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.

Result
Celsius:
Fahrenheit:

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:
\[T(h) = 15°C - 6.5°C/km \times h\]
\[T = 15 - 6.5 \times 8.848\]
\[T = 15 - 57.51\]
\[T = -42.51°C\]
Atmospheric Layers
Troposphere (0-11 km): -6.5°C/km temperature gradient
Stratosphere (11-20 km): Constant temperature ≈ -56°C
Mesosphere (20-47 km): Temperature increase due to ozone
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.

\[T(h) = T_0 - \gamma \cdot h\]
T(h) = Temperature at altitude [°C]
T₀ = Sea level temperature = 15°C
γ = Temperature gradient = 6.5°C/km
h = Altitude [km]
Simplified formula

Direct calculation with numerical values.

\[T = 15 - 6.5 \cdot h\]
Where h is given in kilometers and T in degrees Celsius.
Fahrenheit conversion

Conversion from Celsius to Fahrenheit.

\[T_F = T_C \times \frac{9}{5} + 32\]
Standard conversion between temperature scales.
Altitude calculation

Inversion for altitude determination with known temperature.

\[h = \frac{T_0 - T(h)}{\gamma}\]
Determination of altitude from measured 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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