Camera Lens Equivalent Focal Length Calculator • Photometry — Light • Online Unit Converters (2024)

This calculator determines the 35 mm equivalent (also called effective) focal length of a lens installed in a camera equipped with a smaller sensor. Alternatively, instead of a 35mm equivalent, it can determine another equivalent, for example, APS-C or 1” equivalent. This feature can be used to play with various sensor sizes and focal distances to better understand how this equivalent works.

Example: Calculate the equivalent focal length of a 50mm APS-C lens for a 35mm full-frame sensor.

Input

Focal length

f mm

Camera sensor (usually smaller than the full-frame sensor)

Target camera sensor (35 mm full-frame by default)

Output

To calculate, enter the focal length and select the camera sensor. By default, the calculator will show a 35 mm equivalent focal length of the focal length you entered into the form. This is the focal length of the lens with an entered focal length that would give the same magnification on a 35-millimeter camera.

Definitions and Formulas

We are talking about the equivalent focal length in order to understand how the focal length of the lenses of two cameras should differ if we want to obtain similar looking pictures with the same angle of view using two different cameras having different sensor sizes and without changing our physical position relative to our object. If the sensors are different, then, all other things being equal, the focal lengths of the lenses of the two cameras should be different.

This characteristic is not needed for beginners, those who bought their first camera because the equivalent focal distance will not tell them anything. Experienced photographers, however, who are accustomed to 35 mm cameras, will find this characteristic very useful. It will also be useful for those who are thinking about buying a new camera with a different size of a sensor and want to find out if their old lenses will work on a new camera and how they will shoot.

The magnification and angle of view of a lens depend not only on the focal length, but also on the size of the image sensor or film. Because 35 mm cameras dominated the market since the early 1930s, this format is always used for the comparison of lenses made for various sizes of image sensors. Most photographers who are experienced with interchangeable lenses worked with 35 mm cameras.

What is it — 35 Millimeters?

The 35 mm film was invented by William Kennedy Dickson, the assistant to Thomas Edison. Dickson designed an early motion picture camera and is credited as the inventor of 35 mm film in 1889. He collaborated with the Eastman company to produce a celluloid film having a width of 35 mm with four perforations per frame and a frame size 18.67 × 24.89 mm. Dickson used the 70 mm film stock supplied by Eastman Kodak company, which they cut in half and added perforation (holes placed in the film stock and used for transporting the film) along both sides. This size later changed to the modern 16 × 22 mm format when an optical sound track was added.

In 1895, the French scientists, filmmakers, and manufacturers of photographic equipment Auguste and Louis Lumière publicly demonstrated the first movie to paying audience. The movie was made on celluloid 35 mm film.

In the 1920s, the 35 mm film stock was introduced for use in still cameras. Leica camera popularized the format in the late 1920s and 1930s, however, several cameras used it before Leica. Early cameras used 18 × 24 format, which is half the full-frame size used today. The first camera that used the modern 24 × 36 mm format was the Simplex, introduced in 1914. Unlike later cameras, it could take 400 full-frame shots on 50 ft (15 m) rolls.

Why Compare to 35 Millimeters?

The image formed by any lens in the focal plane of a camera is circular and the size of the film or sensor determines how much of this circle is used to create a picture. This is why the angle of view of the lens is determined by both its focal length and the sensor size. Usually, the standard sensor size is used for comparison, which has a full-frame size of 24×nbsp;36 mm. Why? Because 24×nbsp;36 mm is the most common camera format and most photographers are familiar with the 35 mm film format.

On any 35 mm film or 24 × 36 mm sensor camera, a 35 mm lens is a wide-angle lens, a 50 mm lens is a “normal” lens, which best approximates human vision, and a 500 mm lens is a telephoto lens. At the same time, on cameras with smaller sensors, for example, on Canon Elph 360 point-and-shoot camera, 54 mm focal distance of its lens is equivalent to the 300 mm telephoto lens on a 35 mm camera.

Lenses installed on cameras with a smaller sensor will capture a smaller angle of view. Because with digital cameras with various sizes of the sensor there is no uniform relationship between the focal length and the angle of view, we need to find a way to standardize the focal length of lenses made for sensors of various sizes. This way of standardization is called a 35 mm equivalent focal length. The 35 mm equivalent focal length of a particular sensor–lens combination is the focal length of a lens installed on a 35mm camera that will give the same angle of view.

Note that because of the different aspect ratios of sensors in different cameras (3:2, 4:3, and 16:9 being the most common), this 35 mm equivalent is based on an equal diagonal angle of view. Note also that a 50 mm lens designed for a 35 mm camera will not change its focal length when installed on a camera with a smaller sensor. It will always be a 50 mm lens because this number is determined by the optical characteristics of the lens. What changes when installed in a different camera is its equivalent focal length, which has nothing to do with the actual focal length. What changes is the field of view due to cropping on a smaller sensor.

