Calculate altitude, sea level pressure, temperature, or pressure at altitude with the barometric formula using three known values.
Barometric Formula Formula
The calculator uses the constant lapse-rate barometric formula for the troposphere. It assumes temperature decreases linearly with altitude using a lapse rate of 0.0065 K/m.
P = P_0 \left(1 - \frac{Lh}{T_0}\right)^{\frac{gM}{RL}}To solve for altitude:
h = \frac{T_0}{L}\left[1 - \left(\frac{P}{P_0}\right)^{\frac{RL}{gM}}\right]To solve for sea-level pressure:
P_0 = \frac{P}{\left(1 - \frac{Lh}{T_0}\right)^{\frac{gM}{RL}}}To solve for sea-level temperature:
T_0 = \frac{Lh}{1 - \left(\frac{P}{P_0}\right)^{\frac{RL}{gM}}}- 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)
If you leave altitude blank, the calculator uses the pressure ratio between altitude pressure and sea-level pressure to solve for height. If you leave pressure at altitude blank, it applies the main barometric formula directly. If you leave sea-level pressure blank, it rearranges the same formula to find P0. If you leave sea-level temperature blank, it solves for T0, but altitude cannot be zero because pressure would equal sea-level pressure for any temperature in this model.
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.
P = 101325\left(1 - \frac{0.0065(1000)}{288.15}\right)^{5.25588}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.
h = \frac{288.15}{0.0065}\left[1 - \left(\frac{79495}{101325}\right)^{1/5.25588}\right]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.
