Statement of purpose for US graduate programmes
US graduate admissions for research programmes work through faculty. A committee of professors reads the file, and for PhD admissions the decision often turns on whether one of them wants to advise you and has the funding to do it. Everything else in the application establishes that you are not a risk; the statement of purpose is where you make yourself specifically wanted.
Reviewed

Fit is a claim you have to evidence
Naming three professors is not fit. Fit is naming a professor, describing the problem their recent work leaves open, and saying what you would do about it with the preparation you have. That paragraph is the highest-value 120 words in the document, and it is the part most applicants leave until last and write worst.
It also has to be honest. A committee will notice if you cite a paper from 2016 by someone who has since moved to a different problem, or if you name a professor who has not taken a student in four years.
MS versus PhD
A course-based MS statement is closer to a professional argument: what you want to build, which courses get you there, what you do after. Funded thesis MS and PhD statements are research arguments, and the balance of the page shifts accordingly: roughly two thirds on research preparation and direction.
Applicants who submit a PhD-style statement to a professional MS programme look overqualified and uninterested in the degree they applied for. The reverse looks unprepared.
- PhD: research problem, your preparation, named faculty, what you would work on
- Thesis MS: the same shape, at lower stakes, with more room for coursework
- Course-based MS: career outcome, curriculum fit, and specific technical gaps you are closing
- All three: no restatement of your CV in paragraph form
The personal history statement is not a second SOP
Many US universities, the University of California system prominently, ask for a separate personal history or contributions statement. It asks about your background, obstacles and what you would contribute to the campus community. It is scored separately and often by different readers.
Reusing SOP paragraphs there is a wasted opportunity: the personal history statement is the only place in the application where context for an uneven record legitimately belongs.
Questions about applying to the United States
How long should a statement of purpose be for US graduate school?
One to two pages single-spaced, which is roughly 500 to 1,000 words, unless the programme states otherwise. Some programmes set a hard limit of 500 words and a few allow 1,500. The programme's own instructions override every general guideline, including this one.
Should I email professors before applying?
For PhD programmes, usually yes, with a short and specific message about their work. In some fields, notably parts of biology and psychology with rotation-based admissions, it matters less. In engineering and computer science it often matters a great deal.
Does a low GPA need to be explained in the SOP?
Address it in one or two plain sentences, with what changed afterwards as evidence. Do not spend a paragraph on it, and do not put it in the opening. If the programme has a personal history statement or an addendum field, that is the better home for it.