Model the optics of a DIY smartphone projector. Enter your phone's screen size, the lens focal length, and how far you'll project the image to get the required lens position, magnification, and projected image size.
Magnification m = (di − f) / f. The projected image is inverted, so mirror or rotate the phone video 180° before projecting.
Results
Calculated
Phone-to-lens distance
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Object distance (do) — place the phone this far from the lens
Magnification
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(di − f) / f — how many times larger the image is than the screen
Projected image size
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Diagonal size of the image on the wall or screen
Image width × height
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Approximate projected dimensions
Ready
Enter your phone screen size, lens focal length, and throw distance, then press Calculate.
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How to use this calculator
A DIY smartphone projector works by placing a converging (magnifying or Fresnel) lens between the phone and a wall or screen, forming a real, magnified, inverted image of the phone's display. This calculator applies the thin lens equation to tell you exactly where to place the phone and how big the resulting image will be. Enter your phone's screen diagonal and aspect ratio, the lens's focal length, and your intended throw distance (lens-to-screen), then click Calculate.
Understanding the inputs
Phone screen diagonal and aspect ratio together define the width and height of the glowing screen area being projected — use the diagonal size from your phone's spec sheet. Lens focal length is a fixed property of the lens (in millimeters); it is usually printed on the lens rim or listed in its product page. Throw distance is how far you plan to place the lens from the wall or screen — this is the one variable you control when building the enclosure.
Interpreting the results
Phone-to-lens distance is the object distance (do) — the exact gap to leave between the phone and the lens inside your box for the image to be in focus at your chosen throw distance. Magnification tells you how many times bigger the image is than the phone screen. Projected image size and width × height give the resulting picture dimensions on the wall. If your throw distance is too close to the focal length, no real image can form — increase the distance or use a shorter focal length lens.
Frequently Asked Questions
What formula does a DIY smartphone projector use?
It uses the thin lens equation, 1/f = 1/do + 1/di, where f is the lens focal length, do is the distance from the phone to the lens, and di is the distance from the lens to the screen (the throw distance). Solving for do gives do = f × di / (di − f). The magnification is m = (di − f) / f, and the projected image size is the phone screen size multiplied by m.
Why is the projected image upside-down and mirrored?
A single converging lens always forms a real image that is inverted (upside-down) relative to the object. This is a basic property of lens optics, not a flaw. To view the video right-side up, rotate the phone's playback 180 degrees before projecting, or use an app or video file that has already been flipped.
Why does the image get dimmer as it gets bigger?
The light leaving the phone screen is fixed, but at higher magnification that same light is spread over a much larger area, so the brightness per unit area (illuminance) drops roughly with the square of the magnification. Larger, more magnified images need a fully darkened room and maximum phone screen brightness to stay watchable.
What if the calculator says the throw distance is too short?
The throw distance (lens-to-screen distance) must be greater than the lens focal length, or the lens cannot form a real image at all. If you see this message, move the screen or wall farther from the lens, or switch to a lens with a shorter focal length.