A new method for the determination of the volume fraction nu(f) of fibrils formed inside the crazes in polymers before their brittle fracture has been proposed. The method utilizes small-angle X-ray scattering measured on an absolute scale in combination with the precise measurement of the sample deformation. The method has been applied to the crazes in polystyrene for which the data on nu(f) are abundant. The result nu(f)=0.26 is in good agreement with those obtained by other methods ranging nu(f)=0.21-0.30, which confirms the validity of the proposed method.