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Electron and x-ray diffraction are well-established experimental methods used to explore the atomic scale structure of materials. In this work, a computational method is implemented to produce virtual electron and x-ray diffraction patterns directly from atomistic simulations without a priori knowledge of the unit cell. This method is applied to study the structure of [0 1 0] symmetric tilt low-angle and large-angle grain boundaries in Ni. Virtual electron diffraction patterns and x-ray diffraction 2θ line profiles show that this method can distinguish between low-angle grain boundaries with different misorientations and between low-angle boundaries with the same misorientation but different dislocation configurations. For large-angle 5 (2 1 0), 29 (5 2 0) and 5 (3 1 0) coincident site lattice [0 1 0] symmetric tilt grain boundaries, virtual diffraction methods can identify the misorientation of the grain boundary and show subtle differences between grain boundaries in the x-ray 2θ line profiles. A thorough analysis of the effects of simulation size on the relrod structure in the electron diffraction patterns is presented.