Theoretical Original/Final Gravity Equations

How do you calculate what a theoretical original gravity -should- be?

I.e. what's the equation for using a particular amount of particular grains/extract + a particular volume of water to create an OG?

What about FG?

I've been using extract kits and recipes posted online and I've just taken the OG/FG values for granted, but now I want to create my own recipes and I have no idea how people arrive at the estimated value ranges for both.

John Palmer explains it best in his book on this page

"... the total amount of sugar is constant, but the concentration (i.e. gravity) changes depending on the volume. To understand this, let's look at the unit of points/pound/gallon. This is a unit of concentration, so the unit is always expressed in reference to 1 gallon ("per gallon"). In mashing, you are collecting "x" number of gallons of wort that has a gravity of "1.0yy" that was produced from "z" pounds of malt. To calculate your mash extraction in terms of ppg, you need to multiply the number of gallons of wort you collected by its gravity and divide that by the amount of malt that was used. This will give you the gravity (points per gallon) per pound of malt used."

and on this page
"For an average beer yeast, a rule of thumb is that the FG should be about 1/4 to 1/5 of the OG. For example, a typical beer OG of 1.040 should finish about 1.010 (or lower). A couple of points either way is not unusual."

Also this page for extracts http://www.howtobrew.com/section1/chapter3-4.html

I usually calculate that using Beer Smith (or other such service like Pro Mash etc.) gives me more accurate results than attempting to crunch the numbers myself. In the beginning I ran the numbers myself, these days I just hit the button...

There's a utility that reliably and easily does this? Easy enough, I wasn't aware that one existed.

There's a stickey in the Brewing Software forum that lists software. There's a lot of online calculators also.