Temperature in the Atmosphere
Calculator and formulas for temperature in the atmosphere at a given altitude
Atmospheric Temperature Calculator
Temperature calculation in the troposphere
Calculates the air temperature at different altitudes in the atmosphere up to 20,000 m. Takes into account the linear temperature gradient in the troposphere.
Example Calculation
Example: Temperature on Mount Everest
Problem:
How cold is it on the summit of Mount Everest at approximately 8,848 m altitude? Calculate the temperature using the standard atmosphere model.
Given:
- Altitude h = 8,848 m = 8.848 km
- Sea level temperature: 15°C
- Temperature gradient: -6.5°C/km
- Find: Temperature at altitude
Solution:
Atmospheric Layers
Practical Application
Aviation: Calculation of outside air temperature at flight altitudes for performance calculations and safety planning.
Mountaineering: Prediction of temperature conditions at different altitudes for equipment planning.
Formulas for atmospheric temperature
The temperature distribution in the atmosphere follows a linear gradient in the troposphere. The standard atmosphere assumes a temperature decrease of 6.5°C per kilometer.
Temperature in the troposphere
Calculation of air temperature as a function of altitude up to 11 km.
T₀ = Sea level temperature = 15°C
γ = Temperature gradient = 6.5°C/km
h = Altitude [km]
Simplified formula
Direct calculation with numerical values.
Fahrenheit conversion
Conversion from Celsius to Fahrenheit.
Altitude calculation
Inversion for altitude determination with known temperature.
Important Notes
- The formula only applies to the troposphere (0-11 km)
- Real values may deviate due to weather conditions
- In the stratosphere (11-20 km) temperature remains constant
- The gradient can vary depending on humidity (0.4-0.98°C/100m)
Detailed description of atmospheric temperature
Physical Fundamentals
The temperature distribution in the atmosphere is determined by various physical processes. In the troposphere, temperature decreases with altitude as air cools through adiabatic expansion and solar radiation primarily heats the Earth's surface.
Usage Instructions
Enter the desired altitude and select the unit (meters or feet). The calculator computes temperature according to the standard atmosphere model.
Application Areas
Aviation
Flight planning, performance calculations, engine design. Critical for safety and efficiency in air traffic.
Meteorology
Weather forecasting, climate models, atmospheric research. Foundation for understanding atmospheric processes.
Outdoor Activities
Mountaineering, hiking, paragliding. Planning the right equipment for different altitudes.
Understanding Atmospheric Layers
Earth's atmosphere is divided into different layers, characterized by different temperature profiles:
Troposphere (0-11 km)
Weather phenomena, linear temperature decrease
Gradient: -6.5°C/km
Temperature range: +15°C to -56°C
Stratosphere (11-20 km)
Ozone layer, constant temperature
Temperature: approx. -56°C
Commercial flight altitude
Mesosphere (20-47 km)
Temperature increase due to UV absorption
Temperature range: -56°C to 0°C
Ozone layer region
Note: This calculator uses the standard atmosphere model and applies mainly to the troposphere.
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