TV Size, Viewing Distance & Mount Height Calculator

Understanding the TV viewing distance calculator — concept and principle

This calculator converts a TV's diagonal size into its actual width and height, suggests a viewing distance range for an immersive picture, and gives the wall-mount height so the screen centre sits at your seated eye level. Use it when choosing a TV size for a room, arranging a sofa or marking holes for a wall bracket.

How it is calculated

• Screen size: diagonal in cm = inches × 2.54. With aspect ratio r (16/9 or 21/9), height h = diagonal ÷ √(1 + r²) and width w = h × r.
• Viewing distance: d = (w ÷ 2) ÷ tan(θ ÷ 2). The calculator uses θ = 40° for the near end and θ = 30° for the far end, and shows the result in metres.
• Mount height: screen centre = seated eye height; bottom edge = eye height − h ÷ 2.

The principle

The diagonal, width and height form a right triangle, so Pythagoras' theorem gives the width and height once the aspect ratio is fixed. How big a screen looks depends on the angle it fills in your field of view, not on its size alone. Film and cinema guidance from SMPTE suggests at least about 30° of horizontal view, and THX recommends around 40° for an immersive feel. Half the screen width and the viewing distance make a right triangle with half that angle, which gives the tangent formula. Placing the centre at eye height keeps your gaze level and avoids neck strain.

Worked example

1. Inputs: 65-inch, 16:9, seated eye height 105 cm.
2. Diagonal: 65 × 2.54 = 165.1 cm.
3. Height: 165.1 ÷ √(1 + 1.7778²) ≈ 80.94 cm; width: 80.94 × 1.7778 ≈ 143.90 cm, so the screen is 143.9 × 80.9 cm.
4. Distance at 40°: 71.95 ÷ tan 20° ≈ 197.7 cm, and at 30°: 71.95 ÷ tan 15° ≈ 268.5 cm, giving 1.98 – 2.69 m.
5. Mount: centre at 105 cm; bottom edge at 105 − 40.47 ≈ 64.5 cm.

How to read the result

Sitting nearer than the lower value makes the image fill more than 40° and you may need to move your eyes or head to follow action. Sitting farther than the upper value is comfortable for casual viewing but less immersive. If your sofa is fixed, you can turn the formula around: at 2.5 m, a 40° angle needs a width of about 1.82 m. With 4K content, pixels are generally not visible from these distances; lower-resolution sources look softer when you sit close.

Common mistakes

• Treating the diagonal as the width; a 65-inch 16:9 TV is about 144 cm wide, not 165 cm.
• Mounting above a fireplace, which raises the centre far above eye level.
• Measuring eye height standing instead of seated on your actual sofa.

Frequently asked questions

Is a 21:9 screen the same height as a 16:9 screen with the same diagonal?

No. A wider ratio puts more of the diagonal into width, so the screen is shorter.

Should the screen tilt down if mounted high?

Yes, tilting toward the viewer reduces reflections and colour shift on many panels.

What height is typical for seated eyes?

Often around 100–110 cm on a standard sofa, but measuring your own seating is best.

Sources: SMPTE EG 18, Design of Effective Cine Theaters · Euclid, Elements, Book I, Proposition 47 (Pythagorean theorem)