35 mm equivalent focal length

The EXIF data for cameras give the actual focal length of an image irrespective of whether the sensor is full frame or not, but for comparative study it might be required to get the 35 mm equivalent focal length. 35 mm (also called full frame) is the traditional film size; having an area of 36mm x 24mm (43.3 mm dia).

We can get 35 mm equivalent number from the camera sensor size. For DSLRs, sensor size may be given as L mm x W mm with a crop factor F, such that F x D = 43.3 mm where D=√ (L²+W²), the diagonal of sensor. Small sensors have sizes like 1/2.3″, 1/1.7″ etc. Another thing to note is the sensor aspect ratio – most cameras would have it as 3:2 or 4:3.

35mm eq. Focal Length = Actual Focal Length X Crop Factor

Continued below are detailed calculations for the sensor size and crop factor.

Let us take the example of a camera with 1/2.3″ sensor. This converts to 25.4/2.3 = 11.04 mm. This must be divided by roughly 1.5 (exact factor varies from one sensor manufacturer to other) to obtain the sensor diagonal. The diagonal of usable image plane for 1/2.3″ sensor is 7.7 mm (details).

Aspect Ratio of this sensor = 4:3
If the unit is x, then (4x)² + (3x)² = 7.7²
Whence x = 1.54; 4x (L) = 6.16 mm, 3x (W) = 4.62 mm. Thus the sensor for this camera is 6.16 mm x 4.62 mm.
Crop Factor (F) = 43.3/7.7 = 5.62 (Note that F is unity for a full frame sensor).

Therefore for an image taken with this camera whose EXIF gives the actual focal length as say 20 mm, the 35 mm equivalent focal length will be 5.62 x 20 mm = 112.4 mm.

Practically, it means that to get the same Field of View on a 35mm film (or FX DSLR) camera, we need a 112.4mm lens, whereas for the camera with smaller sensor (having a crop factor of 5.62), we need a 20mm lens. This is the reason why in about the same size as an entry level DSLR with prime lens, we get a 20x superzoom compact camera. The latter needs smaller lens for its smaller sensor.


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