Accurate　calculation　of　the　additional　damping　ratio　provided　by　the　damper　to　the　structure　is　a　necessary　parameter　for　evaluating　and　selecting　the　optimal　damping　design　scheme.　At　present,　bilinear　model　is　usually　adopted　to　calculate　the　additional　damping　ratio　of　buckling-restrained　brace　(BRB)　and　metal　damper,　but　this　method　is　not　accurate.　The　hysteretic　characteristics　of　the　dampers　can　be　simulated　accurately　by　Bouc–Wen　model.　However,　the　traditional　expression　of　Bouc–Wen　model　is　implicit,　and　its　energy　dissipation　cannot　directly　be　quantified.　In　view　of　this,　the　explicit　analysis　of　Bouc–Wen　model　is　carried　out,　and　the　analytical　solution　of　energy　dissipation　of　this　model　is　proposed.　Furthermore,　the　formula　for　calculating　the　additional　damping　ratio　is　obtained.　The　correctness　of　the　analytical　solution　is　verified　by　numerical　examples,　and　compared　with　the　bilinear　model,　the　superiority　of　the　proposed　method　in　the　calculation　accuracy　is　proved.　The　effect　of　the　Bouc–Wen　model　parameters　on　the　additional　damping　ratio　is　studied.　The　difference　between　Bouc–Wen　model　and　bilinear　model　with　various　earthquake　excitations　is　proved　by　finite　element　method,　and　the　difference　of　dynamic　response　between　the　damping　structures　based　on　different　damper　models　is　shown　and　compared.　©　2021　John　Wiley　&　Sons,　Ltd.