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# Find TV Height & Width by TV Size

Television sizes are measured diagonally, leaving many TV shoppers wondering the height and width of TVs at various sizes. After all, when you’re picking the perfect spot to place your TV, most people want to use the rectangular shape of the TV to understand how it will look in their room (and if it will fit).

You can easily determine the height and width of any TV with three pieces of information:

1. The TV Size (diagonal measurement)
2. The Aspect Ratio (typically 16:9)
3. The Bezel Size (TV frame outside the screen)

We’ll first list the Height and Width of popular TV sizes and then provide a detailed explanation of how you can find these measurements yourself using a simple math formula.

## TV Height & Width

These dimensions are based on 4K and 8K flat screen TV models with 16:9 Aspect Ratios rounded the nearest tenth of an inch.

Figures do not include bezels.

## How to Calculate TV Height & Width

The diagonal measurement of a TV – used to describe the TV size – happens to create the hypotenuse of 2 right triangles. There is a mathematical equation to calculate the lengths of the sides in a right triangle that you may remember from grade school called…

#### The Pythagorean Theorem

A2 + B2 = C2

In this case:

• A = TV Height
• B = TV Width
• C = TV Diagonal (Hypotenuse)

You already know the size of your TV so we can plug that directly into the equation.

A2 + B2 = (TV Size)2

#### The Aspect Ratio

Because nearly all TVs have a 16:9 aspect ratio (16 being the width, 9 being the height), we are able to deduce the following as mathematical fact:

B/A = 16/9
If we multiply both sides by A that leaves us with:
B = 16A/9

#### Solve and Replace

Now that we know the value of B (expressed in terms of A), we can plug it into the Pythagorean Theorem above, leaving us with only A remaining to solve the equation.

A2 + B2 = (TV Size)2
A2 + (16A/9)2 = (TV Size)2

Now we can solve for A!
First we square the numerator and denominator of B (16 and 9) leaving us with:

A2 + (256A2/81) = (TV Size)2

Then we create common denominators for A and B so that we can add them together. We do this by both multiplying AND dividing A2 by 81 and then adding the fractions.

(81A2/81) + (256A2/81) = (TV Size)2
(337A2) / 81 = (TV Size)2

Then we multiply both sides by 81 and then divide both sides by 337 to seclude A by itself (cross multiplying):

A2 = 81 * (TV Size)2 / 337

Take the square root of each side and we get the solution for A:
sqrt(A2) = sqrt[81 * (TV Size)2 / 337]
A = sqrt[81 * (TV Size)2/337]

Now we can wrap things up…

Let’s use a 55-inch TV as an example:

A = sqrt[81 * (TV Size)2/337]
A = sqrt[81 * (55)2/337]
A = sqrt[81 * 3025/337]
A = sqrt[245,025/337]
A = sqrt[727.077151335311573]
A = 26.96

We now know that the Height of a 55-inch TV is about 27-inches. To find out the width we simply insert 26.96 back into the aspect ratio equation:

B/A = 16/9
B/26.96 = 1.777
B = 1.777 * 26.96
B = 47.9

We now know that the Height of a 55-inch TV is about 49-inches.

You can follow this mathematical equation for any size TV screen and it will work like a charm. Provided the aspect ratio is 16:9! If the aspect ratio happens to be different (4:3 for example), you can re-solve using whatever ratio you’d like.