distances - Diameter of any galaxy

Given the angular diameter $a$ in radians and the distance $d$ in Mpc, you can get the actual diameter $D$ from:
$$D = dtan{a}$$

Using the small angle approximation, you get:
$$D = da$$

$a$ is in radians, so to get the distance in Mpc from the angular diameter in arc seconds you'd need to convert the angle in arc seconds to the angle in radians: $a = frac{2pi A}{360times3600}$, where the factor $3600$ is used to convert arc seconds to degrees, and $frac{2pi}{360}$ to convert from degrees to radians:

To get the diameter in kpc:
$$D = 1000times d frac{2pi A}{360times3600}$$
$$D = d frac{pi A}{648}$$
$$D approx frac{dA}{206} $$

where $d$ is in $textrm{Mpc}$, $D$ is in $textrm{kpc}$, and $A$ is in $textrm{arcsec}$.

Here $D$ is the diameter for round objects (even for disk galaxies seen at an angle). If the object is not round then this would normally be the maximum diameter.

[EDIT (see answer and comments from HDE 226868)] For irregular galaxies you may also need to have more information (viewing angle) to find the real maximum diameter of the galaxy. But that information is (I think) only available for galaxies in the local group.