View source for Physics:35 mm equivalent focal length

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[[Image:Full-frame vs APS-C.svg|thumb|250px|right|The resulting images from 50&nbsp;mm and 70&nbsp;mm lenses for different sensor sizes; 36x24&nbsp;mm (red) and 24x18&nbsp;mm (blue)]]

In [[Photography|photography]], the '''35&nbsp;mm equivalent focal length''' is a measure of the [[Angle of view|angle of view]] for a particular combination of a [[Engineering:Still camera|camera]] lens and film or [[Engineering:Image sensor format|image sensor size]]. The term is popular because in the early years of digital photography, most photographers experienced with interchangeable lenses were most familiar with the [[135 film|35 mm film]] format.

On any 35&nbsp;mm film camera, a 28&nbsp;mm lens is a [[Engineering:Wide-angle lens|wide-angle lens]], and a 200&nbsp;mm lens is a [[Engineering:Long-focus lens|long-focus lens]]. Because digital cameras have mostly replaced film cameras and the image sensor size that also determines the angle of view is not standardized as the film size was, there is no uniform relation between the lens [[Focal length|focal length]] and the angle of view due to possibilities of using various image sensor sizes at the same focal length (i.e., a different image sensor size resulting in a different angle of view at the same lens focal length). The 35&nbsp;mm equivalent focal length of a particular lens–sensor combination is the focal length that one would need for a 35&nbsp;mm film camera to obtain the same angle of view. Two lens-sensor combinations with the same 35 mm equivalent focal length are expected to have the same angle of view.

Most commonly, the 35&nbsp;mm equivalent focal length is based on equal ''diagonal'' angle of view.<ref name="panorama">[http://www.panoramafactory.com/equiv35/equiv35.html What is "35&nbsp;mm equivalent focal length?"] The Panorama Factory, 2004.</ref> This definition is also in the CIPA guideline DCG-001.<ref name="cipa_guideline">{{Cite web |url=http://www.cipa.jp/std/documents/e/DCG-001_E.pdf |title=CIPA DCG-001-Translation-2005 Guideline for Noting Digital Camera Specifications in Catalogs |access-date=2015-10-19 |archive-url=https://web.archive.org/web/20170202125644/http://www.cipa.jp/std/documents/e/DCG-001_E.pdf |archive-date=2017-02-02 |url-status=dead }}</ref> Alternatively, it may sometimes be based on ''horizontal'' angle of view. Since 35&nbsp;mm film is normally used for images with an [[Aspect ratio (image)|aspect ratio]] (width-to-height ratio) of 3:2, while many digital cameras have a 4:3 aspect ratio, which have different diagonal-to-width ratios, these two definitions are often not equivalent, i.e., the equivalent focal length based on the diagonal angle of view differs from the equivalent focal length based on the horizontal angle of view.

==Calculation==
35&nbsp;mm equivalent focal lengths are calculated by multiplying the actual focal length of the lens by the [[Physics:Crop factor|crop factor]] of the sensor. Typical crop factors are 1.26× – 1.29× for Canon (1.35× for [[Company:Sigma Corporation|Sigma]] "H") APS-H format, 1.5× for [[Company:Nikon|Nikon]] [[Engineering:APS-C|APS-C]] ("DX") format (also used by Sony, Pentax, Fuji, Samsung and others), 1.6× for Canon APS-C format, 2× for Micro Four Thirds format, 2.7× for 1-inch sensors (used in Nikon 1 cameras and some Sony RX cameras), 5× to 6× for compact digital cameras, and even higher for built-in cameras of [[Engineering:Mobile device|mobile device]]s like cell phones or tablets.

According to CIPA guidelines,<ref name="cipa_guideline" /> 35&nbsp;mm equivalent focal length is to be calculated like this:
"Converted focal length into 35&nbsp;mm camera" = (Diagonal distance of image area in the 35&nbsp;mm camera (43.27&nbsp;mm) / Diagonal distance of image area on the image sensor of the DSC) × focal length of the lens of the DSC.

== Depth of field equivalent ==
Quoted 35&nbsp;mm equivalent focal lengths typically ignore [[Depth of field|depth of field]] (DOF), which depends on both focal length and [[Astronomy:Aperture|aperture]]. The DOF of smaller sensors is deeper at a given f number, due to the smaller absolute aperture diameters corresponding to shorter focal length lenses.

Equivalent depth of field can be calculated the same way using the crop factor.<ref name=Atkins_01>{{cite web|last=Atkins|first=Bob|title=Digital Depth of Field|url=http://www.bobatkins.com/photography/technical/digitaldof.html|access-date=23 May 2012}}</ref> For example, a 50mm f/2 lens on a 2× crop factor Micro Four Thirds camera would be equivalent to a 100&nbsp;mm (= 2×50&nbsp;mm) f/4 (= f/(2×2)) lens on a full-frame digital SLR in terms of [[Physics:Field of view|field of view]], depth of field, total light gathered,<ref>{{cite web |last1=Butler |first1=Richard |title=What is equivalence and why should I care? |url=https://www.dpreview.com/articles/2666934640/what-is-equivalence-and-why-should-i-care/2 |website=DPReview |access-date=22 August 2019}}</ref> and diffraction effects.

==Conversions==
A standard 35&nbsp;mm film image is 36&nbsp;mm wide by 24&nbsp;mm tall (35&nbsp;mm refers to the height of the film including the perforations for film transport), and the diagonal is 43.3&nbsp;mm. This leads to the following conversion formulas for a lens with a true focal length ''f'':

{|class="wikitable" style="margin: 1em auto 1em auto;"
! Image size
! diagonal-based EFL
! width-based EFL
|-
| 4:3 (sensor width ''w'')
| ''f''<sub>35</sub> = 34.6 ''f'' /''w'' mm
| ''f''<sub>35</sub> = 36.0 ''f'' /''w'' mm
|-
| 4:3 (sensor diagonal ''d'')
| ''f''<sub>35</sub> = 43.3 ''f'' /''d'' mm
| ''f''<sub>35</sub> = 45.0 ''f'' /''d'' mm
|-
| 3:2 (sensor width ''w'')
| ''f''<sub>35</sub> = 36.0 ''f'' /''w'' mm
| ''f''<sub>35</sub> = 36.0 ''f'' /''w'' mm
|-
| 3:2 (sensor diagonal ''d'')
| ''f''<sub>35</sub> = 43.3 ''f'' /''d'' mm
| ''f''<sub>35</sub> = 43.3 ''f'' /''d'' mm
|}

For historical reasons, sensor size specifications such as 1/2.5" do not match the actual sensor size, but are a bit larger (typically about a factor of 1.5) than the actual sensor diagonal.<ref>Vincent Bockaert, [http://dpreview.com/learn/?/key=sensor_sizes Sensor sizes]. DPreview.com.</ref> This is because these sensor size specifications refer to the size of a camera tube, while the usable sensor size is about 2/3 of the size of the tube. Tubes are not used on digital cameras, but the same specifications are used.

Apart from the width- and diagonal-based 35&nbsp;mm equivalent focal length definitions, there is a third definition: ''EFL'' = 50 ''f'' /''d'' mm.<ref name= "panorama"/> However, it is not clear to what extent this definition is used.{{Citation needed|date=February 2008}}

==References==
{{reflist}}

==External links==
*[https://web.archive.org/web/20080205160043/http://photo.net/equipment/medium-format/focal-length-conversion Focal Length Conversion] for medium format and large format, at photo.net
*[http://www.dpreview.com/learn/?/key=focal+length Focal Length] at dpreview

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[[Category:Science of photography]]

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