The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory is a pulsed source of neutrons and, as a by-product of this operation, an intense source of pulsed neutrinos via stopped-pion decay. The COHERENT collaboration uses this source to investigate coherent elastic neutrino-nucleus scattering and other physics with a suite of detectors. This work includes a description of our Geant4 simulation of neutrino production at the SNS and the flux calculation which informs the COHERENT studies. We estimate the uncertainty of this calculation at the similar to 10% level based on validation against available low-energy pi(+) production data.