Smartphone Projector Calculator

A simple smartphone projector uses a converging lens to form an enlarged real image of a phone screen on a wall or projection surface. Moving the projector farther from the wall generally increases image size, while using a longer focal-length lens generally reduces magnification at the same distance. This calculator provides a convenient geometric estimate for planning a DIY projector enclosure or comparing setup distances. The model approximates magnification as projection distance divided by lens focal length after converting both measurements to the same unit. Projected diagonal is the phone screen diagonal multiplied by that magnification. The calculator then converts diagonal into width and height using a 16:9 aspect ratio. For that ratio, width and height are proportional to sixteen and nine, and the diagonal follows from the Pythagorean theorem. The estimate intentionally simplifies the thin-lens equation. In a physical projector, the phone-to-lens distance must be adjusted slightly beyond one focal length to bring the image into focus. Exact magnification is image distance divided by object distance, and the object and image distances are linked by the reciprocal thin-lens equation. Lens housing, principal-plane location, wall distance measured from the lens, and focusing travel all affect the final result. The approximation is most useful when projection distance is much larger than focal length. Image brightness falls as the picture is enlarged because the phone's available light spreads over a larger area. A projected image that is mathematically large may be too dim to view unless the room is very dark. Lens diameter, transmission, screen brightness, phone brightness, internal reflections, and enclosure light leaks also matter. A larger lens can collect more light, but inexpensive magnifiers may introduce distortion, color fringes, and softness near the edges. The source image must usually be rotated or mirrored because a single converging lens inverts the projected image. Software rotation can correct orientation, while the enclosure must hold the phone and lens square to the screen. If the projector points upward or sideways, keystone distortion makes one edge larger than another. Keeping the optical axis perpendicular to the projection surface provides the most rectangular result. Use the calculated dimensions to choose a wall area, estimate enclosure geometry, and compare focal lengths before construction. Treat the answer as a starting point, then test the actual lens and phone on a movable bench before cutting permanent parts. Commercial phone attachments may use additional optics, so their specified throw ratio should take precedence over this simplified calculation. The tool predicts size only; it does not predict focus quality, brightness, resolution, or viewing comfort.