TV Size Calculator

Enter your TV's diagonal size, aspect ratio, and seating distance to get the recommended viewing distance range, the ideal TV size for your seat, and the actual viewing angle your setup produces — based on the SMPTE (30°) and THX (40°) viewing-angle standards.

Quick Facts

Standard
SMPTE minimum 30° / THX reference 40° horizontal viewing angle
Distance = (screen width ÷ 2) ÷ tan(angle ÷ 2).
Sizing
Screen width and height come from the diagonal and aspect ratio
Pythagorean theorem: width² + height² = diagonal².

Your Results

Calculated
Screen dimensions
-
Width × height for this diagonal
Recommended distance
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THX (40°) to SMPTE (30°) range
Recommended TV size
-
For your entered viewing distance
Your viewing angle
-
Horizontal field of view at your seat

Ready

Enter your TV size, aspect ratio, and seating distance, then press Calculate.

Understanding the TV Size Calculator

This calculator uses the horizontal viewing-angle method — the same approach cited by the SMPTE (Society of Motion Picture and Television Engineers) and THX standards — to relate a TV's diagonal size, its aspect ratio, and your seating distance. Enter a screen diagonal, pick an aspect ratio, and enter how far away you sit; the tool works out the screen's physical width and height, the recommended seating distance for that TV, the recommended TV size for that seating distance, and the actual viewing angle your setup produces.

The formulas

TVs are measured on the diagonal, so the first step is finding the physical width and height using the Pythagorean theorem for the chosen aspect ratio (w:h):

  • Screen width = diagonal × w / √(w² + h²)
  • Screen height = diagonal × h / √(w² + h²)

The horizontal viewing angle (field of view) a screen occupies from a given distance is:

  • Viewing angle = 2 × arctan[(width / 2) / distance]

Rearranged, this also gives the recommended viewing distance for a target angle:

  • Distance = (width / 2) / tan(angle / 2)

SMPTE recommends a minimum horizontal viewing angle of about 30° for critical viewing, while THX recommends 40° as the reference angle used to calibrate cinemas and home theaters for an immersive, edge-to-edge picture. Plugging 30° and 40° into the distance formula gives a recommended distance range for any TV size — the closer, 40° figure is the THX-style "as immersive as reference" distance, and the farther, 30° figure is the SMPTE-style "minimum acceptable" distance. Running the formula in reverse, for a fixed seating distance, gives the range of TV sizes that land inside that same 30°–40° window.

Worked example

A 55-inch, 16:9 TV has a diagonal-to-side ratio of √(16² + 9²) = 18.36, giving a screen width of 55 × 16 / 18.36 ≈ 47.9 inches. At 40°, the recommended distance is (47.9/2) / tan(20°) ≈ 65.9 inches (about 5.5 ft); at 30°, it is (47.9/2) / tan(15°) ≈ 89.5 inches (about 7.5 ft). So a 55-inch 16:9 TV is best watched somewhere between roughly 5.5 and 7.5 feet away.

Reading your result

If your actual viewing angle falls inside 30°–40°, your TV size and seating distance are well matched. An angle below 30° means the screen is small (or you're sitting far) relative to SMPTE's minimum — text and detail may look small for the room. An angle above 40° means the screen is large (or you're sitting close) relative to THX's reference — for very high resolutions (4K/8K) that can still look sharp, but for lower resolutions you may start to notice pixel structure or need to move your eyes to take in the whole screen.

Frequently Asked Questions

What is the 30-40 degree rule for TV viewing?
It refers to the horizontal field of view your TV occupies from your seat. SMPTE recommends a minimum viewing angle of about 30 degrees for critical viewing, while THX recommends 40 degrees as the reference angle used in cinema and home-theater calibration for a more immersive picture. Most recommendations land a TV size and distance combination somewhere in that 30-40 degree range.
How do I calculate the recommended viewing distance for a TV?
First find the screen width from the diagonal size and aspect ratio using the Pythagorean theorem. Then divide half the width by the tangent of half your target viewing angle: distance = (width / 2) / tan(angle / 2). Using 40 degrees gives the closest recommended (THX) distance; using 30 degrees gives the farthest acceptable (SMPTE) distance.
How is TV screen width and height calculated from the diagonal?
TVs are sized by their diagonal measurement. Width and height come from the Pythagorean theorem for the stated aspect ratio: for a 16:9 screen, width = diagonal × (16 / √(16² + 9²)) and height = diagonal × (9 / √(16² + 9²)). The same pattern applies to any w:h aspect ratio.

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