After playing with the youth clubs of CSKA Moscow, Kulagin has played professionally with the Russian clubs
Triumph Lyubertsy, Rossiya Novogorsk, and
CSKA Moscow. After five seasons, he parted ways with CSKA Moscow on 1 June 2020. On 19 August 2020 Kulagin signed with
BC Enisey. On 20 July 2021 he signed for the third time with
Nizhny Novgorod of the
VTB United League. On 29 June 2022 he signed with
UNICS Kazan of the
VTB United League. ==National team career==