# Thin Lens Equation Calculator

URL: https://speedycalculator.com/calculators/physics/thin-lens/
Last updated: 2026-10-25

> The thin lens calculator uses 1/f = 1/dₒ + 1/dᵢ to find where a lens forms an image, and the magnification. Use a positive focal length for converging lenses and negative for diverging lenses.

## Inputs

- Focal length (mm, cm, m)
- Object distance (m, cm, mm)

## Results

- Image distance
- Magnification
- Lens power

## Formula

```
1/f = 1/dₒ + 1/dᵢ
m = −dᵢ ÷ dₒ
```

## Explanation

The lens equation describes cameras, eyes, magnifying glasses and projectors.

### How to use the Thin Lens Equation Calculator

- **Focal length**
- **Object distance**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Solve for the image distance from the focal length and object distance, then divide to get magnification.

### Inputs explained

FieldWhat to enterFocal lengthUnits: mm, cm, mObject distanceUnits: m, cm, mm

### What each result means

- **Image distance** = 1÷(1÷[Focal length] - 1÷[Object distance])
- **Magnification** = -[Image distance]÷[Object distance]
- **Lens power** = 1÷[Focal length]

### Example values

How the main result changes when **Focal length** changes and everything else stays at the example values above:

Focal length (mm)Image distance (mm)2525.31637.538.2175051.28262.564.5167577.922100105.263

## Worked example

Inputs — Focal length: 50 mm; Object distance: 2 m.

Results — **Image distance = 51.282 mm**; Magnification = -0.02564; Lens power = 20 diopters.

## FAQ

**What does a negative image distance mean?**
The image is virtual, on the same side as the object.

**What is a diopter?**
Lens power, the reciprocal of focal length in metres.

**What formula does the Thin Lens Equation Calculator use?**
1/f = 1/dₒ + 1/dᵢ.