Display Geometry UtilityW² + H² = D²
TV Screen Diagonal & Aspect Ratio Calculator
Convert any manufacturer diagonal measurement into true panel width, height, and viewable square area before buying mounts or media cabinets. Solving general triangles or missing legs? Try our root Pythagoras equation solver.
16:9, 21:9, 32:9, 16:10 & 4:3Exact Radical Normalization (√337)Inches & Centimeters Toggle
Result updated: 65 in screen width is 56.65 in, height is 31.87 in, area is 1,805.3 square in.
TV Screen Diagonal & Aspect Ratio Calculator
w = (rw · d) / √(rw² + rh²) · h = (rh · d) / √(rw² + rh²)
Select a common screen size preset or enter custom diagonal and aspect ratio numbers.
Aspect Ratio
Screen Width
56.65 in
Screen Height
31.87 in
Screen Area
1,805.3 in²
Common TV Diagonal Sizes (Width × Height Reference)
1. Compute Aspect Ratio Diagonal Norm
norm = √(16² + 9²) = √337 ≈ 18.3576
2. Solve Width from Pythagorean Scale Factor
w = (16 × 65) / 18.3576 ≈ 56.65 in
3. Solve Height & Verify Area
h ≈ 31.87 in, Area ≈ 1,805.34 in²
| TV Diagonal (16:9) | Width (in) | Height (in) | Area (in²) |
|---|---|---|---|
| 43 in | 37.5 in | 21.1 in | 790 in² |
| 50 in | 43.6 in | 24.5 in | 1,068 in² |
| 55 in | 47.9 in | 27 in | 1,293 in² |
| 65 in | 56.7 in | 31.9 in | 1,805 in² |
| 75 in | 65.4 in | 36.8 in | 2,404 in² |
| 85 in | 74.1 in | 41.7 in | 3,087 in² |
Common TV Diagonal Sizes (Width × Height Reference)
| Class Diagonal | 16:9 Screen Width | 16:9 Screen Height | 16:9 Screen Area | 21:9 Ultrawide (W × H) |
|---|---|---|---|---|
| 43" | 37.5" | 21.1" | 790 in² | 39.5" × 16.9" |
| 50" | 43.6" | 24.5" | 1,068 in² | 46" × 19.7" |
| 55" | 47.9" | 27" | 1,293 in² | 50.6" × 21.7" |
| 65" | 56.7" | 31.9" | 1,805 in² | 59.7" × 25.6" |
| 75" | 65.4" | 36.8" | 2,404 in² | 68.9" × 29.5" |
| 85" | 74.1" | 41.7" | 3,087 in² | 78.1" × 33.5" |
How Screen Diagonals Map to Width & Height
TVs and monitors are always sold by corner-to-corner diagonal screen glass size D. Knowing the aspect ratio W : H (such as 16 : 9), the ratio diagonal norm equals √(16² + 9²) = √337 ≈ 18.3576.
Width = D × (W / √(W² + H²)) | Height = D × (H / √(W² + H²)) | Area = Width × Height