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Screen height from the diagonal
The 16:9 aspect ratio fixes the proportions, so the diagonal determines everything.
The Formula
height = 9 x diagonal / sqrt(337)
The 16:9 aspect ratio fixes the proportions, so the diagonal determines everything.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| h | Screen height | inches | The vertical size of the picture. |
| d | Diagonal | inches | The advertised screen size. |
| 337 | 16^2 + 9^2 | unitless | The squared diagonal of a 16 by 9 rectangle. |
What Each Symbol Means
hinches
Screen height
The vertical size of the picture.
dinches
Diagonal
The advertised screen size.
337unitless
16^2 + 9^2
The squared diagonal of a 16 by 9 rectangle.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate tv viewing distance page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate TV Viewing Distance, filed under Everyday Life. Every number the guide produces comes from substituting into this one line.