Summary: To construct rigidly or locally supersymmetric bulk-plus-boundary actions, one needs an extension of the usual tensor calculus. Its key ingredients are the extended (\(F-\), \(D\)-, etc.) density formulas and the rule for the decomposition of bulk multiplets into (co-dimension one) boundary multiplets. Working out these ingredients for \(d = 4\), \(N = 1\) Poincaré supergravity, we discover the special role played by \(R\)-symmetry (absent in the \(d = 3\) \(N = 1\) case we studied previously). The \(U(1)_{A}\) R-symmetry has to be gauged which leads us to extend the old-minimal set of auxiliary fields \(S,P,A_{\mu }\) by a \(U(1)_{A}\) compensator \(a\). Our results include the “\(F+A\)” density formula, the “\(Q+L+A\)” formula for the induced supersymmetry transformations (closing into the standard \(d = 3 N = 1\) algebra) and demonstration that the compensator \(a\) is the first component of the extrinsic curvature multiplet. We rely on the superconformal approach which allows us to perform, in parallel, the same analysis for new-minimal supergravity.