A 9 000 ft runway at sea level is a comfortable take-off for most light twins. The same aircraft trying the same take-off at Leh (10 682 ft) on a hot summer day — with the altimeter physically reading "10 700 ft" — needs every foot of the runway and a careful look at the climb performance chart, because the air the engine and the wing are actually swimming through corresponds to roughly 14 000 ft of density altitude. The aeroplane has aged 4 000 ft just by sitting on the apron in the sun.
Field elevation, pressure altitude, and density altitude are three different answers to "how high are we, for performance purposes?". The performance charts only ever ask for the last two.
The two corrections, in order
There are exactly two adjustments on top of the field elevation, and they are always applied in the same order.
Pressure altitude — the QNH correction
If the standard pressure of 1013 hPa is set on the altimeter, the instrument will read what is known as pressure altitude — height in the Standard Atmosphere. — Oxford ATPL Meteorology, Ch. 2
In plain terms: pressure altitude is the field's height above the 1013 hPa pressure surface, not above mean sea level. On a high-pressure day (QNH > 1013), the 1013 surface sits below mean sea level, so the field's pressure altitude is lower than its elevation. On a low-pressure day, the opposite. This is the only number the performance chart cares about for the atmosphere-pressure axis.
The standard pilot conversion is:
PA = field elevation + (1013 − QNH) × 30 ft/hPa
The "30 ft per hPa" rule is rounded — the precise value is 27 ft / hPa at sea level — but every JAA/EASA flight-computer uses 30 and so does every ATPL exam.
Density altitude — the temperature correction on top
Density altitude can be defined as the altitude in the standard atmosphere at which the prevailing density would occur, or alternatively, as the altitude in the standard atmosphere corresponding to the prevailing pressure and temperature. — Oxford ATPL Meteorology, Ch. 2
In plain terms: density altitude is the altitude the engine and wing think they're at. Hot air is thin, so a hot day at any field shoves the density altitude higher than the pressure altitude. Cold dense air drags it back down — sometimes below field elevation entirely.
The pilot rule:
DA = PA + 120 × ISA-deviation (°C)
where ISA-deviation = OAT − ISA temperature at PA, and the ISA
temperature at any pressure altitude is 15 − 2 × (PA / 1000) °C.
The order matters
The corrections must be applied field elevation → PA → DA, never the other way round. Here's why:
- The QNH correction is purely about where the pressure datum sits today. It depends only on QNH; temperature plays no part.
- The temperature correction is referenced to the ISA temperature at PA, not at field elevation. If you compute ISA-dev using the ISA temperature at field elevation, you'll be off by ~2 °C per thousand feet of QNH offset — small, but enough to fail an exam question that uses a 30 hPa QNH offset.
The widget walks the rungs in this order so you can see each correction added on top of the previous one.
A worked example — Leh on a summer day
Field elevation 10 682 ft, QNH 1003 hPa, OAT +25 °C.
Step 1 — Pressure altitude.
PA = field elevation + (1013 − QNH) × 30
= 10 682 + (1013 − 1003) × 30
= 10 682 + 10 × 30
= 10 682 + 300
= 10 982 ft
Step 2 — ISA temperature at PA.
ISA temp at PA = 15 − 2 × (PA / 1000)
= 15 − 2 × 10.982
= 15 − 21.96
= −6.96 °C
Step 3 — ISA deviation.
ISA-dev = OAT − ISA temp
= 25 − (−6.96)
= +31.96 °C (call it +32)
Step 4 — Density altitude.
DA = PA + 120 × ISA-dev
= 10 982 + 120 × 32
= 10 982 + 3 840
= 14 822 ft
The engine and wing are flying at roughly 14 800 ft for performance purposes. Compared with the field elevation, density altitude is 4 100 ft higher.
Step 5 — Operational consequence.
Using the rule of thumb that take-off roll lengthens by ~10 % per 1 000 ft of DA, the take-off distance is roughly:
TODR factor = 1 + DA / 10 000
= 1 + 14 822 / 10 000
≈ 2.48 × the sea-level baseline
Climb rate drops by ~8 % per 1 000 ft, leaving close to 0× at the limit — which is why hot-and-high airfields like Leh use seasonal weight or runway restrictions and why most operators publish summer and winter performance tables for the same airframe.
Common mistakes
- Using field elevation as the ISA reference. ISA-dev is computed from the ISA temperature at pressure altitude, not at the physical field. Skipping the PA step bakes a 2 °C-per-thousand error into ISA-dev.
- Subtracting the QNH correction the wrong way. Low QNH makes the 1013 surface sit below sea level, so pressure altitude is higher than field elevation. Cross-check: if QNH is below 1013, PA must be above field elevation.
- Ignoring the temperature correction on a "high-pressure cold day". A pressure altitude lower than field elevation still becomes a density altitude that may be much higher if it's also warm. PA alone never tells you the performance story.
- Applying the 120 ft / °C rule to OAT directly. The 120 factor multiplies ISA-deviation, not OAT. On an ISA day at any altitude, OAT will not be zero, but ISA-dev will be — and DA equals PA exactly.
Why it matters
Every take-off, landing, climb gradient, single-engine ceiling, and en-route obstacle clearance chart in the AFM is indexed on pressure altitude and OAT (or directly on density altitude). Pilots flying out of low-elevation airfields on cool days rarely need to think about it; pilots flying out of Aspen, Leh, Lhasa, La Paz, Quito, or Cusco on a summer afternoon think about almost nothing else. The same airframe at the same weight on the same runway can be perfectly within limits on a February morning and unable to clear a 5° climb gradient on an August afternoon — purely because of how the air thinned out between the two.