Sensor Sizes: Bigger is Better

Sensor sizes are given in a strange imperial format like 1/4" or 1/2.5”. However, this inch size has nothing to do with the actual sensor size. For example, 1/4” is 6.35 mm and the size of this 1/4" sensor is 3.20 × 2.40 mm with the diagonal 4.00 mm.

This confusing way of designating sensor sizes dates back to the 1950s when vidicon camera vacuum tubes appeared on the market. For example, the vidicon in the picture has an outside diameter of 28.6 mm, which is slightly more than 1 inch, and was marketed by Toshiba as a 1” vidicon. The diagonal of its imaging area is 16 mm, which is approximately two-thirds of an inch. So, a 16 mm sensor was commonly referred to as a 1-inch sensor. This resulted in a seemingly odd conversion: 1 inch = 16 mm. This conversion allows a quick calculation of modern photosensors diagonals from the inch sizes.

So, why do they use this old size description for modern image sensors? Most probably because of marketing reasons because the manufacturers can put a slightly bigger number on the sensor box, which looks better. Note that at the same time, the dimensions of sensors larger than 1 inch are indicated in millimeters.

Sensor Size and Crop Factor

Let me remind you what is image cropping. This is a removal of peripheral areas of a photograph. It can be performed on a physical photograph or digitally. The same term is used to describe image sensors, which come in many sizes with the smallest one used in smartphone and digital compact point and shoot cameras and the largest in professional DSLR and mirrorless cameras. Professional DSLR and mirrorless interchangeable-lens cameras use 24 × 36 mm or even larger sensors, which capture more light with less noise. Pictures obtained from larger sensors are sharper, clearer, brighter, and have more details. The disadvantage of larger sensors is that they require larger, heavier, and much more expensive lenses. Their high price is also a factor.

Crop factor is a number used to calculate the difference between the angle of view of a lens installed on cameras with different sensor sized. It is determined as the ratio of diagonals of the two sensors. A crop sensor is exactly a crop from a larger sensor. Put a full-frame camera beside a 1.6 crop camera and if the full-frame camera has a lens with a focal length 1.6 times larger than the lens of a crop camera, the photos taken by both cameras will be identical by the viewing angle. Of course, this is true if all other variables are identical. The formula for equivalent focal length, which is used in this calculator is easy:

Here F_eq is the equivalent focal distance of the lens installed on the target (usually 35 mm) camera, which provides that same viewing angle as the lens with the focal distance F installed on a camera with a smaller sensor.

It is somewhat more complicated, though not much, to find the equivalent focal length if neither camera is full frame, for example, if we are trying to compare an APS-C camera with a smartphone camera with a 1/2" sensor. In this case, the crop factor between these cameras will be equal to the ratio of their sensor diagonals. Of course, this calculator can do this calculation for you. Just select the source and target camera sensors and click or tap the Calculate button.

The smaller the camera sensor, the lower its dynamic range. It means that a camera with a smaller sensor cannot achieve an ideal exposure in shadows and highlights simultaneously — the details in shadow will be lost and highlights will be burnt out. Cameras with larger sensors such as DSLR or mirrorless full-frame cameras can record a broader dynamic range, that is they can retain detail in both the shadows and highlights. For example, imagine a wedding picture: a white dress, a black suit — and most compact and phone cameras cannot take a good picture because this scene easily exceeds the subject brightness range that digital compact cameras can handle.

F-Stop Change

In the picture below, photos of two objects were taken by one camera with a zoom lens at 105 and 24 mm, f/4. You can see that though the fields of view are identical, the depth of field is clearly not identical, though both pictures are taken at f/4. The left picture is uncropped and taken at f/4 and the right picture is cropped and also taken at f/4 on the same camera. This simulates the use of a crop camera with a much smaller sensor having a crop factor of 105:24=4.38. Note that talking about ISO is beyond the scope of the description of this calculator.

So, the conclusion is that if you zoom out at a constant aperture, the depth of field increases like shown in the picture. A photo taken with the lens at 105 mm does not have the same depth of field as a cropped photo taken with the lens zoom out to 24 mm. So, when you crop pictures using a crop-sensor camera, you have a problem with decreasing depth of field. The formula for the equivalent aperture is exactly the same as the formula for the equivalent focal length:

In our example, when we compare the full-frame sensor to 1/1.6” sensor (crop factor of 4.3), the f-number will change from f/4 to f/4 × 4.3 = f/18.

Another lens characteristic is the relative aperture N, which is the ratio of the entrance pupil (diaphragm or iris) diameter d and the focal length f:

The relative aperture is the reciprocal of the f-number:

For example, a lens with an entrance pupil of 28 mm in diameter and a focal length of 50 mm has a relative aperture of 50 : 28 ≈ 1.8. In everyday life, the relative aperture of a lens is commonly referred to as its aperture or even the f-stop or f-number despite the fact that f-number and relative aperture are reciprocal numbers.

This article was written by Anatoly Zolotkov

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