A method and apparatus provides optimized installation site specifications for sprinkler head position and nozzle size for center pivot and/or linear movement type irrigation systems in which a plurality of sprinkler heads are typically mounted at multiple adjacent lateral positions along a water supply boom/line. A sprinkler head spacing and nozzle size computational apparatus and method is disclosed which employs a sprinkler precipitation depth-profile based modeling technique for determining and optimizing lateral positions and nozzle sizes for sprinkler heads disposed along the length of an irrigation system supply distribution boom/line. A required/desired irrigation application delivery rate/depth is specified by an irrigation system user/designer for one or more discrete segments along the irrigation system distribution boom/line according to specific irrigation needs. An optimized nozzle size and position for each sprinkler head disposed along the boom/line is adaptively determined based on the specified required precipitation delivery depth and summations of individual predicted application depth profiles for an initial sprinkler and successively added sprinklers such that a computed delivery accumulation depth falls within a predefined range of error tolerance for the specified required delivery depth for that segment of the distribution line. An associated computer apparatus executing program instructions for implementing the method generates and displays a graphic indication of required and predicted precipitation depth profiles and computed optimized lateral positions and nozzle sizes for the irrigation system sprinklers.