How to use the screen dimensions calculator
- Enter the diagonal of the screen in inches, as sold, for example 55 for a 55 inch television.
- Enter the aspect ratio as two numbers, such as 16 and 9.
- Open More options and enter the horizontal pixel count, such as 3840, to see the pixel density.
- Read the width and height in inches and centimeters, the screen area and the pixel density.
Formula
Height = diagonal / sqrt((w / h)^2 + 1)
Width = height x (w / h)
Area = width x height
Pixel density = pixels across / width
The diagonal, width and height form a right triangle, so the diagonal squared equals width squared plus height squared. The page checks its answer against that identity.
A 55 inch 16:9 television
The height is 55 / sqrt((16/9)^2 + 1) = 26.96 inches and the width is 26.96 x 16/9 = 47.94 inches. The area is 1,292.6 square inches. With 3,840 pixels across, the pixel density is 3,840 / 47.94 = 80.1 pixels per inch, and there are 2,160 pixels down for square pixels.
A 27 inch 16:10 monitor measures 22.9 by 14.31 inches, and a 65 inch 21:9 display measures 59.74 by 25.6 inches. In each case the width and height recover the diagonal when squared and added.
Why the diagonal is not the width
A screen is sold by its diagonal, but you fit it to a wall, a desk or a cabinet by its width and height. For a 16:9 screen the width is about 87% of the diagonal and the height is about 49%. A wider shape such as 21:9 gives a longer width and a lower height for the same diagonal, which is why the same number of inches can look different.
What to check before you buy
The size is the visible picture. The frame, or bezel, and the stand add to the outside size of the set, so check the product's own dimensions before you plan a shelf or a mount. Makers also round the diagonal, so allow a little margin.
To work out ratios from pixel sizes use the Aspect Ratio Calculator, to find a mounting height for the screen use the TV Mounting Height Calculator and to check how large an image prints use the Image DPI Print Size Calculator.
Assumptions and limits
- The diagonal is the visible diagonal and the pixels are square.
- Dimensions exclude the frame, bezel and stand.
- One inch is 2.54 centimeters.
- Nothing is uploaded. Calculations run in your browser.
Frequently asked questions
How do I find the width of a 55 inch TV?
For a 16:9 screen, multiply the diagonal by 0.8716. A 55 inch screen is about 47.94 inches wide and 26.96 inches tall. The page does this for any diagonal and ratio.
What is the aspect ratio?
It is the ratio of the width to the height. Common shapes are 16:9 for televisions, 16:10 for some laptops and monitors and 21:9 for ultrawide monitors.
What is pixel density?
It is the number of pixels per inch of screen width. A higher density gives a sharper picture at the same distance. The page finds it from the pixel count across and the width.
Why do the numbers differ from the product page?
The product page may list the size with the frame, and the diagonal may be rounded. This page computes the visible picture area from the diagonal you enter.