Moist Air Density at Altitude (and the 1.08 Correction)

This page exists to correct three numbers the trade uses every day without stating their conditions. The 1.08, 0.68 and 4.5 rules are sea-level, standard-air constants, and at altitude they are simply wrong.

Unpack 1.08 and there is no physics left in it: 60 min/hr × 0.075 lb/ft³ × 0.240 BTU/(lb·°F) = 1.0800. The 0.240 is the specific heat of air, which barely moves. The 0.075 lb/ft³ — 1.2014 kg/m³ — is a DENSITY, and density is exactly what altitude changes. 0.68 carries the same density with a latent heat instead of a specific heat, and 4.5 is just 60 × 0.075. All three scale together with whatever the air actually weighs, so one correction factor fixes all three.

Calgary sits at about 1 045 m. Standard-atmosphere pressure there is 89.4 kPa against 101.3 at sea level, and at 20 °C the air works out to 1.062 kg/m³ against the assumed 1.201 — a factor of 0.884. Use 1.08 unmodified in Calgary and you overstate sensible capacity by about 13 %. The corrected constants are 0.955, 0.601 and 3.98. Denver at 1 609 m is worse, Mexico City at 2 240 m worse again. This is the mechanism behind a familiar complaint: a rooftop unit sized by the sea-level rule at altitude comes up short, and it comes up short in a specific way — the fan moves exactly the cubic feet it was rated for, and every one of them contains less air to carry heat.

Three honest caveats belong with any answer this page gives. First, the pressure here is a STANDARD-day pressure for that altitude, not today's barometer; a deep low can move it 3 %, which is a real fraction of the correction being applied. Second, the humidity term is genuinely small — 10 g/kg makes air roughly 0.6 % lighter than dry air at the same temperature and pressure — so it is included for correctness rather than because it will change a selection. Third, temperature matters as much as altitude for the density itself: air at 40 °C is 7 % thinner than air at 20 °C at the same place, which is why cooling capacity and the correction to it both want the design condition rather than a round number.

Note also what does NOT change with altitude. Latent heat per kilogram of water is unaffected, and so is the specific heat of air; only the mass in a given volume moves. That is why the correction is a single multiplier across all three rules rather than three separate adjustments, and why an engineer who works at altitude usually just writes the corrected constants at the top of the sheet and forgets about it.