crop factor

Fixing the “crop-factor” issue

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We use the term “cropped sensor” only due to the desire to describe a sensor in terms of the 35mm standard. It is a relative term which compares two different types of sensor, but it isn’t really that meaningful. Knowing that a 24mm MFT lens “behaves” like a 48mm full-frame lens is pointless if you don’t understand how a 48mm lens behaves on a full-frame camera. All sensors could be considered “full-frame” in the context of their environment, i.e. a MFT camera has a full-frame sensor as it relates to the MFT standard.

As mentioned in a previous post, the “35mm equivalence” is used to relate a crop-factor lens to its full-frame equivalent. The biggest problem with this is the amount of confusion it creates for novice photographers. Especially as focal lengths on lenses are always the same, yet the angle-of-view changes according to the sensor. However there is a solution to the problem, and that is to stop using the focal length to define a lens, and instead use AOV. This would allow people to pick a lens based on its angle-of view, both in degrees, but also from a descriptive point of view. For example, a wide angle lens in full-frame is 28mm – its equivalent in APS-C in 18mm, and MFT is 14mm. It would be easier just to label these by the AOV as “wide-74°”.

It would be easy to categorize lenses into six core groups based on horizontal AOV (diagonal AOV in []) :

  • Ultra-wide angle: 73-104° [84-114°]
  • Wide-angle: 54-73° [63-84°]
  • Normal (standard): 28-54° [34-63°]
  • Medium telephoto: 20-28° [24-34°]
  • Telephoto: 6-20° [8-24°]
  • Super-telephoto: 3-6° [4-8°]
Lenses could be advertised using a graphic to illustrate the AOV (horizontal) of the lens. This effectively removes the need to talk about focal length.

They are still loosely based on how AOV related to 35mm focal lengths. For example 63° relates to the AOV of a 35mm lens, however it no longer really relates to the focal length directly. A “normal-40°” lens would be 40° no matter the sensor size, even though the focal lengths would be different (see table below). The only lenses left out of this are fish-eye lenses, which in reality are not that common, and could be put into a
specialty lens category, along with tilt-shift etc.

Instead of brochures containing focal lengths they could contain the AOV’s.

I know most lens manufacturers describe AOV using diagonal AOV, but this is actually more challenging for people to perceive, likely because looking through a camera we generally look at a scene from side-to-side, not corner-to-corner.

AOV98°84°65°
MFT8mm10mm14mm
APS-C10mm14mm20mm
FF16mm20mm28mm
Wide/ultra-wide angle lenses

AOV54°49°40°
MFT17mm20mm25mm
APS-C24mm28mm35mm
FF35mm40mm50mm
Normal lenses

AOV28°15°10°
MFT35mm70mm100mm
APS-C45mm90mm135mm
FF70mm135mm200mm
Telephoto lenses

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What is a crop factor?

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The crop factor of a sensor is the ratio of one camera’s sensor size in relation to another camera’s sensor of a different size. The term is most commonly used to represent the ratio between a 35mm full-frame sensor and a crop sensor. The term was coined to help photographers understand how existing lenses would perform on new digital cameras which had sensors smaller than the 35mm film format.

How to calculate crop factors?

It is easy to calculate a crop factor using the size of a crop-sensor in relation to a full-frame sensor. This is usually determined by comparing diagonals, i.e. full-frame sensor diagonal/cropped sensor diagonal. The diagonals can be calculated using Pythagorean Theorem. Calculate the diagonal of the crop-sensor, and divide this into the diagonal of a full-frame sensor, which is 43.27mm.

Here is an example of deriving the crop factor for a MFT sensor (17.3×13mm):

  1. The diagonal of a full-frame sensor is √(36²+24²) = 43.27mm
  2. The diagonal of the MFT sensor is √(17.3²+13²) = 21.64mm
  3. The crop factor is 43.27/21.64 = 2.0

This means a scene photographed with a MFT sensor will be smaller by a factor or 2 than a FF sensor, i.e. it will have half the physical size in dimensions.

Common crop factors

TypeCrop factor
1/2.3″5.6
1″2.7
MFT2.0
APS-C (Canon)1.6
APS-C (Fujifilm Nikon, Ricoh, Sony, Pentax)1.5
APS-H (defunct)1.35
35mm full frame1.0
Medium format (Fuji GFX)0.8

Below is a visual depiction of these crop sensors compared to the 1× of the full-frame sensor.

The various crop-factors per crop-sensor.

How are crop factors used?

The term crop factor is often called the focal length multiplier. That is because it is often used to calculate the “full-frame equivalent” focal length of a lens on a camera with a cropped sensor. For example, a MFT sensor has a crop factor of 2.0. So taking a MFT 25mm lens, and multiplying it by 2.0 gives 50mm. This means that a 25mm lens on a MFT camera would behave more like a 50mm lens on a FF camera, in terms of AOV, and FOV. If a 50mm mounted on a full-frame camera is placed next to a 25mm mounted on a MFT camera, and both cameras were the same distance from the subject, they would yield photographs with similar FOVs. They would not be identical of course, because they have different focal lengths which modifies characteristics such as perspective and depth-of-field.

Things to remember

  • The crop-factor is a value which relates the size of a crop-sensor to a full-frame sensor.
  • The crop-factor does not affect the focal length of a lens.
  • The crop-factor does not affect the aperture of a lens.