The calculation of the indirect carbon emission is essential for power system policy making, carbon market development, and power grid planning. The embedded carbon emissions of the electricity system are commonly calculated by carbon emission flow theory. However, the calculation procedure is time-consuming, especially for a country with 500–1000 thousand nodes, making it challenging to obtain nationwide carbon emissions intensity precisely. Additionally, the calculation procedure requires to gather all the grid data with high classified levels from different power grid companies, which can prevent data sharing and cooperation among different companies. This paper proposes a distributed computing algorithm for indirect carbon emission that can reduce the time consumption and provide privacy protection. The core idea is to utilize the sparsity of the nodes' flow matrix of the nationwide grid to partition the computing procedure into parallel sub-procedures executed in multiple terminals. The flow and structure data of the regional grid are transformed irreversibly for privacy protection, when transmitted between terminals. A 1-master-and-N-slave layout is adopted to verify the method. This algorithm is suitable for large grid companies with headquarter and branches in provinces, such as the State Grid Corporation of China.