Everyone asks "how many inches?" The better question is "how far away do I sit?" Screen size is a ratio, and your sofa sets the other half of it.

The angle, not the inches

A screen is only "big" or "small" relative to your eye. What matters is how much of your field of view it fills: the horizontal viewing angle. Put the same 55-inch TV two metres away and it is a window; put it five metres away and it is a postage stamp.

Two industry yardsticks are worth knowing. The film and television engineers' body SMPTE recommends a viewing angle of at least 30 degrees. THX, the cinema-sound and picture certification company, recommends 36 degrees. Sound & Vision magazine's worked examples put it in numbers: from a seat 7 feet (about 2.1 m) away, a 16:9 screen of roughly 52 inches fills 30 degrees, and roughly 63 inches fills 36 degrees. The calculator below does the same trigonometry for any distance.

Try your room

Reading the result

The 30-degree figure is the floor: below it, a screen starts to feel like furniture rather than a film. The 36-degree figure is the one to aim for if the room is yours alone and you mostly watch films. Neither is a law. They are comfortable defaults, and plenty of people sit closer for games or further back for a family sprawl on the sofa.

If the answer is bigger than you would ever fit on the wall, you have two honest choices: sit closer, or accept a smaller angle. If the answer is smaller than the TV you already own, nothing is wrong. It means you sit close, and you are getting an immersive picture for free.

Three things the formula hides

• Resolution lets you sit closer. On a 4K screen the pixel structure is finer, so a given size looks clean from nearer than it would at 1080p. If you are close to the line between two sizes, 4K is the reason to pick the bigger one.
• Wide films don't use the full height. Many modern films are framed around 2.39:1. On a 16:9 screen that leaves black bars and the picture fills roughly three quarters of the height, though the full width. The viewing angle is about width, so the calculator still holds; the bars are not lost screen, they are the shape of the film.
• Eye height matters too. Mount or place the screen so the middle of the picture is near eye level when you are seated. A big screen perched high turns every film into a neck exercise.

A quick room check

1. Measure from where your eyes sit, not from the sofa's front edge. Metres to one decimal is plenty.
2. Read the diagonal for 36 degrees, then for 30. That is your window.
3. Pick the nearest size you can afford and fit. A touch too big is easier to live with than a touch too small, but don't go so far that you are scanning the image side to side.
4. Rough budgets scale with size: a mid-sized TV in the 50-to-65-inch range often costs around €500–1,200, and the very large sizes climb quickly from there. Prices vary by country and week.

The projector question

Everything above applies to a projector too, with one difference: the screen size is something you choose rather than something you buy. That makes the calculator more useful, not less. Work out the width you want from your seating distance, then check that the projector can throw that width from where you plan to put it.

Sources

The 30-degree (SMPTE) and 36-degree (THX) viewing angles and the 7-foot example come from Sound & Vision's Screen Size and Seating Distance. The diagonal calculation is plain geometry: width = 2 × distance × tan(angle ÷ 2), and a 16:9 screen's diagonal is its width divided by 0.8716.