Lift is the density difference times volume times g
Archimedes’ principle gives a buoyant force F = (ρair − ρhot) V g. For an ideal gas at the same pressure, ρhot/ρair = Tair/Thot (absolute temperatures), so F = ρair (1 − Tair/Thot) V g. Density is taken as p / (R T) with the same dry-air constant used on this site’s atmosphere pages, R = 287.05287 J/(kg·K), unless you are at a pressure you type. A 2,800 m³ envelope, 15 °C outside, 100 °C inside, and ISA sea-level pressure has about 781 kg of gross lift; subtract the empty weight you enter for useful lift.
Humidity, venting, a partially filled envelope, and the real temperature distribution in the bag all change the number. Fabric and basket limits are in the flight manual, not in this ideal-gas estimate. For a density at altitude, you can also start from the standard atmosphere and type that pressure here.
Sources
- Archimedes’ principle; ideal-gas law at uniform pressure.
- U.S. Standard Atmosphere / this site’s standard-atmosphere page, Rspecific for dry air.
- FAA Balloon Flying Handbook, lift from a temperature difference (conceptual).
Frequently asked questions
Why do I need absolute temperature?
The density ratio is T_air / T_hot in kelvin (or rankine). Using Celsius in that ratio would be wrong; the page converts for you.
Does this include humidity?
No. Moist air is slightly less dense than dry air at the same temperature and pressure, which changes both sides of the density difference a little.
Can I use this as a loading chart?
No. Useful lift here is only gross buoyant lift minus the empty weight you type. The flight manual’s weight schedule, including fuel and equipment, is the limit that matters.