what would be the formula to convert diagnal tv measurement to square inches?

Question

for a 16x9 "widescreen" TV

would the formula be linear or have be a squared formula because
it is based on pythagorem theorem?

what I have so far is:
16^2 + 9^2= 256 +81=337
square root of 337 is 18.35755(etc)
this tv is 144 square inches (16x9)
it would be called a 18.357... inch TV

thanks

note: tvs are sold using the diagnal measurement.

I doubled it and got
32^2 + 18^2 = 36.71^2
36.71 "inch" tv
has area of 576 square inches
the ratio of square inches to diagnal is 15.688 in this one and only 7.844 in the smaller tv
so it is exponential (not linear)

any idea how to turn this into a formula?

some years ago computer monitor makers started listing the viewable size.
so a 15" monitor had a viewable size of 14.1" as I recall

ok g4, how would I use your formulas?
I have the diagnal measurement, now what?
thanks

Answer 1

If the aspect ratio (w/h) = r, then the diagonal d = √[w^2+h^2]

d = h*√[(w/h)^2 + 1] = h*√[r^2 + 1]

Then h = d/√[r^2 + 1] and w = r*h = r*d/√[r^2 + 1]

The area is h*w: A = d/√[r^2 + 1] * r*d/√[r^2 + 1]

A = d^2 * r/(r^2 + 1)

For r = 16/9, r/(r^2 + 1) = .427
For r = 4/3, r/(r^2 + 1) = .480

Answer 2

It depends on the aspect ratio. there are only a few different ones that tv manufacturers use, so you could come up with a formula for each one.

it would have to be a "squared" formula as you put it. if all the linear dimensions (including diagonal) change by a factor of n then the area changes by a factor by a factor of n^2.

Answer 3

16 multiplied by 9 would give the square inches. Your premise is a bit flawed, I believe since you may have not included the plastic mask around the screen which is precisely what the manufacturers do.