Can You Get Emancipated if You Can't Stand Living With Your Parents

I'm a 16 year old girl in Montana and can't stand living with my parents anymore. They are divorced and neither one of them let me leave my house, despite the fact that I have a steady job 5 days a week that pays $10 an hour. I also have straight A's in school. My parents have rules that I do not agree with and I've tried to reason with them and make things work but they never listen or care about anything I say. They just yell at me, make me feel stupid, ground me for months at a time closing off any communication I could have with any of my friends, and take my phone and paychecks.
At the time I was very suicidal and harming myself because all my parents do is judge every decision I make, don't put anything I say into consideration, and beat me down and make me feel like I'm a disgrace to my family and that I shouldn't be here anymore; they saw cuts on numerous places on my body and grounded me for it. I've talked to my mom about me moving out and she said she wouldn't allow it unless I got emancipated, so I have her consent. Right now I have living choices with either my 19 year old sister and her boyfriend in Utah while still going to school and working, or one of my best friends who lives in my town and goes to school with me and offered me a place to stay if I need it. I have money saved up from work and am able to pay for my own needs, and when summer approaches I will be able to work longer hours, make double the money I'm making right now, and drive myself to work, as I will have my license by June. I currently only have my learners permit.
Thank you for reading this. I've been thinking about this for a long time and believe being emancipated would allow me to be happy for once, and teach me good things in life. What are my chances?

Slim to none.

Given what you write here, I have to concur that your chances of emancipation are slim. It's not about being unhappy at home, it's about what is in your overall best interests. Emancipating you to go live with other relatives and likely going onto public assistance is not the path to emancipation.

Here is a link to info from the MT courts:

http://courts.mt.gov/library/topic/emancipation

Emancipation is not and never was intended to be a means for a minor to leave home. It was and is intended to be a means of providing legal protection to those minor who, for reasons outside their own control, found themselves living alone.

Emancipation is based on NEED. You do not NEED emancipation - you just WANT it.

Odds? I'd say the above posters are optimistic in allowing even a slim chance. My own estimate would be that your chance is zero.

You go to school and have a steady job. But, your parents won't let you leave the house ?