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Aspect Ratio Formula

The formula for finding aspect ratio is:

AR = W / H

Where:

  • AR is the aspect ratio
  • W is the width of the displayed image
  • H is the height of the displayed image

Note that W and H are measured in inches or millimeters.

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Screen Diagonal Formula (Pythagorean Theorem)

The diagonal of a screen can be calculated using the Pythagorean Theorem:

 A2+ B2 = C2

 Where:

  • A is the height of a screen
  • B is the width of a screen
  • C is the diagonal length of a screen

Screen Diagonal Example

The height of the screen is 54 inches (1372 mm) and the width is 72 inches (1829 mm). What is the diagonal?

Step one:

Determine the diagonal dimension of the screen.

  • Substitute A for screen height, 54 inches (1,372 mm).
  • Substitute B for screen width, 72 inches (1,829 mm).

Step two:

Recall the Order of Operations: first, complete the exponents, then perform the addition.

A2 + B2 = C2

542 + 722 = C2

2,916 + 5,184 = C2

8,100 = C2

Step three:

The length of the diagonal squared is 8,100 inches (205,740 mm). To find the diagonal, C, calculate the square root of 8,100. 

√8100 = √C

√8100 = C

C = 90 inches (2,286 mm)

Aspect Ratio Example

You need to project an image that has a 4:3 aspect ratio onto a screen. You measure the screen height and determine that it is 90 inches (2,286 mm) and 120 inches (3,048 mm) wide. Can you use this screen for the 4:3 image?

Step one:

Determine the aspect ratio of the screen.

  • Substitute W, 120 inches (3,048 mm).
  • Substitute H, 90 inches (2,286 mm).

Step two:
Calculate.

AR = 120 / 90
AR = 1.33

Yes, you can use this screen because the aspect ratios match.