What pressure altitude is and why charts use it
Pressure altitude is the altitude at which the ICAO Standard Atmosphere has the same pressure you are currently experiencing. It is not a height above the ground, and outside standard conditions it is not a height above the sea either. It is a pressure, relabelled in feet.
That relabelling is what makes it useful. An aeroplane's performance depends on air density, and density depends on pressure and temperature. Rather than print charts against hectopascals, manufacturers print them against pressure altitude and temperature, because pilots already have an instrument that reads pressure in feet. Set 29.92 inHg in the Kollsman window and the altimeter is a pressure gauge with a convenient scale.
The same logic runs the flight-level system. Above the transition altitude every aircraft sets 29.92 (1013.25 hPa), so all aircraft measure the same pressure surfaces and stay vertically separated from each other even when nobody's altimeter is reading true height. FL350 is not 35,000 ft above the sea; it is the pressure surface that corresponds to 35,000 ft in the standard atmosphere. On a cold day that surface can sit well over a thousand feet lower.
Pressure altitude is also the first step towards density altitude. Add the temperature and you have the number that governs takeoff and climb.
The formula, and the rule of thumb it replaces
Two steps get you there. First recover the station pressure — the pressure actually acting on the aerodrome. The altimeter setting is not that pressure; it is the sea-level pressure that would produce your station pressure in the standard atmosphere. Because standard-atmosphere pressure raised to n = 0.190263 is exactly linear in altitude, that reduction inverts cleanly: pn = QNHn − K·h with h in metres and K = 8.417286×10−5.
Second, convert that pressure back to an altitude in the standard atmosphere: PA = 145441.6 × (1 − pn/1013.25n). The constant is 288.15 K divided by the 6.5 K/km lapse rate, expressed in feet.
The cockpit rule — add 1,000 ft for every inch of mercury the setting is below 29.92 — is the tangent to this curve at sea level. Near sea level and near 29.92 it is good to a few tens of feet. It drifts for two reasons. The pressure gradient is about 27 ft per hPa at sea level but nearer 32 ft per hPa at 5,000 ft, so at altitude each inch of mercury is worth more than 1,000 ft. And the exact relation is a power law, so it curves away from the straight line as the setting departs from standard. At sea level with a setting of 28.00 inHg, the exact answer is 1,825 ft while the rule says 1,920 ft — a 95 ft optimism in the rule that always errs on the conservative side for low pressure.
For settings given in hectopascals the equivalent shortcut is 27 ft per hPa, which is simply 1,000 ÷ 33.86 × 0.914 rounded to a number you can do in your head.
Worked example: 4,000 ft field elevation, QNH 30.42 inHg
You are at a 4,000 ft aerodrome under a strong high, altimeter setting 30.42 inHg.
- Convert the setting. 30.42 × 33.8639 = 1,030.14 hPa.
- Raise it to n. 1030.140.190263 = 3.743205. For reference, 1013.250.190263 = 3.731451.
- Subtract the elevation term. 4,000 ft = 1,219.2 m, so K·h = 8.417286×10−5 × 1,219.2 = 0.102622. That leaves pn = 3.743205 − 0.102622 = 3.640583.
- Recover station pressure. p = 3.6405831/0.190263 = 890.20 hPa.
- Convert to pressure altitude. PA = 145441.6 × (1 − 3.640583 ÷ 3.731451) = 145441.6 × 0.024352 = 3,542 ft.
The rule of thumb gives 4,000 + (29.92 − 30.42) × 1,000 = 3,500 ft, 42 ft lower. Either number takes you to the same row of a performance chart, but the exact value is what you want if you are computing density altitude for a marginal runway, and it is the number a flight management system uses.
Notice the sign: a high altimeter setting produces a pressure altitude below field elevation, because high pressure means the standard-atmosphere altitude matching that pressure is lower down.
How to use the number
Take pressure altitude straight to the performance section of the flight manual. Most light-aircraft takeoff, landing and cruise tables are indexed by pressure altitude down the side and temperature across the top, so you need this figure and the OAT and nothing else. Charts that ask for density altitude instead want the output of the density altitude calculator, which takes this value as its input.
The altimeter correction figure tells you how far the current pressure has displaced you from your geometric position in chart terms. A correction of +500 ft on a low-pressure day means your aeroplane will perform as though the aerodrome were 500 ft higher than it is. A correction of −458 ft, as in the worked example, means the opposite: high pressure buys you a little performance.
