Screen Diagonal to Side Lengths

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Screen Diagonal to Side Lengths

Screen Diagonal to Side Lengths Calculation:

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 D =
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Diagonal

Measured diagonal of the screen.
```
 W =
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Aspect Width

Width portion of the aspect ratio.
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 H =
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Aspect Height

Height portion of the aspect ratio.
```
 u =
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Units

Unit label for the diagonal and side lengths.
```
 w =
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Screen Width

Calculated horizontal width of the screen.
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 h =
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Screen Height

Calculated vertical height of the screen.
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 A =
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Screen Area

Approximate front surface area of the screen.
Decimals

Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

Screen Diagonal to Side Lengths Formula

Use the aspect ratio as the shape of a right triangle and scale it to the known diagonal using the Pythagorean theorem.

width = diagonal x aspect width / √(aspect width² + aspect height²)

height = diagonal x aspect height / √(aspect width² + aspect height²)

Live Diagram

The rectangle is drawn to the current aspect ratio and labeled with the calculated screen dimensions.

Screen Diagonal to Side Lengths Variables

Diagonal: The corner-to-corner size of the screen.
Aspect Width and Aspect Height: The ratio that defines the screen shape, such as 16:9 or 4:3.
Screen Width and Screen Height: The calculated side lengths.
Screen Area: The approximate front surface area of the screen.

How the Calculation Works

Treat the aspect ratio as a proportional width and height.
Find the diagonal of that proportional rectangle.
Scale both sides so the diagonal matches the real screen diagonal.
Multiply width by height to get area.

Screen Diagonal to Side Lengths Example

What are the side lengths of a 27-inch 16:9 screen?

ratio diagonal = √(16² + 9²) = √337
width = 27 x 16 / √337 ≈ 23.53
height = 27 x 9 / √337 ≈ 13.24
area ≈ 311.50 square inches

A 27-inch screen with a 16:9 aspect ratio is about 23.53 inches wide and 13.24 inches tall.

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