Hello.
I'm new to electronics and arduino. I have arduino Due board.
Im thinking about using TIP120 transistor, but little bit stuck in calculations. This schema would be good.
http://cdn.instructables.com/F9L/KDFG/GU7FXUMH/F9LKDFGGU7FXUMH.MEDIUM.jpg
But i dont know how to calculate that resistor size from arduino board to base.
This schema would be good.
No, it looks like you have the diode in series with the motor not in parallel.
The TIP120 has a very high current gain of over 1000 so if you want to calculate the maximum resistor value you can use you have to know the current the motor is going to pull. Then make the base resistor such that when connected to 3V it passes 1/1000 th of that current.
Oh yes, i took that image from some site. I think that i will have about 12-14v and ~2a.
No not some site, you have now edited that first post and we can all see it is the instructiables site which explains why it is crap.
I think that i will have about 12-14v and ~2a.
The motor?
If that is the case then 1K5 is the biggest value, but 1K is good enough.
Its motor gasoline injector, so its solenoid if i say right.
eeds35:
Its motor gasoline injector, so its solenoid if i say right.
What has that got to do with anything we have been discussing?
Well i want that arduino will open the injector. But i dont know if tip120 is best transistor for this job.
eeds35:
But i dont know if tip120 is best transistor for this job.
That's easy no.
It is a darlington transistor, with 2A you need to use a FET something like they use here:-
http://bildr.org/2012/03/rfp30n06le-arduino/
Okay if i go with RFP30N06LE, how i can calculate the resistor here now ?
You don't, it is just a pull down to stop the gate floating.
Ok, if i understand right then i can use that schema all time no matter what current flows?
eeds35:
Ok, if i understand right then i can use that schema all time no matter what current flows?
No only up to the rated current of the FET and the power dissipation of the FET.
eeds35:
Its motor gasoline injector, so its solenoid if i say right.
I would seriously try and learn something about electronics before playing with gasoline.
Of course i will try. My plan is to make ecu, lets see how it goes. Thanks for your help 
use logic level MOSFETs like IRL540. Use freewheel diode across the solenoid, even, its builtin inside IRL540. and why using TIP120 you can go with same price but high voltage handling using TIP122. Both can work with maximum 500mAmp. If you want to controll more solenoid u can use ULN2803 etc a darlington array IC.