Motivated by a renewed interest for the “additive dilogarithm” appeared recently, the purpose of this paper is to complete calculations on the tangent complex to the Bloch-Suslin complex, initiated a long time ago and which were motivated at the time by scissors congruence of polyedra and homology of $\mathrm {SL}_2$. The tangent complex to the trilogarithmic complex of Goncharov is also considered.