What this calculator does
Find out how far to sit from your TV, or what size TV suits the spot where you sit. There's no single correct distance, but there are well-established guidelines. Most are based on how much of your view the screen fills. Around 30 degrees side to side is widely recommended for everyday mixed viewing. Around 40 degrees is often suggested for a more immersive, cinema-like picture. A third approach asks how close you need to be to see all the detail a 1080p, 4K or 8K screen can show.
This calculator works both ways. Enter a screen size to get the guideline distances, or enter how far your sofa is from the wall to see which screen sizes suit that distance. Treat the results as a starting range, not a rule. Comfort, room layout and what you watch matter just as much.
Where it's used
Why this math matters outside the classroom:
- Living rooms. Families measuring from sofa to wall use the guideline to pick a screen size that fills a comfortable view.
- Viewing angle. For a 30° view, a 65 inch 16:9 screen about 1.44 m wide puts the seat about 1.44 ÷ (2 × tan 15°) ≈ 2.7 m away.
- Home theaters. Home theater builders choose screen size and seating rows together so every seat sees a similar viewing angle.
- Resolution. Shoppers see why 4K matters more on big screens viewed up close, where 1080p pixels can become visible.
Grade level and standards: Grades 10–11; Common Core State Standards for Mathematics HSG.SRT.C.8. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose whether you know the screen size or the viewing distance.
- Pick inches and feet or centimeters and meters, and the screen's resolution.
- Enter the screen's diagonal size, or the distance from your eyes to the screen.
- Read the 30° and 40° results as the ends of a comfortable range, and the resolution result as a check on whether you will see all the detail.
What the inputs mean
- Screen resolution
- The number of pixel rows: 1080 for Full HD, 2160 for 4K and 4320 for 8K. Only the resolution-based result depends on it.
- Screen size (diagonal)
- The advertised diagonal size of a 16:9 screen, corner to corner.
- Viewing distance
- Measure from where your eyes will be, not from the front of the seat, to the screen.
Formula and method
width = diagonal × 16 ÷ √337, height = diagonal × 9 ÷ √337 (16:9 screen) distance for a viewing angle θ = width ÷ (2 × tan(θ ÷ 2)) 30°: distance ≈ 1.866 × width; 40°: distance ≈ 1.374 × width full-detail distance = (height ÷ pixel rows) ÷ tan(1 arcminute)
A 16:9 screen's sides are in the ratio 16 to 9, so by Pythagoras its diagonal is √(16² + 9²) = √337 ≈ 18.36 units. That turns the advertised diagonal into a width and height.
θ (theta) is the viewing angle: how wide the screen looks from your seat, in degrees. If you sit at distance d from a screen of width w, then tan(θ ÷ 2) = (w ÷ 2) ÷ d. Here tan (tangent) is the calculator button that links an angle to the sides of a right triangle. Solving for d gives the viewing-angle distances. Solving for w, then the diagonal, gives the screen-size mode.
The resolution guideline uses a common figure: normal 20/20 vision can pick out detail down to about one arcminute (1/60 of a degree). Pixel rows are the horizontal lines of dots that make up the picture. When one pixel row spans one arcminute, you can just make out every line of detail. Farther away, neighbouring pixels blur together and some of the resolution is wasted.
Worked example
Someone is placing a 65-inch 4K television.
- Width: 65 × 16 ÷ √337 = 56.65 in; height: 65 × 9 ÷ √337 = 31.87 in.
- 30° view: 56.65 ÷ (2 × tan 15°) = 56.65 ÷ 0.5359 = 105.7 in = 8.8 ft.
- 40° view: 56.65 ÷ (2 × tan 20°) = 56.65 ÷ 0.7279 = 77.8 in = 6.5 ft.
- 4K detail: (31.87 ÷ 2160) ÷ tan(1′) = 50.7 in = 4.2 ft.
Result: A comfortable range is roughly 6.5 to 8.8 ft. To see every bit of 4K detail with 20/20 vision you would need to sit within about 4.2 ft, so at normal distances the screen still looks fully sharp.
Understanding the result
Sitting between the 40° and 30° distances is a reasonable target for most living rooms. Closer feels more immersive; farther feels more relaxed but less engaging.
If your seat is much farther than the resolution distance, a higher resolution adds little visible sharpness at that size. That's not a reason to avoid it. It's just a sign that a larger screen would make better use of it.
In screen-size mode, the 30° result is a sensible minimum and the 40° result a sensible maximum for that distance.
Assumptions and limitations
- The screen has a 16:9 aspect ratio, as almost all televisions do.
- Distances are measured to the viewer's eyes, sitting roughly centred on the screen.
- The resolution guideline assumes 20/20 vision and content that actually uses the full resolution.
- These are guidelines, not standards you must follow; personal preference varies widely.
- Ultrawide monitors and projector screens in other aspect ratios need their own width calculation.
- Viewing height, glare and seating angle also affect comfort and are not included.
Frequently asked questions
What is a good TV size for 8 feet away?
By the field-of-view guidelines, roughly 59 to 80 inches for a 16:9 screen: about 59 inches fills a 30° view and about 80 inches a 40° view. Enter your own distance in screen-size mode for a precise range.
Can I sit too close to a TV?
Sitting closer than the 40° distance can mean turning your eyes or head to follow the action at the edges. Some people find that tiring. It does not damage eyesight, but it may be less comfortable for long viewing.
Why is the 4K distance so short?
Because 4K pixels are tiny. On a 65-inch screen each pixel row is under 0.4 mm tall, so you must be fairly close for it to span one arcminute. At typical living-room distances a 4K picture already looks as sharp as your eyes can tell.
Does this work for a computer monitor?
The geometry does, if the monitor is 16:9. Desk viewing is usually much closer than the TV guidelines suggest, so most people end up with a wider viewing angle than 40°.
How this calculator is checked
Method: Viewing-angle geometry (d = w ÷ 2tan(θ/2)) for commonly cited 30° and 40° guidelines, and a one-arcminute visual acuity criterion for resolution. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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