How to Use Smartphone Projector Calculator
The Smartphone Projector Calculator helps you estimate the projected image size before building or testing a DIY phone projector setup.
- Choose your length unit — Select cm, inches, or meters. All inputs and results use the same unit.
- Enter phone screen diagonal — The diagonal size of your smartphone screen. This is usually printed on the phone’s spec sheet in inches (e.g., 6.1 inches). Convert to cm or meters if needed, or simply select the inches unit.
- Set aspect ratio — The default is 16:9, which covers most modern smartphones. Adjust for other ratios such as 20:9 or 4:3.
- Enter projection distance — The distance from the lens to the projection surface (wall or screen). Longer distances produce bigger images.
- Enter focal length (optional) — The focal length of the converging lens you are using. If left blank, the Smartphone Projector Calculator assumes a 10 cm object distance for the estimation.
- Read the results — The calculator shows the projected width, height, diagonal, magnification factor, and confirms the aspect ratio.
Formula & Theory - Smartphone Projector Calculator
The Smartphone Projector Calculator applies the thin lens equation and simple proportion scaling to estimate projected image dimensions.
Thin Lens Equation
1/f = 1/d_o + 1/d_iWhere d_o is the object distance (screen to lens) and d_i is the image distance (lens to projection surface).
Solving for magnification:
m = d_i / d_o = d_i / f − 1When focal length f is provided:
d_o = 1 / (1/f − 1/d_i)
m = d_i / d_oProjected Dimensions
Screen width (W_s) = d_screen / √(1 + 1/AR²)
Screen height (H_s) = W_s / AR
Projected width = W_s × m
Projected height = H_s × m
Projected diagonal = √(W² + H²)| Symbol | Meaning |
|---|---|
| f | Focal length of the projector lens |
| d_i | Projection distance (lens to screen) |
| d_o | Object distance (phone screen to lens) |
| m | Linear magnification |
| AR | Screen aspect ratio (width/height) |
| d_screen | Phone screen diagonal |
Assumptions and Limits
The Smartphone Projector Calculator uses the paraxial (thin lens) approximation. Real lenses exhibit chromatic and spherical aberrations that reduce sharpness. The model assumes the lens is aligned with the phone screen center. Keystone distortion occurs if the phone is tilted relative to the lens. For best results, the lens focal length should be shorter than the projection distance; if f ≥ d_i, no real image is formed and the calculator returns no result.
Use Cases for Smartphone Projector Calculator
The Smartphone Projector Calculator is useful for:
- DIY projector planning — Before building a cardboard or 3D-printed phone projector, use the Smartphone Projector Calculator to predict the image size and pick a suitable box depth.
- Lens selection — Compare how different focal lengths affect magnification and required projection distance for a target image size.
- Classroom and event setup — Estimate whether a phone projector can produce a large enough image for a classroom wall, presentation backdrop, or party screen.
- Camping and outdoor use — Check if your improvised phone projector will cast a viewable image at the available distance, accounting for your screen size and the lens you have on hand.
- Education in optics — Students can use the Smartphone Projector Calculator to explore the relationship between focal length, object distance, image distance, and magnification in a tangible, hands-on context.
The Smartphone Projector Calculator gives you a fast, transparent estimate so you can make informed decisions about your projection setup without guesswork.