Density altitude
Works out the density ratio properly and accounts for humidity — which raises density altitude, not lowers it, and is worth more than the rule of thumb's own error.
The rule of thumb is worst exactly when it matters
Nearly every density altitude calculator is one line — pressure altitude plus 120 feet per degree above ISA — presented as though it were exact. It is a straight-line approximation to a curve.
Near standard conditions it is excellent, good to a few tens of feet. As the temperature deviation grows it drifts, and at 5,000 feet on a 35 °C day it is out by around 250 feet.
That is backwards. On a cool day at sea level, where the rule is nearly perfect, density altitude barely matters. On a hot afternoon at a high strip, where you are genuinely deciding whether the aeroplane will clear the trees, the rule is at its least accurate.
So this works the density ratio out properly and shows the rule of thumb beside it. Keep using the rule as a mental check — it is a good one. Just do not let it be the last word.
Humid air is thinner, not thicker
This one is genuinely counter-intuitive and almost universally left out.
A water molecule is lighter than the nitrogen and oxygen molecules it displaces. So adding water vapour to air makes it less dense, not more. The heavy, oppressive feeling of a muggy day is your body failing to cool itself by evaporation. It is not the air being heavy.
The effect is not small. At 35 °C with a 25 °C dew point it is worth about 460 feet of density altitude — bigger than the rule of thumb's own error, and going the same way. Enter a dew point and it is handled through the virtual temperature, which is the standard method.
Two altitudes, one of which matters
Pressure altitude is where you are in pressure terms: field elevation corrected for the altimeter setting. Temperature does not enter into it.
Density altitude is that corrected for temperature and humidity — the height in the standard atmosphere where the air is as thin as the air you are in. It is the one your propeller, wing and engine actually respond to, because all three respond to density.
On a standard day the two are equal. That is a useful check on any calculator, this one included.
Not just aeroplanes
A naturally aspirated engine loses roughly 3% of its power per thousand feet of density altitude, which is why motorsport teams re-map for it and why a drone at its weight limit at sea level may refuse to climb at a high strip on a hot afternoon. Anything that pushes against air is affected.
Questions pilots actually ask
Why is your answer different from the 120 feet per degree rule?
Because that rule is a linearisation, and this works out the density ratio properly.
The rule of thumb — pressure altitude plus 120 feet for every degree above ISA — is good to a few tens of feet near standard conditions and drifts steadily as the deviation grows. At 5,000 ft and 35 °C it is out by around 250 feet. It is least accurate on exactly the hot high days when density altitude actually matters, which is backwards.
Both figures are shown here so you can see the gap rather than take it on trust. The rule of thumb is still a good mental check; it just should not be the final number.
Does humidity really matter?
More than most people expect, and in the direction most people guess wrong.
Humid air is LESS dense than dry air, not more. A water molecule weighs less than the nitrogen and oxygen it displaces, so adding water vapour to a parcel of air makes it lighter. "Heavy muggy air" is a feeling, not physics.
At 35 °C with a 25 °C dew point it is worth about 460 feet of density altitude — larger than the rule of thumb’s own error, and almost every calculator ignores it entirely. Enter a dew point and it is accounted for through the virtual temperature.
What is the difference between pressure altitude and density altitude?
Pressure altitude is where you are in terms of pressure: field elevation corrected for the altimeter setting being something other than 29.92. It ignores temperature entirely.
Density altitude is pressure altitude corrected for temperature — and for humidity, if you account for it. It is the altitude at which the standard atmosphere has the same air density as the air you are actually sitting in.
Density altitude is the one that matters, because it is density that your propeller, wing and engine all respond to. On a standard day they are the same number, which is a good check on any calculator.
What does a high density altitude actually do?
Thinner air, so less of everything. Less thrust from the propeller, less lift at a given indicated airspeed, and less power from a normally aspirated engine, all at once.
The practical results are a longer take-off roll, a shallower climb gradient, and a higher true airspeed for the same indicated airspeed — so you touch down faster over the ground and use more runway at both ends.
Do not estimate the performance penalty. Work it from the charts in your flight manual using the density altitude figure; the relationship is not linear and it varies by aircraft.
Why do you ask for the altimeter setting rather than pressure altitude?
Because the altimeter setting is what you actually have — it is on the ATIS or in the METAR. Pressure altitude is derived from it and the field elevation.
You can get pressure altitude by winding 29.92 into the altimeter and reading it, which is the traditional method and works perfectly. This just saves the step.
One detail: the familiar "1,000 feet per inch" conversion is itself an approximation. This inverts the standard atmosphere properly, which matters a little at settings well away from standard.
Is this only useful for pilots?
No. Anything that breathes air or pushes against it cares about density altitude.
Naturally aspirated engines lose roughly 3% of their power per 1,000 feet of density altitude, which is why motorsport teams re-jet and re-map for it. Drone operators hit the same ceiling on a hot day — a multirotor at its weight limit at sea level may simply not climb at 8,000 ft density altitude. It matters for turbocharger sizing, for HVAC, and for anything with a fan.
Notes
A cross-check, not a performance calculation. Density altitude is an input to your aircraft's performance charts, not a substitute for them. The penalty in take-off roll and climb gradient is not linear and varies by aircraft, so work it from the manual.
Everything here is the International Standard Atmosphere and the gas laws. Pressure altitude inverts the standard atmosphere rather than using the "1,000 feet per inch" approximation. Humidity is handled through the virtual temperature, with vapour pressure from the Magnus formula. No aircraft data and nothing licensed. The FAA's own treatment of the subject is in chapter 4 of the Pilot's Handbook of Aeronautical Knowledge, which is a US government work.
The rule of thumb figure is shown alongside deliberately, because it is what most other calculators return and the difference is worth seeing. Tell me if something here disagrees with your own reference.