# Smartphone Projector Calculator

URL: https://speedycalculator.com/calculators/physics/smartphone-projector/
Last updated: 2026-10-30

> The smartphone projector calculator finds where to place a phone behind a magnifying-glass lens in a shoebox projector, the size of the projected image and the magnification, from the lens focal length and the distances.

## Inputs

- Lens focal length f (cm, mm, m, in, ft)
- Phone-to-lens distance u (cm, mm, m, in, ft)
- Phone screen diagonal (in, cm)

## Results

- Lens-to-wall distance for a sharp image
- Magnification
- Projected image diagonal
- Setup

## Formula

```
1/f = 1/u + 1/v,  M = v/u,  image size = M × screen size
```

## Explanation

A shoebox, a magnifying glass and a phone make a simple projector. The phone must sit just outside the lens's focal length to throw a large, sharp, inverted image onto a wall.

### How to use the Smartphone Projector Calculator

- **Lens focal length f**
- **Phone-to-lens distance u**
- **Phone screen diagonal**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the lens focal length, the phone-to-lens distance and the phone's screen diagonal.

### Inputs explained

FieldWhat to enterLens focal length fUnits: cm, mm, m, in, ftPhone-to-lens distance uUnits: cm, mm, m, in, ftPhone screen diagonalUnits: in, cm

### What each result means

- **Magnification** = [Lens-to-wall distance for a sharp image]÷[Phone-to-lens distance u]
- **Projected image diagonal** = [Magnification]×[Phone screen diagonal]

## Worked example

Inputs — Lens focal length f: 20 cm; Phone-to-lens distance u: 22 cm; Phone screen diagonal: 6.1 in.

Results — **Lens-to-wall distance for a sharp image = 2.2 m**; Magnification = 10 ×; Projected image diagonal = 61 in; Setup = Real image – it works.

## Key terms

- **Real image**: Image formed where light rays actually converge.

## FAQ

**Why is the image upside down?**
A single convex lens forms an inverted real image – lock your phone's rotation and flip it.

**How do I get a bigger picture?**
Move the phone closer to the focal point and the wall farther away.

**Why is it dim?**
Light spreads over a large area; use a dark room and maximum brightness.

**What lens works best?**
A large-diameter magnifier with a focal length of 15–30 cm.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)