altitude airports, density altitude can be thousands of feet above field elevation, significantly degrading takeoff performance.
How do I convert between TAS, CAS, and EAS?
The key relationship is TAS = EAS / sqrt(sigma), where sigma is the density ratio (rho/rho0). For example, at FL350 (10,668 m) with CAS of 250 knots and sigma approximately 0.3099, TAS equals 250 / sqrt(0.3099) which is approximately 449 knots. To convert from Mach number to TAS: TAS = M x a, where a is the speed of sound at altitude. At FL350, the speed of sound is 295.1 m/s, so Mach 0.78 gives TAS of 230.2 m/s (447 knots).
How does the speed of sound change with altitude?
The speed of sound depends only on temperature: a = sqrt(gamma x R x T), which simplifies to approximately 20.05 x sqrt(T) in m/s. At sea level (288.15 K), the speed of sound is 340.3 m/s (661.5 knots). At the tropopause (11,000 m, 216.65 K), it drops to 295.1 m/s (573.6 knots). This means the same TAS corresponds to a higher Mach number at higher altitudes.
What are the ISA atmospheric conditions at Mount Everest (8,848 m)?
At 8,848 meters in the ISA model: temperature is -42.5 degrees C (230.64 K), pressure is 31,436 Pa (314.4 hPa), density is 0.4748 kg/m3, speed of sound is 304.5 m/s, and the density ratio is 0.3876. This means pressure is only about 31% of sea-level pressure, with oxygen partial pressure at dangerously low levels for unacclimatized humans.
How do I calculate ISA values programmatically?
This reference includes ready-to-use Python and JavaScript code. For the troposphere (0-11 km), the key equations are T = 288.15 + (-0.0065) x h, P = 101325 x (T/288.15)^5.2559, rho = P/(287.058 x T), and a = sqrt(1.4 x 287.058 x T). For the full 7-layer model (0-84 km), the Python code iterates through layer boundaries with appropriate lapse rate or isothermal formulas for each layer. Both implementations are provided in the Code Examples category.