How do QNH, QFE and flight levels relate?

How it works

An altimeter is a barometer: it measures air pressure and shows it as height in the standard atmosphere (ICAO Doc 7488). The number in its setting window decides where zero is. With QNH set it reads altitude above mean sea level, with QFE set it reads height above the aerodrome, and with the standard 1013.25 hPa (29.92 inHg) it reads pressure altitude. Flight levels are pressure altitude in hundreds of feet, so everyone above the transition altitude shares one setting (ICAO Doc 8168).

The tool finds the air pressure at your level from the reading and the setting, p = p_set · (1 − L·H / T₀) to the power 5.256, where H is the reading, L = 6.5 °C per km and T₀ = 288.15 K, and then the reading on the other setting. Example: at 3,000 ft with QNH 1003 hPa the pressure altitude is about 3,275 ft, FL033: near sea level each hectopascal is roughly 27–30 ft. The transition level is the lowest flight level above the transition altitude, and the cruising levels follow ICAO Annex 2 Appendix 3: odd thousands for magnetic tracks 000–179°, even for 180–359°, with 500 ft added for VFR.

Cold air is denser, so pressure levels sit closer together and a correctly set altimeter reads too high. ICAO Doc 8168 corrects a height H above the aerodrome by H · (15 − t₀) / (273 + t₀ − 0.5 · L₀ · (H + h)), where t₀ is the aerodrome temperature reduced to sea level, L₀ = 0.00198 °C/ft and h the aerodrome elevation. At −10 °C, 3,000 ft above a sea-level aerodrome needs 290 ft more, as in the ICAO table published in the FAA AIM.

This is a learning aid. It assumes a standard-atmosphere altimeter with no instrument or position error, the ICAO table of cruising levels (states may publish their own) and the linear cold-temperature method, which is meant for up to 5,000 ft above the aerodrome and down to −50 °C.