Well, cross sectional area of the inner tube is given by pi*r*r where r is half of however 'fat' the tyre is (in mm). The length of it is pi * (622 + 2r) Multiply them together and that's your volume in cubic millimeters. Assumming you're on a 700c wheel...

That's treating the toroid as a cylinder whose ends just happen to be stuck together, which should be OK.

OK, working this for a 700*28 , pi*14*14 = 615.75mm^2

Length is pi * (622+28 ) = 2042.033 mm

volume is therefore 1257385 mm^3 or 1.26 litres. At a pressure of 6 bar, that's 6*1.26*20 g or 151g of air in your tyre.

I'm going away now. I can't believe I just bothered with that!

I also can't believe I looked up the formula on t'interweb, and the above logic is OK. I need to get out more.