It's impossible to calculate because you don't know the strength of the wall structure.
As Lucid stated. professionals go for "belt & braces".
If it were mine, I'd fit a floor-to ceiling section of marine ply, at least 12mm thick. The floor would be taking the weight. By the time it was painted, it would be a "feature", not an eyesore. I'd round off and paint at least the edges before final fitting.
The strongest part of your wall is the studs. They run floor to ceiling and they transfer the weight to the rest of the building. Just use a 12mm / 0.5" plywood panel that will cover the width of the studs plus 10cm either side, and that extends higher and 15cm lower and 15cm higher than the vertical footprint size of the bracket.
It's up to you whether you cut out the plasterboard and sink this, or whether you simply screw it to the studs on top. Personally, I'd cut the board, and I'd also cut a hole in the ply to use for cable access. Once the layout is done I'd then glue and screw the panel in place and allow the glue to cure overnight (Gorilla Glue, before you ask). Remember to pilot drill before screwing. You don't want the studs to split. While the glue is drying you can fill up to the edges of the board.
Fixing the board to the studs: Don't try to put two screws into the width of a stud (as per your drawing). You'll weaken the stud and there's more chance of compromising each fixing point. One fixing point done properly is better than two bad ones. Hit the centre of each stud.
For fixings I use these. http://www.screwfix.com/p/rawlplug-intersets-m6-x-37mm-pack-of-20/40813 They're called "intersets". Add larger washers to adequately cover the large fixing holes in the bracket. I prefer these intersets to toggle bolts because the fixing holes are smaller, the anchors have a harpoon-like fixing, and if unscrewed you don't drop half the fixing down the back of the wall. The setting tool is useful if doing a lot or fixing directly in to plasterboard but it's unnecessary when fixing in to ply. Use a hand screwdriver rather than an electric for doing the initial setting.
6 intersets on the top row and four on the bottom row will be more than enough to get the job done.
For power, I'd bring a spur up and set a dry-lining box in to the wall with a switched socket. There's really not much more to be said. You have more than enough detail now to go do the job safely.
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Look at your design. You're basically creating 4 cranks which will want to rotate around the off-centre fixing points, which are 3 screws. Most of your fixing strength comes from the 4 screws in the single centre stud, but the arrangement of those screws side-by-side weakens timber because it almost cuts it in half if they don't miss-align and poke out of the side walls. Now contrast that with the large ply wall plate anchored by glue and (at a guess) 15 screws (5 per) spreading the load across not one but three studs.
It's up to you. Do what you feel works. I've given you the benefit of about £80 in consultancy plus you've had Sam Gangee's assistance. He's another seasoned professional with more than 40 years commercial and domestic install experience. If you feel you have the right solution then go with your gut.
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