We have investigated droplet nucleation and bubble cavitation in the quantum fluid helium-3 based on a nonlocal density-functional approach. A marked effect of droplet (or bubble) curvature on the rate of droplet nucleation or cavitation has been found. Without considering this curvature effect (as in the classical theory of nucleation) the droplet nucleation rate for helium-3 could be underestimated (i.e., near 1 K) or overestimated (i.e., near 2.5 K) by orders of magnitude, respectively; for bubble cavitation, the rate could be underestimated by more than twenty orders of magnitude (near 1 K).