How to use it
- Choose Calculate from: Altitude to find the values at a height, or Pressure to find the altitude of a pressure.
- Type the Altitude in feet, or the Pressure with its Pressure unit.
- Read ISA temperature, ISA pressure, Air density and Speed of sound, then open Working for the formulas.
- Use the table under the result to compare the values every 1,000 ft.
How the standard atmosphere is built
The International Standard Atmosphere (ISA) is a reference model of the air. It is a set of values and formulas, not a measurement, and it is the reference that instruments and aircraft performance are compared with. The IFH defines it with sea level at 29.92 inHg and 15 °C, and a standard lapse rate of 2 °C per 1,000 ft up to the tropopause (11,000 m, 36,089 ft); above it, in the lower stratosphere, the model keeps the temperature constant.
This page uses two layers, as the standard does. In the troposphere, below 11,000 m (36,089 ft), the temperature falls linearly with height. In the lower stratosphere, from 11,000 m to 20,000 m (65,617 ft), it stays at 216.65 K. The altitudes are geopotential altitudes of the standard.
Troposphere (h ≤ 11,000 m): T = 288.15 K − 0.0065 × h; p = 101,325 Pa × (T ÷ 288.15 K)^5.2559
Lower stratosphere (11,000 m < h ≤ 20,000 m): T = 216.65 K; p = 22,632 Pa × exp(−9.80665 × (h − 11,000 m) ÷ (287.05 × 216.65 K))
Density: ρ = p ÷ (287.05 × T)
Speed of sound: a = √(1.4 × 287.05 × T)- The gas constant of dry air is 287.0528 J/(kg K), and the adiabatic index of air is 1.40.
- The inverse uses the same two layers: the troposphere formula above 22,632 Pa and the stratosphere formula below it.
- Speed in knots is the speed in metres per second divided by 0.514444 (1 kt is 1,852 m per hour).
What this page does not cover
- The real air. Temperature, pressure and density change from day to day and place to place: use the forecast and the observed values.
- Altimeter corrections, density altitude and performance charts. Those are in the aircraft's manual and the operating data.
- Heights above 20,000 m, where the standard uses other layers that this page does not take.
- This page is for training and planning practice, not for real flight.
Worked example: 10,000 ft in the standard atmosphere
At 10,000 ft, which is 3,048 m, the troposphere formula gives the temperature 288.15 − 0.0065 × 3,048 = 268.34 K, which is −4.8 °C. The pressure is 101,325 Pa × (268.34 ÷ 288.15)^5.2559 = 69,682 Pa, which is 696.8 hPa or 20.58 inHg.
The density is 69,682 ÷ (287.05 × 268.34) = 0.9046 kg/m³, and the speed of sound is √(1.4 × 287.05 × 268.34) = 328.4 m/s, which is 638.3 kt.
| Output | Value |
|---|---|
| Temperature | -4.8 °C (268.34 K) |
| Pressure | 696.8 hPa (20.58 inHg) |
| Density | 0.9046 kg/m³ |
| Speed of sound | 328.4 m/s (638.3 kt) |
Frequently asked questions
What is the International Standard Atmosphere?
It is a reference model of the air that the ICAO and other standards bodies publish. It gives the temperature, pressure and density at each altitude for a standard day, and instruments and aircraft performance are compared with it.
Why does the temperature stop falling at 36,089 ft?
The standard has a tropopause at 11,000 m (36,089 ft). Above it, in the lower stratosphere, the temperature is 216.65 K (−56.5 °C) and stays there up to 20,000 m in this model.
What is the standard lapse rate?
The IFH gives 2 °C per 1,000 ft, which is about the same as the 6.5 K per km used in the formulas above. Real air often lapses differently, so this is a reference only.
How is the altitude found from a pressure?
The formulas are inverted for the layer the pressure falls in. Above the tropopause pressure the troposphere formula gives the height, and below it the stratosphere formula does.
Can I use these values for a real flight?
No. The values are a standard reference. For a real flight use the altimeter setting, the forecast, and the performance data in the aircraft's manual.
Sources
- Wikipedia: International Standard Atmosphere (layer table, base values and gas constant)
- NASA Glenn Research Center: Speed of Sound (a = square root of gamma R T)
- FAA Instrument Flying Handbook FAA-H-8083-15B, chapter 4: International Standard Atmosphere
Figures and text last checked on Tuesday, November 10, 2026.