What is the Point of Diminishing Returns for TV Screen Sizes?

TV screens continue grow.  According to CEA, the average TV sold in 1997 had a diagonal screen size of just 22 inches.  Today that same figure has ballooned to 36 inches. The average TV screen size is expected to continue to grow for at least the next three years as households opt for larger screen TVs.

With the continued growth in average TV screen sizes and the recent launch of uber large Ultra HD 4K TVs,  I’ve recently been asked frequently if there is a point of diminishing returns to ever-increasing TV screen sizes.

There is a wide variety of opinions on this topic and you can see some of these opinions together with some of the technical discussion summarized here.

Here’s a look at the math involved:

$$\huge\textrm{VD}=\frac{\textrm{DS}}{\sqrt{\left(\frac{\textrm{NHR}}{\textrm{NVR}}\right)^2+1} \cdot \textrm{CVR} \cdot \tan{\frac{1}{60}}}$$

Where:

VD: Viewing distance

DS: Display’s diagonal size

NHR: Display’s native horizontal resolution (in pixels)

NVR: Display’s native vertical resolution (in pixels)

CVR: Vertical resolution of the video being displayed (in pixels)

Take a current 55″ Full HDTV and the math looks like this:

$$\huge\textrm{VD}=\frac{\textrm{55}}{\sqrt{\left(\frac{\textrm{1920}}{\textrm{1080}}\right)^2+1} \cdot \textrm{1080} \cdot \tan{\frac{1}{60}}}=85.8 inches = 7.15 feet$$

In other words, if you are watching Full HD content on a Full 55″ HDTV, you will have the most immersive experience if you sit about 7 feet from the screen. Farther away and you’ll lose detail. As you get closer, you’ll be able to see more individual pixels as image pixelation happens.

Considering most seating areas in typical living room settings are 6 feet to 10 feet from the TV, the optimal TV size is  between 46 inches and almost 77 inches. So many of today’s living room settings can support larger TVs and we could see the average TV screen size continue to grow.

The introduction of Ultra HD 4K TVs can push this size/distance relationship even further.  Ultra HD TVs have twice the horizontal resolution and twice the vertical resolution (for a total of four times the resolution) of Full HDTVs which changes the above formula to this:

$$\huge\textrm{VD}=\frac{\textrm{55}}{\sqrt{\left(\frac{\textrm{3840}}{\textrm{2160}}\right)^2+1} \cdot \textrm{2160} \cdot \tan{\frac{1}{60}}}=42.9 inches = 3.58 feet$$

In other words, watching 4K content on an Ultra HD cuts the optimum viewing distance by roughly half.

Now a television in a standard living setting should be 92 inches to 153 inches to provide that same immersive experience.

With Ultra HD televisions and 4K content, households can support much larger screens.