Calculate atmospheric pressure from altitude or altitude from pressure using ISA lapse-rate or isothermal models with pressure units, temperature, and density.
Barometric Formula
The calculator offers pressure-from-altitude and altitude-from-pressure modes. ISA troposphere mode assumes a lapse rate of 0.0065 K/m, standard sea-level temperature of 288.15 K and altitude at or below 11,000 m. Isothermal mode holds the entered temperature constant and uses P = P0 exp[−gh/(Rair T)].
To solve for altitude:
To solve for sea-level pressure:
To solve for sea-level temperature:
- P = pressure at altitude
- P0 = pressure at sea level
- h = altitude above sea level
- T0 = temperature at sea level, in kelvin
- L = temperature lapse rate, 0.0065 K/m
- g = gravitational acceleration, 9.80665 m/s²
- M = molar mass of Earth’s air, 0.0289644 kg/mol
- R = universal gas constant, 8.31447 J/(mol·K)
Select the value to solve for explicitly. Altitude and atmospheric pressure are entered in their respective modes; the sea-level pressure remains a required reference, initially 101.325 kPa. The sea-level pressure and temperature rearrangements above are reference equations, not additional blank-field solve modes. Isothermal temperature must be above absolute zero.
Standard Atmosphere Reference Values
These reference values use standard sea-level pressure of 101325 Pa and standard sea-level temperature of 288.15 K.
| Altitude | Approx. pressure | Approx. pressure | Pressure as % of sea level |
|---|---|---|---|
| 0 m | 101325 Pa | 1.000 atm | 100% |
| 1000 m | 89875 Pa | 0.887 atm | 88.7% |
| 2000 m | 79495 Pa | 0.785 atm | 78.5% |
| 3000 m | 70109 Pa | 0.692 atm | 69.2% |
| 5000 m | 54020 Pa | 0.533 atm | 53.3% |
Pressure and Temperature Unit Conversions
| Quantity | Conversion |
|---|---|
| Feet to meters | m = ft × 0.3048 |
| Atmospheres to pascals | Pa = atm × 101325 |
| PSI to pascals | Pa = psi × 6894.757 |
| Celsius to Kelvin | K = °C + 273.15 |
| Fahrenheit to Kelvin | K = (°F – 32) × 5/9 + 273.15 |
Example Problems
Example 1: Find pressure at altitude
Suppose altitude is 1000 m, sea-level pressure is 101325 Pa, and sea-level temperature is 288.15 K.
The pressure at altitude is about 89874.8 Pa, or about 0.887 atm.
Example 2: Find altitude from pressure
Suppose sea-level pressure is 101325 Pa, sea-level temperature is 288.15 K, and pressure at altitude is 79495 Pa.
The altitude is about 2000 m.
FAQ
What altitude range is this formula best for?
This version of the barometric formula is best for the lower atmosphere where the lapse-rate assumption is reasonable. It is commonly used for the troposphere, up to about 11 km above sea level under standard atmosphere assumptions. At higher altitudes, the temperature profile changes and a different atmospheric layer model may be needed.
Why does temperature need to be in kelvin?
The formula uses absolute temperature. Celsius and Fahrenheit are relative scales, so they must be converted to kelvin before the calculation. A temperature of 0 K is absolute zero, and the calculator requires sea-level temperature to be greater than 0 K.
Why is pressure at altitude lower than sea-level pressure?
Air pressure decreases with altitude because there is less air above you pushing downward. In this formula, increasing altitude makes the term inside the parentheses smaller, so the calculated pressure at altitude is lower than the sea-level pressure.
