Screen Size Comparison Calculator

Diagonal inches do not measure screen area

A screen size is quoted as a diagonal, which is the distance from one corner of the lit panel to the opposite corner. That single number is enough to describe a rectangle only when the shape is known, and it says nothing directly about area. Two 55 inch screens with different aspect ratios have the same diagonal and different areas.

Area grows with the square of the diagonal. Double the diagonal from 50 to 100 inches and the area goes up four times, from 1,068 to 4,273 square inches on a 16:9 panel. That is why the jump from 65 to 75 inches feels bigger than the 10 inch number suggests: the area rises by a third, not by 15 percent.

The practical consequence is that a 75 inch set needs a wall about 9 inches wider than a 65 inch set, and delivers 599 more square inches of picture. Both numbers come out of the same two formulas, which the rest of this page works through.

Read the last column as a multiplier on the 55 inch set in the middle of the table. The 40 inch screen is 53 percent of its area, and the 85 inch screen is 239 percent, which is more than twice the picture from a diagonal that grew by 30 inches.

Width and height from the diagonal and aspect ratio

The arithmetic is the Pythagorean theorem in reverse. An aspect ratio of 16:9 means the width and height are 16 and 9 units of the same size, so the diagonal is the square root of 16 squared plus 9 squared, which is the square root of 337, or 18.358 units. One unit is therefore the diagonal divided by 18.358, and the width is 16 of those units.

For a 65 inch screen that is 65 divided by 18.358, which is 3.541 inches per unit. The width is 16 times 3.541, or 56.65 inches, and the height is 9 times 3.541, or 31.87 inches. Multiply the two and the area is 1,805 square inches, about 12.5 square feet.

Swap in a 21:9 ratio and the diagonal divisor becomes the square root of 441 plus 81, which is 22.847. The same 65 inch diagonal now gives a width of 59.74 inches and a height of 25.60 inches, and the area falls to 1,530 square inches because the rectangle is thinner.

16:9 against 21:9 at the same diagonal

The ultrawide ratio buys width with height. At the same diagonal a 21:9 panel is wider than a 16:9 panel, but shorter, and the area is smaller because a long thin rectangle encloses less than a squarer one of the same diagonal.

The 55 inch row shows the trade clearly. Going from 16:9 to 21:9 adds 2.6 inches of width and removes 5.3 inches of height, and the area drops 15 percent. The 4:3 row goes the other way, with 3.9 inches less width and 6.0 inches more height, and 12 percent more area.

For a desk, the width is what determines whether a monitor fits between speakers, so the ultrawide shape is worth its lost area. For a TV at the end of a room, height drives the viewing angle more than width does, which is why 16:9 remains the default for television.

Worked example: 65 inch against 75 inch

Two 16:9 sets, one step apart in the catalog. Both dimensions come from the same divisor, 18.358.

• 65 inch: 65 divided by 18.358 is 3.541. Width is 16 times 3.541, or 56.65 inches. Height is 9 times 3.541, or 31.87 inches. Area is 56.65 times 31.87, or 1,805 square inches.
• 75 inch: 75 divided by 18.358 is 4.085. Width is 65.37 inches and height is 36.77 inches, for an area of 2,404 square inches.
• Difference: 2,404 divided by 1,805 is 1.331, so the larger set has 33.1 percent more area. The width grows by 8.72 inches and the height by 4.90 inches.

Pixel density moves the other way. A 4K panel has 3,840 by 2,160 pixels and a pixel diagonal of 4,406, so the 65 inch set runs at 67.8 PPI and the 75 inch set at 58.7 PPI. The bigger screen shows the same number of pixels across a wider surface, which is a real trade rather than a free upgrade.

Pixel density, resolution and distance

Pixels per inch is the pixel diagonal divided by the screen diagonal. A 4K panel is 3,840 by 2,160, so its pixel diagonal is the square root of 3,840 squared plus 2,160 squared, which is 4,406. Divide that by the screen diagonal in inches and you have PPI.

