The formula
distance = (width ÷ 2) ÷ tangent(angle ÷ 2)
Where it comes from
There are two criteria and they answer different questions. The viewing-angle one says how much of your field of view the screen fills: THX recommends 40 degrees for an immersive experience and SMPTE 30 degrees as a cinema reference, while ordinary living-room use sits around 20. The visual-acuity one says something else: from what distance the eye can no longer separate two adjacent pixels and, therefore, from where a 4K set looks the same as a Full HD one.
How to work it out by hand
- Work out the screen width from the diagonal and the 16:9 ratio
- Halve that width
- Divide by the tangent of half the angle you are after
- The result is the recommended distance
What is worth knowing
The acuity limit is the figure that undoes much of television marketing. On a 55-inch 4K screen it sits at little over a metre: if the sofa is three metres away — normal in a living room — the eye cannot separate the pixels of a 4K set or a Full HD one, and resolution stops contributing anything. What does still show at that distance is contrast, brightness, colour fidelity and motion handling. Put another way: for the same money, a better panel almost always beats a panel with more pixels.