Barometric Altitude
Altitude derived from the ratio of sea-level to measured pressure.
Formula
Variables
Example
Altimeters work by comparing measured air pressure to the pressure at sea level.
How it works
This equation estimates how high you are by comparing the local air pressure to a reference pressure, usually sea-level pressure. It comes from combining the hydrostatic balance of the atmosphere with the ideal gas law: as you go up, there is less air above you, so pressure drops in a predictable way. The logarithm appears because pressure decreases exponentially with altitude in the simplest constant-temperature model.
When to use it
Use this when you need a quick pressure-based estimate of altitude in aviation, meteorology, or atmospheric experiments. It is most appropriate for standard-atmosphere calculations or situations where temperature can be treated as approximately constant over the height range of interest.
Worked example, step by step
Given: P0 = 101325 Pa, P = 54019 Pa, T = 288 K, R = 287 J/(kg·K), g = 9.81 m/s² Step 1: Write the formula: h = (RT/g) ln(P0/P) Step 2: Compute the pressure ratio: P0/P = 101325 / 54019 ≈ 1.876 Step 3: Take the natural log: ln(1.876) ≈ 0.629 Step 4: Compute RT/g: (287 × 288) / 9.81 ≈ 8427.2 Step 5: Multiply: h ≈ 8427.2 × 0.629 ≈ 5300 m Final answer: the estimated altitude is about 5.3 km above sea level.
Common mistakes to avoid
- Using base-10 log instead of the natural logarithm
- Mixing up P and P0, which gives a negative or nonsensical altitude
- Using the wrong gas constant or inconsistent units for pressure, temperature, or gravity
Did You Know?
Altimeters are really barometers — they infer height from air pressure, which is why pilots must set the local pressure.
Share this formula
More in Aviation & Aeronautics
View allTrue Airspeed (rule of thumb)
BasicQuick estimate: true airspeed increases about 2% per 1000 ft of altitude above indicated airspeed.
Ground Speed
BasicGround speed is true airspeed adjusted for the headwind/tailwind component.
Flight Time
BasicTime en route equals distance divided by ground speed.
Fuel Required
BasicTotal fuel needed is the fuel-burn rate multiplied by flight time.
Rate of Climb
BasicVertical speed is the altitude gained per unit time (ft per minute).
3-Degree Descent Rate
BasicOn a standard 3° glide path, required descent rate (fpm) is roughly ground speed (kt) times 5.