The theory of similarity is applied to scale-up or down steam cracking coils. Dimensional analysis of the model equations shows that scale-up is possible under partial similarity only. Inevitably this leads to differences in product yields between units of different scale. However, careful relaxation of the criteria of similarity can limit scale dependent influences. Two different relaxation strategies are distinguished; the first one aims at realizing the same axial pressure profile neglecting radial non-uniformities, the second focuses on realizing the same radial temperature profile. Neglect of similarity of the radial temperature profile leads to larger differences as compared to differences resulting from neglect of the similarity of the axial pressure profile. In the case of ethane cracking, differences between units of different scale resulting from neglecting the similarity of the radial temperature profile can be up to 4.0% (rel.) for the conversion and up to 1.8% (rel.) for the ethylene yield. This insight is used to design the ideal pilot plant reactor to scale down different industrial reactors. (c) 2007 Elsevier B.V. All rights reserved.