General forms of Wirtinger-type inequalities are proved in both one and n dimensions. Since singular endpoints and unbounded intervals are allowed, a large class of new one-dimensional results are generated as well as previously known results. In the (usual) case that the admissible functions are identically zero on the boundary $\partial G$ of a bounded domain G in $E^n $, the sharp form of Wirtinger’s inequality in G is proved without any regularity hypotheses on $\partial G$. If the admissible functions are not so restricted, the companion inequality is proved for domains with ${\bf C}^2 $ boundaries.