Active illumination 3D imaging systems based on Time-of-flight (TOF) and Structured Light (SL) projection are in rapid development, and are constantly finding new areas of application. In this paper, we present a theoretical design tool that allows prediction of 3D imaging precision. Theoretical expressions are developed for both TOF and SL imaging systems. The expressions contain only physically measurable parameters and no fitting parameters. We perform 3D measurements with both TOF and SL imaging systems, showing excellent agreement between theoretical and measured distance precision. The theoretical framework can be a powerful 3D imaging design tool, as it allows for prediction of 3D measurement precision already in the design phase.