The flight-level equivalent is a direct read of what your altimeter would show with 29.92 set. Below the transition altitude it has no operational meaning, but it is a quick sanity check when you are handed a level in a flight plan. Note that the transition altitude differs by country — 18,000 ft in the United States and Canada, commonly 3,000 to 6,000 ft in Europe, and published on the approach charts everywhere.
A cold-weather caution belongs here. Pressure altitude corrects for pressure only. When the air is much colder than standard, your true height above the terrain is lower than your indicated altitude, sometimes by several hundred feet on an approach, which is why cold-temperature altitude corrections are published separately for aerodromes in cold climates.
Pressure altitude at sea level for common altimeter settings
| Setting (inHg) | Setting (hPa) | Exact PA (ft) | Rule of thumb (ft) | Difference (ft) |
|---|---|---|---|---|
| 28.50 | 965.1 | 1,341 | 1,420 | −79 |
| 29.00 | 982.1 | 862 | 920 | −58 |
| 29.50 | 999.0 | 392 | 420 | −28 |
| 29.92 | 1,013.2 | 1 | 0 | +1 |
| 30.50 | 1,032.9 | −532 | −580 | +48 |
| 31.00 | 1,049.8 | −983 | −1,080 | +97 |
The rule of thumb overstates the magnitude of the correction at every setting shown, and the gap widens as the setting moves away from 29.92. At non-zero elevations both columns shift by the elevation.
Where pressure altitude calculations go wrong
- Correcting an indicated altitude that is already on 29.92. If the standard setting is in the window, the altimeter is displaying pressure altitude directly. Applying the correction again double-counts it.
- Using QFE instead of QNH. QFE is set so the altimeter reads zero on the ground. Combining a QFE with a field elevation gives a station pressure that is wrong by the whole height of the aerodrome.
- Mixing inHg and hPa. 1013 entered in an inHg field, or 29.92 entered in a hPa field, produces a result that is obviously absurd — which is why this calculator warns outside 28.00-31.00 inHg.
- Expecting pressure altitude to give true height. It does not. Above the transition altitude nobody's altimeter shows true height, and that is the point: everyone is wrong by the same amount, so separation is preserved.
- Ignoring temperature on an approach in cold air. Pressure altitude has no temperature term. In very cold conditions your true clearance over obstacles is less than indicated and a published cold-temperature correction may be mandatory.
- Reading a QNH from a station far away. Altimeter settings are local. Regional pressure settings and distant aerodrome QNHs can differ by several hectopascals, which is tens of feet of error each.
The Q codes, in plain language
- QNH
- The setting that makes the altimeter read aerodrome elevation on the ground — that is, altitude above mean sea level. This is what you enter here.
- QFE
- The setting that makes the altimeter read zero on the ground, so it shows height above the aerodrome. Still used at some fields and in gliding.
- QNE
- The standard setting of 1013.25 hPa / 29.92 inHg. With QNE set, the altimeter reads pressure altitude, and above the transition altitude that reading is a flight level.
- Station pressure
- The actual atmospheric pressure at the aerodrome, unreduced. Meteorological offices report the reduced sea-level value; this calculator recovers the station value from it.
Where this fits in the altitude family
There are five altitudes a pilot deals with and they are easy to blur. Indicated altitude is whatever the instrument reads. True altitude is the actual height above mean sea level. Absolute altitude is the height above the terrain, which is what a radio altimeter measures. Pressure altitude is this page. Density altitude is pressure altitude corrected for temperature and humidity, and it is the one that predicts performance.
In practice you compute them in that order: read the indicated altitude, convert to pressure altitude here, then take pressure altitude and temperature into the density altitude calculator, then take density altitude into takeoff distance and landing distance. Pressure altitude also feeds the airspeed conversions: true airspeed depends on pressure altitude and temperature, and true airspeed with the wind gives you ground speed and your en-route timings.
If you need the reverse conversion — a flight level to a pressure in hectopascals — invert the same formula: p = 1013.25 × (1 − PA/145441.6)5.255885. FL350 gives 238.4 hPa, which is the value tabulated in every standard atmosphere table.
This tool is planning information. Where an aircraft flight manual, an operations manual or a State's regulations prescribe a particular altimetry procedure, that procedure governs.