Outgassing rates from the walls of a fully baked vacuum chamber made of type 304 stainless steel (volume : 0.005 m3, surface area : 0.4 m2) were measured by two methods, the throughput method, where the outgassing rate is determined from the pressure drop (measured by two ionization gauges) across an orifice with a conductance of 0.0047 m3/s for nitrogen during evacuation and the pressure rise method, where the chamber is sealed off at 10-8 Pa and the rise in pressure with time is measured by a spinning rotor gauge. In both measurements the major outgassing species is hydrogen. The pressure rise is linear for as long as 115 h with the pressure increasing by a factor as large as 106 indicating a constant outgassing rate and zero sticking probability of the desorbed hydrogen on the stainless surface. The outgassing rates measured by the two methods in several sequences of air exposure and baking agree well with each other and lie in the range of 4-5×10-10 Pam/s, which is a typical value for fully baked stainless steel UHV chambers. A quadrupole mass spectrometer shows some pumping action against desorbed gas species, particularly hydrogen, while outgassing methane and carbon monoxide. A nude Bayard-Alpert gauge pumps methane but produces carbon monoxide.