Im going to buy mi first mtb bike. Im not sure if some measures of my road bike are useful for example the crank and stem lenght.
Also im not sure if i can corelate my road bar size and mtb width. Im using in my road bike a size 40, im a tiny guy, 170cm and 56 kg.
The frame is a chinese brand, its not very aggressive. Im not planning to use it for competitions yet, mostly to start riding in easy mountains.
Im also having doubts with the rotor size.
Hi. MTB geo and road geo are poles apart due to the differing body positions needed (low and tight with little body movement for road, more upright, open and a lot of body movement for mountain.)
Take handlebar widths. On road you are likely to max out at 44cm. On MTB you will be anything from 720mm to 800mm. The reason for this is that on road you are hardly ever standing, and when you do, nothing is disrupting your balance. Off road you need a wider purchase to provide better balance. Do you instinctively put your arms in or out when trying to keep your balance walking along a balance beam?
Stem length too works in the opposite direction. On the road you have swooping corners where you lean more than steer, and you want lazy slow response from you turning the bars a little at higher speeds.
MTB is at lower speeds (50% or less on average) and there are obstacles pushing your front wheel this way and that. Corners are tight. Rocks need to be weaved around. For this you need a responsive attitude, so shorter stems and longer (frame) reach are the order of the day.
Even your seat height will be slightly lower off road (personally I have 20mm difference).
As a smaller person you probably want a reach of about 420mm with no more than a 60mm stem. Handlebar will probably feel good at 730 or 740mm.
If for any other purpose than to check out some scientific height v bike geo, go to Canyons website and go to their Exceed bike section (in MTB), pick any model and then use their body fit system calculator to choose you the best sized frame. Scroll down to the geometry chart and compare their geo to the frame you are looking at.
A good dimension that they have is seat height range. Most cyclists know this number and it really helps when judging the frame size.
At 5’7 I’d recommend a medium in most bikes, or potentially a reach measurement of around 430 to 450mm. The best thing would be to visit an LBS and try a few out, especially if it’s your first ever MTB.
Unless you’re planning to race then an XC carbon hard tail may not be the best choice - you might be better off buying an aluminium full sus instead. They tend to be more forgiving for beginners.
Rotor size. The larger the better, always!
I would never go smaller than 180mm on the front and 160mm on the rear.
140mm off road is a joke.
450mm might be too much of a reach (ha) for a first time MTB purchase. At 170cm, that 450mm will feel like a Nicolai Geometron! Haha.
But 420mm to 430mm reach would be the goldilocks zone. At 178cm myself, 450mm is damn near spot on for my riding.
Crank length…most common these days is 170mm just for that extra ground clearance. You’ll be hard pressed to find much shorter as standard, but 165mm do exist. Crank length is probably the least of your concerns, unless you want 180mm cranks, which is just crazy talk lol 
MTB is not constant cadence or perfect circles pedalling. You have to move your body fore and aft, let the bike dance under you, stand and have bike and body separation. And have copious amounts more fun, and not a car to dodge…
I am roughly 20mm taller than you.
Rough idea on handlebar size is to get into the pushup position and measure that. Start wide, you can cut down easy enough. For non competition use, wider is better (as long as it is comfortable). My old XC bike was 680mm which was great for competition use, but I think I have 720 on there now which is manageable and feels better, we’ll see how that feels in my next big race.
My current XC bike is a medium and a reach of 420mm, and a moderate stem length (60mm I think). 440 would probably feel better for me, but the 420 is better in tight racing.
Bigger brakes are better. 180/160 should be fine for your weight. 160 is pushing it on the front, but you can do it. Not much to gain from that tiny weight savings.
Cranks are personal preference. I like longer cranks (175) but have a lot of experience managing pedals strikes. My big bike (E29) is a totally different machine from my XC.
My two cents: a lot of people end up on bikes that are too big for them. Check out Dialed by Lee McCormack Lee gives some good advice.
