ZBARYCORR determines the barycentric redshift (z_B) for a given star. It calculates the positions and velocities of solar system objects, applies the rotation, precession, nutation, and polar motion of the Earth, applies the stellar motion using the Markwardt library (ascl:1807.016), Shapiro delay, and light-travel term, and finally calculates the quantity z_B—the barycentric correction independent of the measured redshift. A Python wrapper, BARYCORR (ascl:1807.018), is available.