Calculate projected image size, brightness, and lens placement for a DIY smartphone projector. Includes lens comparison and contrast analysis.
Building a projector from a smartphone and a magnifying lens is a popular DIY project that demonstrates fundamental optics. The thin lens equation 1/f = 1/dₒ + 1/dᵢ governs the relationship between focal length, object distance (phone to lens), and image distance (lens to wall). By placing the phone just outside the focal length of a convex lens, you create a magnified real image on the wall.
However, brightness is the main challenge. A phone screen at 600 nits is vastly dimmer than a projector lamp at 2,000+ lumens. The projected image spreads that light over a much larger area, so contrast ratio drops rapidly with magnification. A dark room is essential, and the largest practical lens diameter helps capture more light.
This calculator helps you design your DIY projector by computing the exact phone-to-lens distance for focus, the projected image size, the approximate brightness, and the contrast ratio against ambient light. Choose your lens, enter your phone specs, and find the optimal setup.
It lets you estimate focus distance, image size, and likely brightness before you cut cardboard or buy lenses. That saves time on trial-and-error builds and sets realistic expectations about room darkness and screen size. It also helps show whether a build is a fun demo or a genuinely usable projection setup.
Thin Lens: 1/f = 1/dₒ + 1/dᵢ → dₒ = f·dᵢ/(dᵢ − f). Magnification: M = dᵢ/dₒ. Image size = phone size × M. Luminous flux ≈ L × A_phone × Ω_lens. Screen illuminance = flux / image area. Contrast = illuminance / ambient.
Result: ~100 × 50 cm image
With an 80 mm focal lens and 200 cm projection distance, the phone sits about 6.7 cm from the lens. The image is magnified ~30× but brightness drops to a few lux — you need a very dark room.
The phone screen acts as the object and the wall acts as the image plane. For a sharp image, the phone must sit just beyond the focal length of the lens, and small changes in distance can shift focus noticeably. The calculator helps you find that spacing without repeatedly moving the phone by hand.
A phone display can look bright up close but still produce a dim projection because its light is spread over a much larger area. Doubling the image width roughly quarters the illuminance on the wall. Lens diameter matters too: a larger lens captures more of the light leaving the screen, which is why page-magnifier Fresnel lenses work better than tiny hobby lenses.
DIY smartphone projectors work best in a dark room, with a modest image size and a well-darkened enclosure. Matte-black interior surfaces, careful lens alignment, and a flat projection surface improve the result more than chasing extreme magnification. If the goal is readable text rather than a novelty demo, keep the image small and the throw distance short.
Phone screens emit about 500-1500 nits over ~50 cm². Spreading that over a 1 m² image reduces brightness by 200×. A very dark room is essential.
Yes. A single convex lens inverts the image. Either flip the phone upside-down or use a screen rotation app to mirror the display.
Shorter focal length = closer phone placement but more magnification. 80-120 mm is a good range for room-scale projection.
Use a larger lens (captures more light), shorter projection distance (smaller image = brighter), and a completely dark room. Some people add a second lens for better light collimation.
Simple lenses have field curvature and chromatic aberration. An achromatic doublet lens reduces color fringing. Stopping down the lens improves edge sharpness but reduces brightness.
Only in a very dark room with a small image size. For readable text, keep the image under 50 cm diagonal and use maximum phone brightness.