Screen Size Calculator

width = W × k · height = H × k · k = diagonal × 2.54 ÷ √(W² + H²)

W:H

The aspect ratio as a pair of numbers, such as 16:9 or 21:9

diagonal

Screen diagonal, the size the panel is sold by (in)

k

How long one unit of the ratio is on the real screen (cm)

width

Width of the screen (cm)

height

Height of the screen (cm)

W and H are the two numbers in the ratio, and only their proportion matters: 16:9, 1920:1080 and 16:09 all describe the same shape and therefore the same screen. The square root is the diagonal of one rectangle of that shape — for 16:9 it is √(16² + 9²) = 18.36 — so on a 55-inch screen each unit is 2.54 × 55 ÷ 18.36 = 7.61 cm, the width is 16 of those units at 121.76 cm, and the height is 9 of them at 68.49 cm. To get the height, count the short side instead; to go the other way, divide a measured width by k and you are back at the diagonal.

1. A 55-inch television, the size on the box

   1. Known: diagonal 55 inches, aspect ratio 16:9.
   2. One unit of the ratio: 2.54 × 55 = 139.7 cm of diagonal, ÷ √(16² + 9²) = ÷ 18.36 = 7.61 cm.
   3. Width: 16 × 7.61 = 121.76 cm.
   4. Height: 9 × 7.61 = 68.49 cm.
   5. Area: 121.76 × 68.49 = 8339 cm², about 0.83 m².
   6. Check the ratio: 121.76 ÷ 68.49 = 1.78, which is 16 ÷ 9. ✓

   This is the row the manufacturers print: a 55-inch 16:9 panel is quoted as 121.8 × 68.5 cm on specification sheets, and the small difference is nothing but rounding.

2. A 65-inch television, for the wall you have

   1. Known: 65 inches, 16:9.
   2. One unit: 2.54 × 65 = 165.1 cm, ÷ 18.36 = 8.99 cm.
   3. Width: 16 × 8.99 = 143.9 cm.
   4. Height: 9 × 8.99 = 80.94 cm.
   5. Area: 143.9 × 80.94 = 11 647 cm².

   Everything scales with the diagonal, so the 65-inch set is 1.18 times the 55-inch one in both directions and 1.4 times the area — 65 ÷ 55 twice over.

3. The same 55 inches in ultrawide 21:9

   1. Known: 55 inches, 21:9.
   2. √(21² + 9²) = √522 = 22.85.
   3. One unit: 139.7 ÷ 22.85 = 6.11 cm.
   4. Width: 21 × 6.11 = 128.4 cm.
   5. Height: 9 × 6.11 = 55.03 cm.
   6. Area: 128.4 × 55.03 = 7066 cm² — 15% less than the 16:9 panel of the same diagonal. ✓

   Same diagonal, wider and shorter, and less total area: a taller shape always encloses more area for a given diagonal, which is why square is the largest screen a diagonal can buy.

4. An old 24-inch 4:3 monitor

   1. Known: 24 inches, 4:3.
   2. √(4² + 3²) = 5.
   3. One unit: 2.54 × 24 = 60.96 cm, ÷ 5 = 12.19 cm.
   4. Width: 4 × 12.19 = 48.77 cm; height: 3 × 12.19 = 36.58 cm.
   5. Area: 48.77 × 36.58 = 1784 cm². ✓

   The denominator is not 16. A page that only works for widescreen would give 53.13 × 29.89 cm here, which is the 16:9 answer — 4.4 cm too wide and 6.7 cm too short.

These numbers describe a bare panel rather than the set around it. The quoted diagonal runs corner to corner across the glass, so the lit picture inside the bezel is a fraction smaller, and marketing sizes are rounded — a 55-inch class television is rarely 55.00 inches. The area is the rectangle's area, which matters when comparing curved and flat screens of the same diagonal, because a curved panel's surface is longer than its footprint. And the ratio here is the shape of the panel, not of the picture on it: a 21:9 screen showing 16:9 material is the same panel with bars down the sides.

How do I work out the width and height of a TV from its size?

Treat the two sides and the diagonal as a right triangle. For 16:9, one unit of the ratio is the diagonal divided by √(16² + 9²) = 18.36, so a 65-inch screen has units of 2.54 × 65 ÷ 18.36 = 8.99 cm: the width is 16 units, 143.9 cm, and the height is 9 units, 80.94 cm. Multiply both figures by 0.3937 to get inches, or divide by 2.54.

Why do I need the aspect ratio as well as the diagonal?

Because a diagonal is a single length and a screen needs two. The ratio is what splits that length into a width and a height, and different shapes use the same diagonal very differently: at 55 inches the 16:9 panel is 121.76 cm wide and 68.49 cm tall, the 21:9 one is 128.4 cm wide and 55.03 cm tall, and the old 4:3 shape is 111.76 × 83.82 cm. All three are 55-inch screens, and only one of them fits a given shelf.

What is the width of a 65-inch TV?

143.9 cm, with a height of 80.94 cm, if it is 16:9 — which nearly every television is. Allow for the frame as well as the panel: the quoted 65 inches is the glass, while the set's body adds a centimetre or two on each side and rather more at the bottom for the stand. If you are checking against a wall unit, the number that decides it is the width.

Does a bigger diagonal always mean a wider screen?

Usually, but the shape can outweigh a modest difference in size. A 50-inch 21:9 ultrawide is 116.7 cm across, which is wider than a 55-inch 4:3 panel at 111.76 cm, even though the ultrawide is the smaller screen on paper — and it is far shorter as well, 50.03 cm against 83.82 cm. When two sets are within a few inches of each other, check the aspect ratio before assuming the larger one is the wider one.

What aspect ratio do I enter for an old 4:3 monitor?

4:3, or any pair of numbers in that proportion — 8:6, 1600:1200 and 1024:768 all describe the same shape, and the calculator reads them as the same thing. A 24-inch 4:3 panel measures 48.77 × 36.58 cm, against 53.13 × 29.89 cm for the same diagonal in 16:9: taller, narrower, and 11% more area, which is why the change from 4:3 to widescreen made screens look shorter for the same diagonal.

How do I convert the width and height to inches?

Divide by 2.54, since an inch is exactly 25.4 mm. The 65-inch television is 143.9 ÷ 2.54 = 56.65 inches wide and 80.94 ÷ 2.54 = 31.87 inches tall, and the diagonal those two sides make is 65 inches — the same number you started from. Entering the diagonal in centimetres instead is fine too: the unit menu next to the box has both.

• Recommendation ITU-R BT.2020: Parameter values for ultra-high definition television systems — ITU-R
• Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — NIST