TV viewing distance calculator
Geometric distances for 40°/30° screen angles and an assumed 1′ pixel.
Fill in the fields and the result will appear here automatically.
A geometric comparison of distances for horizontal screen angles of 40° and 30°. These chosen angles are not presented as universal comfort settings or THX/SMPTE standards. A third estimate assumes one pixel subtends 1′. It describes geometry, not a medical vision threshold, the benefit of 4K or a safe viewing distance.
How it works
Formula and logic
Diagonal is converted to cm by 2.54. For ratio a:b, width W=D·a/√(a²+b²) and height H=D·b/√(a²+b²). Distance at horizontal angle θ is W/[2tan(θ/2)], then cm are converted to metres. The one-pixel estimate is (H/vertical lines)·3438/100m; 3438 is a rounded small-angle factor for one arcminute. Ratio 21:9 here means literally 21/9.
Example
A 55″, 16:9 screen with 2160 vertical lines is about 121.76cm wide and 68.49cm high. The 40° distance is 1.673m and the 30° distance 2.272m; the 1′-pixel model gives 1.09m. The last number does not guarantee invisible resolution differences.
Fields and units
- Diagonal — in
- Screen ratio — list option
- Resolution lines — px
How to use
- — Enter the active screen diagonal in inches and its ratio.
- — Set the integer vertical pixel count, such as 2160 for 3840×2160.
- — Compare the 40°/30° distances separately from the assumed 1′-pixel estimate.
Method and limitations
- Calculation method
- Formula and logic
- Limitation
- Geometric model of chosen angles, not an ophthalmic, THX or SMPTE recommendation. The pixel estimate is not a vision measurement or guarantee of invisible detail.
FAQ
Why do the 40° and 30° distances differ?
For the same width, a wider horizontal angle requires a shorter distance. These are two cases of one formula, not universal comfort or eye-health recommendations.
What does the 1′-pixel estimate mean?
One pixel occupies an assumed arcminute in a small-angle model. It does not account for individual vision, contrast, subpixels, image processing or scene content.
Does this estimate decide whether 4K is needed?
No. Resolution benefit depends on content, scaling, distance and the viewer. A single geometric number cannot establish that 4K/FullHD differences are invisible.
Why use width rather than diagonal?
The model uses horizontal field of view. The diagonal first determines width through the screen ratio. Equal diagonals with 4:3 and 21:9 have different widths.