PPI alone does not tell you what you will see, because distance changes the angle each pixel subtends. Pixels per degree is the number that matters: multiply PPI by the viewing distance in inches and by pi divided by 180. At 9 feet, or 108 inches, a 65 inch 4K screen gives 67.8 times 108 times 0.01745, which is 128 pixels per degree. The same set at 12 feet gives 170.

Higher pixels per degree means a smoother image and less visible pixel structure, and the gain from a higher resolution shrinks as you move back. That is why a 4K set looks sharper at 6 feet than at 12, and why 8K is hard to distinguish at living room distances on a 65 inch panel.

What a bigger screen does to the viewing angle

The horizontal viewing angle is twice the arctangent of half the width divided by the distance. A 65 inch 16:9 screen is 56.65 inches wide, so at 9 feet, or 108 inches, half the width is 28.33 inches and the angle is 2 times the arctangent of 28.33 divided by 108, which is 29.4 degrees.

A 75 inch screen at the same distance is 65.37 inches wide, and the same arithmetic gives 33.7 degrees. The diagonal grew 15 percent and the angle grew 14.6 percent, close to linear because the angles are small.

Turn the formula around and you get a seating distance for any angle you want. For 30 degrees, distance equals width divided by twice the tangent of 15 degrees, which is width times 1.866. For a 65 inch screen that is 105.7 inches, or 8.8 feet. For 20 degrees the multiplier is 2.836, which puts the seat 13.4 feet back.

Studio standards treat this as a fixed parameter rather than a preference. SMPTE ST 2080-3, the reference viewing environment for HDTV evaluation, specifies a viewing distance and a viewing angle so that two graders see the same image. A living room has no such constraint, which is why the angle people choose ranges from about 20 to 40 degrees.

Aspect ratios that are not 16:9

Television settled on 16:9 because it is the shape that contains both a 4:3 broadcast and a 2.39:1 film without too much waste, but monitors and phones use other ratios. Each one changes the width, the height and the area at a fixed diagonal.

A 21:9 monitor is the common ultrawide, and a 32:9 is a double wide panel that behaves like two 16:9 screens side by side. At 55 inches the 32:9 shape is 52.95 inches wide and only 14.89 inches tall, with 788 square inches of area, 39 percent less than 16:9. The width is impressive and the height is cramped.

At the other end, 4:3 and 16:10 are taller shapes. A 16:10 monitor at 55 inches has 5 percent more area than 16:9, and a 4:3 panel has 12 percent more, which is why old square monitors felt large for their diagonal. The extra area sits in the height, which is useful for text and useless for cinema.

Resolution is separate from shape. A 4K UHD panel is 3,840 by 2,160, which is 16:9, while a 21:9 monitor at the same pixel height is 3,440 by 1,440 or 5,120 by 2,160. The ENERGY STAR television page puts the UHD jump plainly: 4K has four times as many pixels as conventional high definition.

Picking a size for a room

Start with the wall, not the diagonal. Measure the width and height available, subtract two inches for ventilation and cables, and convert those limits into a maximum diagonal with the aspect ratio formula reversed: diagonal equals width times 18.358 divided by 16 for 16:9, which is width times 1.147.

Then check the seating distance against the angle you want. A 65 inch screen at 9 feet gives 29.4 degrees, which most people find comfortable for mixed viewing. A 75 inch screen at the same 9 feet gives 33.7 degrees, better for film and worse for news, where the eye has to travel further across the frame.

Finally check pixels per degree at the seat. A 65 inch 4K set at 9 feet gives 128, which is more resolution than most content delivers, while a 65 inch 1080p set gives 64 at the same distance. If the seat is 12 feet back, 1080p is closer to enough and the case for 4K weakens.

Dimensions here describe the lit panel only. Bezel width, stand depth and speaker clearance vary by model, so check the published dimensions before you buy a set for a fixed opening.