The cell nucleus must continually resist and respond to intercellular and intracellular mechanical forces to transduce mechanical signals and maintain proper genome organization and expression. Altered nuclear mechanics is associated with many human diseases, including heart disease, progeria, and cancer. Chromatin and nuclear envelope A-type lamin proteins are known to be key nuclear mechanical components perturbed in these diseases, but their distinct mechanical contributions are not known. Here we directly establish the separate roles of chromatin and lamin A/C and show that they determine two distinct mechanical regimes via micromanipulation of single isolated nuclei. Chromatin governs response to small extensions (<3 ?m), and euchromatin/heterochromatin levels modulate the stiffness. In contrast, lamin A/C levels control nuclear strain stiffening at large extensions. These results can be understood through simulations of a polymeric shell and cross-linked polymer interior. Our results provide a framework for understanding the differential effects of chromatin and lamin A/C in cell nuclear mechanics and their alterations in disease.