Smartphone Projector Calculator
Build a better DIY smartphone projector by getting the optics right before you cut a single piece of cardboard. Enter your lens focal length and either the phone-to-lens or lens-to-screen distance, and this calculator solves the missing measurement using the thin lens equation. It also gives you magnification, projected screen size, and total throw distance. Switch between millimetres and centimetres at any time.
Formula
Worked example
A magnifying lens with f = 150 mm, phone placed at do = 170 mm from the lens. Image distance: 1/di = 1/150 - 1/170 = 0.00667 - 0.00588 = 0.000784, so di = 1 / 0.000784 approx 1275 mm. Magnification M = 1275 / 170 = 7.5x. A phone screen 65 mm tall projects to 65 x 7.5 = 487 mm (about 48.7 cm) on the wall. Total throw distance is 170 + 1275 = 1445 mm from phone to wall.
How a DIY smartphone projector works
A DIY smartphone projector uses a single convex (magnifying) lens to project the light from your phone screen onto a wall or sheet. The lens bends light rays outward from every point on the screen so they converge again on the far side, forming a magnified but inverted real image. The physics is the same as a slide projector, just with your phone acting as the slide. Because the image is inverted, you need to rotate your phone 180 degrees so the projected picture appears the right way up. The sharpness of the image depends on how accurately you position the phone relative to the lens: the thin lens equation tells you the exact phone-to-lens distance (object distance, do) for a given lens-to-screen distance (image distance, di).
The thin lens equation and magnification
The thin lens equation is 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance from the phone screen to the lens centre, and di is the distance from the lens centre to the projection screen. Rearranging for any one unknown gives: di = 1 / (1/f - 1/do) when you know the lens and phone position; do = 1 / (1/f - 1/di) when you have set the projector at a fixed distance from the wall; and f = do times di divided by (do + di) when you want to find the focal length of an unlabelled lens. Magnification M is simply di divided by do. If M equals 7, the image is 7 times taller and 7 times wider than the phone screen, so the image area is 49 times larger. Because the same number of lumens now cover 49 times the area, brightness per unit area drops by the same factor, which is why very high magnifications need complete darkness.
Choosing a focal length and phone position
Magnifying lenses with focal lengths between 130 mm and 180 mm are the most popular choice for smartphone projectors. Shorter focal lengths give higher magnification for a given throw distance but create more edge blurring from aberrations. Longer focal lengths are gentler on image quality but need a larger box. For a typical bedroom setup with 1 to 2 metres of throw distance and a phone placed 160 to 200 mm from the lens, a 150 mm lens gives magnifications of roughly 5x to 12x. Remember that the phone must always sit further from the lens than the focal length: if do is equal to or less than f, the lens cannot form a real image at all.
Brightness, image quality, and common problems
Brightness is the biggest practical limitation of single-lens smartphone projectors. A phone screen typically produces 400 to 800 nits, but that light is spread over an image area that grows with the square of magnification. At 8x the image area is 64 times larger, so apparent brightness on the screen drops to roughly 6 to 12 nits, comparable to a dim night light. Using your phone at maximum brightness, covering the lens aperture to reduce aberrations, and viewing in complete darkness helps considerably. Edge blurring (from spherical aberration and field curvature) is another common issue: an achromatic doublet lens, available cheaply online, corrects most of it. The final issue is colour fringing, caused by chromatic aberration splitting different wavelengths to slightly different focal points. Again, an achromatic lens solves this.
Magnification ranges and what to expect
| Magnification | Viewing condition | Image brightness | Practical use |
|---|---|---|---|
| Below 2x | Any lighting | Bright | Too small to be useful as a projector |
| 2x - 4x | Dim room | Good | Small screen replacement, close viewing |
| 4x - 8x | Dark room | Moderate | Best balance of size and brightness |
| 8x - 12x | Complete darkness | Low | Large images but poor in ambient light |
| Above 12x | Complete darkness | Very low | Usually too dim for comfortable viewing |
Practical guide to how magnification affects image quality and brightness for a typical smartphone projector using a single convex lens.
Frequently asked questions
Why does my projected image appear upside down?
A convex lens forms a real inverted image on the far side. This is a fundamental property of the optics, not an error. To correct it, rotate your phone 180 degrees in the box so the projected image appears right-side up. You may also need to enable auto-rotate lock or use developer options to force landscape or portrait orientation.
What focal length lens should I buy for a smartphone projector?
A focal length of 130 mm to 160 mm is the most widely recommended range for DIY projectors. Shorter focal lengths give larger images at closer distances but show more edge blurring. A 150 mm lens with the phone placed at about 170 mm gives a magnification of around 7x to 9x for a typical living-room throw distance of 1.2 to 1.5 metres. You can find the exact focal length you need by entering your desired image size and available throw distance into this calculator.
How can I measure the focal length of an unlabelled lens?
On a sunny day, hold the lens over a piece of paper and move it up and down until sunlight converges to the smallest, sharpest point. Measure the distance from the centre of the lens to the paper: that is the focal length. Alternatively, set your projector up so it projects a sharp image, then measure do (phone to lens) and di (lens to wall) and enter them into this calculator with "solve for focal length" selected.
Why is my projected image blurry at the edges?
Single-element magnifying lenses suffer from spherical aberration and field curvature, which causes peripheral rays to focus at a slightly different distance than central ones. Three fixes help: use an achromatic doublet lens instead of a simple glass lens, reduce the effective aperture by taping a cardboard ring with a smaller hole over the lens (this cuts out the worst peripheral rays at the cost of some brightness), or accept a slight focus compromise at a distance between the centre and edge optimal points.
What is the best magnification for a DIY smartphone projector?
Between 4x and 8x is the practical sweet spot. Below 4x the projected image is not much bigger than the phone screen and the effort is not worthwhile. Above 8x the image becomes noticeably dim even in a dark room, because brightness per unit area falls with the square of magnification. If you want a very large image and can live with dim output, magnifications up to 12x are achievable with the phone at full brightness in a completely dark room.
Can I use this calculator for any convex lens, not just a magnifying glass?
Yes. The thin lens equation applies to any thin convex lens: magnifying glasses, reading glasses lenses, Fresnel lenses cut from overhead projector sheets, and even some inexpensive achromatic doublets. Fresnel lenses are popular because they are large and inexpensive, though they show some visible diffraction artefacts. What matters is the focal length, not the physical form of the lens.