# Angular Diameter, Parallax - Perceived size of Objects

I'm currently in the process of writing a 2.5D Application that should display the perceived size of an Object. For example, When I have a ball that has a diameter of 1meter, how big would it appear if the ball would be 5 meters away from me? I know that there is angular diameter, but how can I tranlate the angle that I get to a size or scale?

-
You have the object's distance and real size and you already know how to calculate the angular diameter. You want to translate this angle to something more intuitive, for readability? – Diego Oct 22 '11 at 14:43

It is not entirely clear from you question which scale you want to translate it to.

An angular diameter corresponds to different spatial distances depending on the distance to the object or surface of projection, so you have to make a choice regarding this before you can get any further.

Once you have done this, if your "ball" is small compared to the distance to it, you can use the small-angle approximation:

$$\theta_{arcsec} = 206,265 \times\frac{d}{D},$$

with $d$ and $D$ being the size of and distance to the object, respectively.

How to achieve this in practice depends entirely on the details of your project.

-