# Standard Atmosphere Calculator – ICAO/ISA

Calculate standard atmospheric conditions (ISA) at a given altitude.

## ICAO Standard Atmosphere Calculator

This ICAO Standard Atmosphere Calculator provides accurate atmospheric properties such as temperature, pressure, density, and the speed of sound based on the altitude input by the user. It allows you to enter the altitude in feet or meters and offers results in multiple units for better usability, making it convenient for aviation professionals, engineers, and students.

The calculator also identifies the atmospheric layer (Troposphere, Stratosphere, or Mesosphere) and displays the corresponding Flight Level (FL) for a given altitude. This is an ideal tool for simulating and understanding the conditions encountered by aircraft at different altitudes according to the International Standard Atmosphere (ISA) model.

## Formulas to Calculate Standard Atmosphere Parameters

Below are the formulas used to calculate various atmospheric properties based on altitude:

### Temperature (T)

Below 11,000 meters (36,089 feet), the temperature decreases linearly with altitude according to the lapse rate of -6.5°C per km:

**T = T0 - L * h**

- where:
- T is the temperature at altitude h (in Kelvin).
- T0 = 288.15 K is the temperature at sea level.
- L = 0.0065 K/m is the lapse rate.
- h is the altitude in meters.

### Pressure (p)

Below 11,000 meters, the pressure decreases with altitude, calculated by the following relation derived from the hydrostatic equation and the ideal gas law:

**p = p0 * (T / T0) ^ (g0 / (L * R))**

- where:
- p is the pressure at altitude h.
- p0 = 101325 Pa is the pressure at sea level.
- g0 = 9.80665 m/s^2 is the acceleration due to gravity.
- R = 287.05 J/kg.K is the specific gas constant for dry air.
- L = 0.0065 K/m is the lapse rate.
- T is the temperature at altitude h in Kelvin.
- T0 is the sea level standard temperature in Kelvin.

For altitudes above 11,000 meters (where the temperature remains constant), the pressure is calculated using an exponential decay:

**p = p11 * exp(-g0 * (h - 11000) / (R * T11))**

- where:
- p11 is the pressure at 11,000 meters.
- T11 is the temperature at 11,000 meters.
- h is the altitude in meters.

### Density (ρ)

The air density at a given altitude is derived from the ideal gas law:

**Below 11,000 meters or 36,089 feet:**

**ρ = p / (R * T)**

- where:
- ρ (rho) is the air density at altitude h.
- p is the pressure at altitude h.
- R = 287.05 J/kg.K is the specific gas constant.
- T is the temperature at altitude h.

**Above 11,000 meters or 36,089 feet:**

**ρ = p / (R * T11)**

- where:
- ρ (rho) is the air density at altitude h.
- p is the pressure at altitude h.
- R is the specific gas constant for air.
- T11 is the temperature at 11,000 meters.

### Speed of Sound (a)

The speed of sound decreases with altitude as temperature drops in the troposphere but remains constant above 11,000 meters where the temperature is stable.

**Below 11,000 meters or 36,089 feet:**

**a = sqrt(γ * R * T)**

- where:
- a is the speed of sound at altitude h.
- γ (gamma) = 1.4 is the ratio of specific heats for air.
- R is the specific gas constant.
- T is the temperature at altitude h.

**Above 11,000 meters or 36,089 feet:**

**a = sqrt(gamma * R * T11)**

- where:
- a is the speed of sound at altitude h.
- γ (gamma) is the ratio of specific heats for air.
- T11 is the temperature at 11,000 meters.

**Note:** ICAO Standard Atmosphere, 1976 Standard Atmosphere, and ISA (International Standard Atmosphere) are all the same.