MotionShine01 / THX
Diagonal ÷ 0.835
One comfortable distance, from THX's published rule.
Free tool
TV size calculator, and how far to sit.
Type a TV's diagonal to get its width, height and screen area for 16:9, 21:9, 4:3 or 16:10. Then see how far to sit by the THX rule, by SMPTE's figure and by the pixel distance for HD, 4K and 8K, with a drawing next to your sofa. It works the other way from your seat distance too.
Type your seat distance below. The TV sizes each rule points to appear on the right.
Try an example
The shape 21:9 is a sales name. Many such TVs are a little wider, so pick Other shape for an exact one.
Worked out in your browser. Nothing is sent anywhere.
Three rules
Each answers a different question.
02 / SMPTE
3 to 3.2 heights
The seat in a grading room for an HD reference display.
03 / Pixels
One arcminute
The distance where single pixels blend. An assumption, not a standard.
Guide
How to size a TV and choose a viewing distance, with worked examples.
A TV size and viewing distance calculator tells you how big a TV is from its diagonal size and how far from it to sit. It gives the width, height and screen area for 16:9, 21:9, 4:3 and 16:10 screens, then three distances: the rule THX publishes, the figure in SMPTE's standard for a reference display, and the distance where pixels stop showing for HD, 4K and 8K. It also works the other way, from your seat distance to a TV size, and draws the TV beside your sofa.
How to use the TV size and viewing distance calculator
- Stay on I have a TV and type the TV diagonal, such as 55. Choose inches or centimetres.
- Pick the Screen shape. Most TVs are 16:9. For a shape not in the list, choose Other shape and type its two numbers.
- Choose the Picture quality of what you watch, from 720p to 8K, for the pixel distance.
- Optionally type your Seat distance to see the angle the screen fills from where you sit.
- To find a TV for a room, press I have a seat distance and type how far your seat is from the wall.
- Check the to-scale drawing. Your sofa sets the length shown under the TV. The table lists other common sizes.
From diagonal to width and height
The diagonal is the hypotenuse of a right triangle whose sides are the width and height. For a 16:9 screen the diagonal is √(16² + 9²) = 18.358 units long, so the width is the diagonal × 16 ÷ 18.358 and the height is the diagonal × 9 ÷ 18.358. A 55 inch 16:9 TV is 47.94 inches wide, which is 3 ft 11.9 in, and 26.96 inches high. The screen area is 47.94 × 26.96 = 1,292.6 square inches. The frame is not counted.
The THX rule
THX's page on what size TV to buy says to measure the distance between your couch and the TV in inches, then multiply by 0.835 to get the screen size. Turned round, the distance is the diagonal divided by 0.835. For a 55 inch TV that is 65.87 inches, or 5 ft 5.9 in. THX says 4K sets are different because you can sit nearer to see more detail, but it gives no number for that. Checked on thx.com, 27 Oct 2026. For a 16:9 screen, this rule makes the screen fill about 40 degrees of your view across, by our own calculation.
The SMPTE figure
SMPTE ST 2080-3:2017 describes a reference viewing room for judging HD pictures. It puts the viewer 3 to 3.2 picture heights from the centre of the display. A 55 inch 16:9 TV is 26.96 inches high, so that is 80.9 to 86.3 inches, or 6 ft 8.9 in to 7 ft 2.3 in. This is a grading room standard, not advice for a living room, and it covers HD only. For a 16:9 screen it makes the width fill 31 to 33 degrees of view.
When pixels stop showing
This is not a published rule. It uses one arcminute, a sixtieth of a degree, as the smallest detail an eye with sharp sight can see. One pixel is the picture height divided by the number of lines. The distance at which a pixel is one arcminute across is that pixel size divided by the tangent of one arcminute. For a 55 inch screen that is 85.8 inches for 1080p, 42.9 inches for 4K and 21.5 inches for 8K. Sit farther than that and you cannot pick out single pixels. Eyes differ, so treat it as a guide.
Common sizes
| Diagonal | Width × height (in) | THX distance | SMPTE distance |
|---|---|---|---|
| 43 in | 37.5 × 21.1 | 4 ft 3.5 in | 5 ft 3.2 in to 5 ft 7.5 in |
| 50 in | 43.6 × 24.5 | 4 ft 11.9 in | 6 ft 1.5 in to 6 ft 6.4 in |
| 55 in | 47.9 × 27.0 | 5 ft 5.9 in | 6 ft 8.9 in to 7 ft 2.3 in |
| 65 in | 56.7 × 31.9 | 6 ft 5.8 in | 7 ft 11.6 in to 8 ft 6 in |
| 75 in | 65.4 × 36.8 | 7 ft 5.8 in | 9 ft 2.3 in to 9 ft 9.7 in |
| 85 in | 74.1 × 41.7 | 8 ft 5.8 in | 10 ft 5 in to 11 ft 1.4 in |
All sizes are 16:9. The two rules differ because they answer different questions: THX sets one comfortable distance, and SMPTE sets the seat for a grading room. Between them you have a range, and your room usually decides the rest.
Seat distance to TV size
Press I have a seat distance and type, for example, 9 ft. That is 108 inches. By THX, the TV is 108 × 0.835 = 90.2 inches, which is bigger than most rooms need. By SMPTE, a 16:9 TV 3.2 to 3.0 heights away is 68.8 to 73.4 inches. By the pixel rule, a 4K TV can be up to 138.4 inches before single pixels show, so for 4K, size is limited by the wall and by taste rather than by sharpness.
Common problems
- The size is not what the box says. Makers round the diagonal. Type what is on the box and expect a small difference from a tape measure.
- An ultrawide TV is called 21:9 but measures a little wider. Choose Other shape and type 2.39 and 1 if you know the exact shape.
- Your result is outside both rules. These are guides, not limits. Sitting closer than the pixel distance just shows more pixel detail on lower quality video.
To find the sharpness of a particular screen, use the PPI calculator. To work out a shape from two sizes, try the aspect ratio calculator.
Questions
Good to know.
How do I find the width and height of a TV from its diagonal?
Multiply the diagonal by the shape. For 16:9, width = diagonal × 16 ÷ 18.358 and height = diagonal × 9 ÷ 18.358. A 55 inch TV is 47.9 by 27.0 inches.
How far should I sit from a 55 inch TV?
By THX's rule, about 5 ft 5.9 in. By SMPTE's reference figure, 6 ft 8.9 in to 7 ft 2.3 in. Both are guides, and many people sit in between or farther.
What is the THX viewing distance rule?
THX says to multiply your seat distance in inches by 0.835 to get the screen size. The calculator reverses that to give the distance from a screen size.
What does SMPTE say about viewing distance?
SMPTE ST 2080-3:2017 puts the viewer 3 to 3.2 picture heights from a reference display. It is written for grading rooms.
Can I sit closer to a 4K TV?
Yes, because 4K has more pixels per inch, so single pixels show only at a shorter distance. THX says the process differs for 4K but gives no number.
Is there an official figure for 8K?
None was found. The pixel distance here comes from maths on one arcminute of eyesight, not from a standard.
What is the picture ratio of an ultrawide TV?
It is sold as 21:9 and can be a little wider. Pick Other shape to type an exact one.
Does the calculator count the TV frame?
No. Sizes are for the screen only. Measure the frame yourself for the space on a wall or a stand.
Is anything sent anywhere?
No. Everything is worked out in your browser.
