Bear with me here, This is my first instructable and I already built this but I thought I'd give it a go.
First: Attempt at your own risk, don't hurt yourself and I am not responsible for any damages from anything that may occur.

Motivation: I just recently purchased a 18V cordless tool set and couldn't find a radio to run off the batteries (as some of the big brands make such radios), so i decided to make one.

Parts: (some are optional, all depends on what exactly you want it to do)
-Car Stereo (I had an old Pioneer laying around)
-Speakers (I got 5.5" Boss Marine speakers on Amazon, they shouldn't be bothered by a little water)
-Antenna (Pyramid 3800 from amazon, keep in mind how to mount it, I had to buy a longer screw for the thickness of the wood)
-Fuse Block (protect all those delicate components, ebay)
-12V Power Supply (I got a 5A light supply from ebay, just search for "12V 5A Power Supply" they are like $10)
-120V Relay (once again ebay, make sure it has 3 separate sets of contacts)
-Switches (1 toggle, and 1 push button)
-Wood for the box (I had some OSB with Mossy Oak print on it laying around)
-Digital Panel Mount Voltmeter (ebay for up to 20 Volts, to keep an eye on the battery)
-12V outlet
-18V drill battery charger
-Corner braces
-hinges
-window lock
-handle
-misc Screws
-Extension cord to use as a power cord and plug for the charger
-Metal to mount the switches in etc (I had the metal inserts from old Radio Shack project boxes)
-Aluminum tape (cover the edges of the box, mainly for aesthetic reasons)
(these parts are for the circuit to knock the 18V down to 12V)
-3x 100n ceramic Capacitors
-100uF Electrolytic Capacitor
-4.7uF Electrolytic Capacitor (I used a bigger one but this is the one the circuit called for)
-1N4007 Diode
-7812 Voltage Regulator IC
-2N3055 Power Transistor
-Heatsinks (one small one huge)

Step 1: 18V to 12V Voltage Regulator Circuit

I found a schematic for increasing the current capabilities of the 7812 voltage regulator on http://powersupplycircuit.net/2n3055.html that worked out really nicely, however It might not be a bad idea to look up a way to add more power transistors for high current handling, one works but it does get toasty warm, even with the huge heatsink I put on it.

(I know I soldered the components on the wrong side of the board, no need to remind me, noob mistake. Still works fine)

-3x 100n ceramic Capacitors
-100uF Electrolytic Capacitor
-4.7uF Electrolytic Capacitor (I used a bigger one but this is the one the circuit called for)
-1N4007 Diode
-7812 Voltage Regulator IC
-2N3055 Power Transistor
-Heatsinks (one small on huge)

Step 2: Build the Box

My Box was made out of 1/2" OSB with a mossy oak print, I piked it up a Menards one day (I just stumbled upon it)

When I designed my box, I wanted everything to be serviceable without disassembling the wooden box (i.e. through the access door and speaker holes)

The box is made of 7 pieces:
-4x 25" x 8" for the top, bottom, front, and back
-2x 8" x 7" for the sides
-the last piece is the door, which I just cut from the back (6"H x 7.5"W) set 1" in from the right side of the back

Cut the Holes for the speakers and stereo and any control panels you want to have.

I then assembled the pieces with a finishing nail gun and 1.5" brads. The pieces are cut so the nails go through the bottom and top pieces into the ends of the front back and sides. (top and bottom overlap the sides/front/back). Also Be careful with the nails near the openings, I accidentally put a nail into the top of one of the speaker holes, I just had to cut it off but it could have been worse.

I used corner braces to reinforce the box, I was able to install them in 5 corners through the speaker holes and door.

I then attached the door with the hinges and the window latch (I used some scrap wood and foam weather strip to "spring" the door against the latch for a more positive hold.

I covered all the edges with the aluminum tape for a cleaner look.

last I attached the handle on top with bolts through the top and into reinforcements in the top of the box (I used some scrap metal I had) and drill a hole for the antenna.

later I notched the access door to allow the power cord to pass through and still latch the door.

Step 3: Modify the Battery Charger

DON"T DO THIS IF YOU DON"T KNOW WHAT YOU ARE DOING

The charger for my batteries is a simple injection molded plastic enclosure with 2 contacts that clip inside and contact the battery, as well as a small "driver" board with 2 LEDs and some resistors.

One of the LEDs lights when the battery is charging and goes out when it is done, I cut this LED off the board (noting polarity) soldered wires to it that extend out of the charger housing.

I also soldered a couple of wires to the Battery contacts and extended them out of the housing.

last I noted where it was safe to drill holes in the charger housing and drilled 2 holes big enough for a screw driver. This will allow me to put screws through the bottom of the charger housing into the bottom of the stereo box after the charger is re assembled.

Step 4: Mount the Components

Mount the major components:

I put a screw in the back near the top inside the right speaker hole, this lines up with a notch in the power supply then another screw in the bottom of the supply secures it to the box.

I drilled 2 holes in the voltage regulator board and screwed it to the bottom of the box in the center near the back.

I secured the charger to the bottom of the box, I used a couple drywall screws around the transformer for the charger to hold it in place and taped it to the end of an extension cord which is how the charger is powered.

secure the fuse block next to the charger where it is easily accessible from the door.

The stereo Head Unit is held in place with its installation sleeve by bending the prongs tightly against the wood

I drilled a hole in the top big enough for the base of the antenna. I had to purchase a longer screw as the antenna was designed to be installed in a sheet metal fender, I also replaced the "angle adjust" screw with a thumb screw for easy folding of the antenna.

Step 5: Wire Everything Up

Now The Tricky Part: The wiring is a Nightmare, but everything has a reason. (there are cars with simpler wiring diagrams)

I have a lot of wire laying around which made this a lot nicer as I could roughly color code everything.

Basically this is how it works:

When there is no Mains Power (unplugged) the relay is unpowered which connects the voltage meter and regulator (built in step 1) to the battery connection wires (attached in step 3) through one of the fuses. The stereo is then powered by the output of the regulator (as well as the 12V outlet).

When Mains are turned on/plugged in the relay switches connecting the battery charger transformer (24V supply in the diagram) to mains, disconnects the battery contacts from the regulator, and connects the 12V 5A power supply to the stereo.

I was planning on adding a power inverter to allow the stereo to run/charge on 12V power from an automobile [project for later] but that is why the relay switches the charger transformer

The Power switch signals the stereo to turn on, the Voltmeter switch allows the voltmeter to be turned on and off to preserve battery life.

I connected a large Capacitor (10000uF) between the Constant 12V and ground of the stereo, with the hopes it would smooth the transition between mains and battery power and back. This works great when going from mains to battery. However, the 12V 5A power supply takes a little bit to get up to operating voltage so when you connect back to mains, the stereo shuts off momentarily.

The AUX is just a female 3.5mm TRS (headphone) jack wired up to RCA inputs on the back of the stereo.

The speakers are hooked straight up to the stereo.

I mounted the relay and capacitor by warping them in some electrical tape and using pipe hangers to keep them from moving around.

When Not in use the Mains Power Cord can be rolled up and placed inside the door, even with a battery in it.

Couple downsides to the design: If you unplug the unit without a battery in it, stereo memory is lost and On battery, the radio only lasts about an hour or so but that is plenty for my needs.

Hope you enjoyed this, and good luck on your next project.