How much wood and which length should I get

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I am trying to partition my new extension. There are 2 bathrooms to partition, 2m by 2m each and the hight is 2.24m. I appreciate help with the following: -


1. Do I need 4by2 or 3by2?

2. How many meter of wood do I need?

3. And at which length, 2.4, 3, 3.6,4.2 or longer so that I can minimise my waste
 
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4 x 2 makes for a stiffer wall than 3 x 2 and will accommodate more Insulation (sound or heat) should it be required, but TBH on a 2.2m high wall 3 x 2 should be stiff enough, even on 400mm centres. To work out your materials requirement you need to do a cutting list first. Remember to add in enough extra material for corners (to carry the PB or cement board on the insides), door headers (ideally doubled up), wall sole plates, wall headers, etc. Also have you considered the need for plywood or OSB pattresses inside the walls to carry radiators, towel rails, toilet roll holders, shower heads, sinks etc? And what about the framing (if required) for the ceiling?
 
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2.24 minus top and bottom plate [88mm]=2152
then at 400 centres =[2x44or 2x38=44 or 76 from 400=312/324]
so assume 100x47 actual used 2152+352 =2504 so wasteful with 2.4 as no noggins
2152 +352+352= 2856 still a bit wasteful [3m]
2152 3x 352 =3208 getting better [3.3]
2152 4x352=3560 [3.6]
2152 5x352 wont work [3.9][3912+30mm saw]
2152 6x352 wont work [4.2][4264+35mm saw]
now iff you can get 4.8 you can get 2x2152=4304x352=4656

also 352x10=3520 plus 9x4mm[saw cut]=36 total 3556

dont forget top and bottom plate and an extra stud [one at zero]

any way you can overthink it or order 15% more than you think you need find a use for the extra lol
please note corrections above
 
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please note points corrected above as in noggins at 400mm c/l are only minus one 47mm not two
 

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