We have developed a generalized semi-analytic approach for efficiently computing cyclization and looping J factors of DNA under arbitrary binding constraints. Many biological systems involving DNA-protein interactions impose precise boundary conditions on DNA, which necessitates a treatment beyond the Shimada-Yamakawa model for ring cyclization. Our model allows for DNA to be treated as a heteropolymer with sequence-dependent intrinsic curvature and stiffness, yet faithfully reproduces the results of Shimada and Yamakawa for the ring and unconstrained loop. In this framework, we independently compute enthlapic and entropic contributions to the J factor and show that even at small length scales (∼ℓ_p) entropic effects are significant. We propose a simple analytic formula to describe our numerical results for near planar loops of homogenous DNA, which can be used to predict experimental cyclization and loop formation probabilities as a function of loop size and binding geometry. We also introduce an effective torsional persistence length that describes the coupling between twist and bending of DNA when looped.