At constant pressure, air loses about 0.34% of its density for every degree Celsius it warms near room temperature — about 15% between a −5 °C winter day and a 35 °C summer one.
A gas at fixed pressure has a density proportional to 1/T, with T in kelvin. One degree on 293 K is 1/293 of it, which is 0.34%; near freezing it is 0.37%, at 100 °C 0.27%. The same fraction holds for every gas, because it depends only on the temperature, not on what the gas is. Pressure is the other lever and pulls harder: climbing one kilometre in the standard atmosphere takes about 9% off the density, as much as twenty-seven degrees of warming, which is why altitude matters more than the weather to anything that breathes air.
It is a constant-pressure rule. A parcel of air that rises expands and cools as it goes, so its density does not follow the ground-level rule. Humid air is lighter again by up to a couple of per cent in hot weather. And for a gas close to condensing — carbon dioxide under pressure, propane in the cold — the real-gas correction adds to the change.
Estimate with the rule, then check it against the calculator that models it properly.
Open Air & Gas Density →