Megapixels

Let's start with the question of how many megapixels the human eye can actually recognise as a first point of reference.

The resolving power of the eye | When an ophthalmologist measures visual acuity, the angle of view that the eye can resolve is what matters. 100% visual acuity means that you can distinguish an angle of 1' = 1 minute of arc = ¹⁄₆₀ degree. This corresponds to about 1.5 mm at a distance of 5 m, in other words: If you recognise two dots 1.5 mm apart from 5 m distance as two separate dots and not as a single small spot, your eye can ”resolve“ them and you have 100% visual acuity. Or, when testing eyesight you need to recognize where a 1.5 mm wide opening in the black ring is from 5 m away. At any other distance, the same applies with accordingly larger or smaller gaps.

Image size | In order to obtain a meaningful number of pixels from the human eye's resolution ability, an assumption about the width of the field of view is necessary.

A reasonable figure is an angle of view of about 50°, which occurs when the viewing distance from an image is equal to the image diagonal. In examples, this is approximately

• the field of view of a lens with a normal focal length or
• the view of an A4 or 8"×11" sheet of paper from a distance of just under 40 cm or
• the view of a 50×75 cm poster from just under 1 m away.

This brings us to a resolution of about 3,000 pixels on the diagonal (50° with 60 pixels each, one per minute of arc). With a little geometry, you can get a reasonable megapixel number from this, it is about 5 MP. I skip the calculation behind it, round up and the result is:

6 megapixels in the final image are enough for a perfectly sharp image impression at a "normal" viewing distance.

It is obvious that more megapixels are needed for a perfectly sharp resolution when you get close to a large print and less when you hold, for example, a postcard-sized image in front of you at a normal reading distance. But even a large advertising poster could look crisp with 6 MP when viewed from an appropriate distance.

I write about 6 megapixels in the " final image" because it can be cropped, in which case you need more pixels when you take the picture.

Printing resolution | The resolution of the human eye also provides a guideline as to how small a pixel should be on a screen or in print so that the eye just does not perceive any more individual dots.

At a reading distance of 30 cm to the eye, 100% vision corresponds to a resolution of just under 12 dots per mm - and that is pretty much the resolution of 300 dpi (=300 dots per inch, 1 inch = 25.4 mm) commonly used for paper prints.

Support for this value can be found in Apple's high-resolution displays, marketed under the name Retina. Apple introduced them with the hint that Retina displays are supposed to be so fine that the eye can no longer recognise any dots there. They were introduced by Steve Jobs, who has since died, with the explanation that a resolution of approx. 300 dpi is what the human retina can recognise from a distance of approx. 25-30 cm.

The common printing resolution of 300 dpi corresponds with the resolution of the human eye at a viewing distance of about 30 cm.

This print resolution can be used to calculate the megapixels required for a specific output size:

2.1 MP for 10×15 cm (approx. A6 / postcard size)
6.0 MP for 18×24 cm (approx. 7"×9")

8.4 MP for 20×30 cm (approx. A4/8"×11")
18.8 MP for 30×45 cm (approx. A3/11"×17").

A print in A3 size will rarely be viewed from a distance of only 30 cm, a resolution of e.g. 12 MP is sufficient for razor-sharp prints in this size.

First a big BUT as a supplement to the resolutions just explained:

In reality, a much lower resolution is often sufficient for a really sharp image impression.

• The resolution ability is measured with sharp black and white contrasts. You find these in symbols of an eye test and printed text – not in photos. As soon as neighbouring dots are similar in brightness and colour, but have less contrast, the recognisable resolution is significantly lower.
  

Even a photo printed at 150 dpi can look tack sharp. I have already had a poster on the wall that looked sharp with only about 100 dpi and did not show any pixels; in snow-covered mountains and rocks they were not even visible with a magnifying glass.

• The impact of a picture does not only depend on resolution and sharpness. Content, colour, composition, emotional response... all that counts too, only very few photos need high resolution and perfect sharpness to impress. Please do not overrate either.
  
• If you look closely at individual pixels at the resolutions we're talking about ×here, other blurs easily come into play - camera shake, motion blur, lens aberration, areas out of depth of field. As soon as one of these other possible blurs is greater, a higher resolution in megapixels or dpi gives no advantage at all.
  

Very high standards and cropped enlargements are reasons for more megapixels.

Large-format display in best quality can be a reason to strive for more megapixels. However, for today's usual approx. 20-24 MP to be insufficient, it needs really large prints in at least A2 format, approx. 40×60 cm / 16×24" and a short viewing distance, and there needs to be a subject that needs perfect sharpness and you have to get everything else that can affect the image sharpness right.

Cropping needs a lot of reserve | In the other direction, a reserve for cropping photos is certainly the most important reason for taking more megapixels. Since the number of megapixels is calculated from length×width and grows with the area, you can therefore need considerably more quite quickly: If you crop an image to half its length and width, the area afterwards is only a quarter – and has only a quarter of the megapixels.

The other way round: If you want to have a reserve to crop an image to half its length and width, you need four times the final megapixel count.

This brings us from the 6 megapixels explained above into the range of 24 megapixels – as found in modern high-quality cameras. If you should have e.g. 20 instead of 24 MP: No problem...

With larger megapixel numbers, differences play an ever smaller role | Because of the dependence on the area, it is important by which factor megapixel numbers are different, not the difference. 24 MP are 1.2 times 20 and that is the result of only 10% more pixels in length and width. (To do the math: 1.1 times the length times 1.1 times the width gives 1.21 times the area). In practice, you won't notice a visible difference between 20 and 24 MP.

Smartphones are often in the 10-12 MP range. Both the smaller sensors and the predominant viewing of their photos on small smartphone displays makes this reasonable.

An excessively high number of megapixels does not make sense | With the above-mentioned orders of magnitude, cameras also reach limits where a further increase does not make sense, not even for very demanding photographers. The highest-resolution cameras from Nikon, Canon and Sony are at 45-50 MP in 2021, where good photographers can still tease out a little more detail for really high demands. But these camera models need really first-class optics and careful handling to exploit their high resolution. It is unlikely that such high resolutions will become commonplace in smaller models or in the masses, even if prices were to fall. The vast majority of photographers would simply not benefit from it.

For comparison, let's take a look at how many megapixels common devices display:

They are within the range of 6 MP presented above; only 4K monitors with a solid 8 MP are slightly above that. However, 4K monitors are so large that you usually sit further than 30 cm away from them and then it is no longer possible to recognise every single pixel anyway.