Defect　curvature　was　developed　based　on　our　previous　proposed　direction　curvature　theory.　Defect　curvature,　as　a　universal　criterion,　was　used　to　identify　reactivities　of　mono-　and　di-vacancies　in　single-walled　carbon　nanotubes.　Calculated　results　at　B3LYP/6-31G*　level　showed　that,　regardless　of　mono-　and　di-vacancies,　vacancy　formation　energies　E-f　decreased　with　increasing　defect　curvatureKv(1),　(for　mono-vacancies)　orKv(2)　(for　di-vacancies).　Each　defect　model　of　mono-vacancies　had　two　types　of　structural　products.　However,　each　defect　model　of　di-vacancies　was　only　corresponding　to　one　structural　product.　In　mono-　or　di-vacancies,　large　included　angles　between　new　formed　C-C　bonds　(for　mono-vacancies)　or　the　linked　C-C　bonds　of　the　5-ring　and　8-ring　(for　di-vacancies)　and　the　tubular　axis　were　corresponding　to　short　C-C　bonds　and　small　Ef.　These　product　structures　for　di-vacancies　were　related　to　the　magnitude　of　Kv(2).　(C)　2014　Elsevier　B.V.　All　rights　reserved.