The outgassing rate of a small test chamber made of type 304 stainless steel has been measured as a function of pumping speed in the range from 0.3 to 200 l/s. The chamber was first exposed to air and then pumped with different pumping speeds for three days at 20 degrees C without baking. Typical outgassing rates of the chamber are determined from the measurement of steady pressures at the pumping time of 72 h. It is found, as a result, that measured outgassing rates q obey a set of power laws of q(1) = C-1(S/A)(m1) and q(2) = C-2(S/A)(m2), where S/A is the ratio of pumping speed S to the surface area A of the chamber, C-1 and C-2 are constants, the exponents m(1) and m(2) are 0.8282 for S/A greater than or equal to 10(-3) l/s cm(2) and 0.4655 for S/A greater than or equal to 10(-3) l/s cm(-2). It is shown that the observed power law can be derived from theoretical consideration and is useful to estimate the ultimate pressure of an unbaked vacuum system.