## focal length calculator

Get the Focal Length of the Needed Lens

The Horizontal Field of View is

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The Focal Length on {{ lens }} is

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## How is an image captured?

An object is seen by reflecting the light from a light source (such as a bulb or the sun) or being the light source. The camera lens can transmit and cast the light from the object to an image sensor, which will then produce an image.

## Image circle

The light cast to the image sensor forms a circle of light, also known as the image circle. Most times, we want the image circle large enough to shed light on the whole image sensor, otherwise, we will see dark areas on the edges of the image. However, for some fisheye lenses, we want the whole image circle inside the image sensor frame so that we never miss any detail of the whole 180-degree hemisphere.

## Sensor and Optical Format

Sensor format refers to the size and aspect ratio of an image sensor, usually with fractions such as 1/4”, 1/3”, 1/2.5”. The 1/4” image sensor has a diagonal of 4.5mm (the 1/4” of 18mm), and an aspect ratio of 4:3. The optical format describes the lens image circle with a similar measurement, except that the sensor format is measured by the diagonal while the optical format represents the lens image circle’s diameter. Therefore, if the lens optical format equals the image sensor format, the image circle is just large enough to produce a decent image without poorly exposed dark pixels on the corners.

## Focal length

The focal length of a lens indicates its ability to converge light, and it’s measured by the distance between the lens center and focal point. The shorter the distance is, the more sharply it bends the light, and the larger field it’ll be able to squeeze into its image circle. As M12 lenses are made up of several pieces of glass (or plastic), the term “effective focal length (EFL)” is used to present this ability.

## Field of View

Field of View (FoV) usually refers to the field an image sensor captures. It is not a constant value because further scene results in a larger captured field.  Therefore, FoV is usually represented in angles of view – the larger, the wider. The lens casts an image circle while the sensor captures a rectangular section, so the native FoV of the lens is different from the field the sensor captures. Most times, the sensor crops a rectangular section inside the image circle. For the fisheye lens, the image circle is totally inside the rectangle so that the sensor captures the whole cast field.

## How do the optical format and sensor format and affect the Field of View?

The optical format decides the size of the image circle where the whole field will be squeezed into, and the sensor format decides the rectangular area to catch the image circle. In most camera setups, the sensor rectangular area crops a section inside the image circle.
In an ideal case, the optical format would equal the sensor format, where the sensor’s diagonal equals the image circle’s diameter, so the diagonal field of view of the sensor (DFoV) equals the native FoV of the lens.
It’s also common to have a lens with a larger optical format than the image sensor format. However, the field outside the sensor rectangle will be missed, resulting in a smaller field of view. With lenses of the same optical format, the smaller the sensor is, the smaller the field of view we will get. If the optical format is smaller than the sensor format, dark unexposed surroundings will occur, but it’s helpful to capture the whole field of the fisheye lenses.

## How does the focal length affect the Field of View?

FoV is highly dependent on the lens focal length because the image sensor catches the field squeezed into the image circle by the lens. A shorter focal length means the lens can squeeze more fields into its image circle within a certain distance. As focal length represents the ability to converge light, lenses with the same focal length will similarly bend the light, resulting in a similar field of view on a certain format of sensors.