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Placement Diagnostic  |  Sample Course Progressions  |  Frequently Asked Questions  |  Introductory Math Courses

Online Math Placement Diagnostic:


The Placement Diagnostic for the 2019-20 academic year will open August 1. Please check back then.

Placement Diagnostic 

The placement diagnostic is required to enroll in the courses listed below unless you’ve already taken one of the following courses at Stanford.

Course Placement Diagnostic or Prerequisite Course
Math 19
Math 20 or Math 19
Math 21 or Math 20
Math 51 or Math 21 or Math 42/42A


The placement diagnostic will recommend the initial math course in which to enroll, and this recommendation is purely advisory. The diagnostic will help identify areas you may want to review. For additional information regarding the courses recommended in the diagnostic, please see the Introductory Math Courses page.

Please note: 

The diagnostic gives you the most useful feedback if taken in the quarter before you enroll in your first Math department course at Stanford (if at the level of Math 51 or below). Completing the diagnostic between August 1, 2018 and July 15, 2019 gives you permission to enroll in Math 19, 20, 21, and 51 for the 2018-19 academic year as your first Math department course here. Therefore, if you are planning to not take a first Math department course here at the level of Math 51 or below until the 2019-20 academic year or later then you will need to retake the diagnostic at that point.


Please note that after you have completed a first Math department course here at the level of Math 51 or below, you never need to retake the diagnostic for enrollment in another Math department course.  For example, you can take Math 21 this year and put off Math 51 until next year or later without retaking the diagnostic.


Please also note that the outcome of this diagnostic has no effect on AP calculus credit at Stanford. However, choosing to enroll in a course for which you’ve received Transfer or Advanced Placement credit is subject to the Registrar’s policy on the duplication of credit.


Sample calculus course progressions

The following table lists course plans according to your recommended placement.  If the placement diagnostic recommends that you review specific precalculus topics, we urge you to do this before enrolling.

Recommended Placement




Math 19

Math 19 Math 20 Math 21

Math 20

Math 20 Math 21 Math 51

Math 21

Math 21 Math 51 Math 52 or 53*

Math 51

Math 51 Math 52 or 53* Math 52 or 53*

*Math 52 and 53 are independent of each other, but taken after Math 51.

Each of Math 20, Math 21, Math 51, Math 52, and Math 53 are offered in every quarter of the academic year.  Math 19 is offered only in the fall and winter quarters.


Frequently Asked Questions

Diagnostic Logistic Questions

Placement Recommendation Questions

Diagnostic Logistic Questions

How long will the placement diagnostic take?
Please plan for approximately 60 to 90 minutes to complete the diagnostic. There is NO time limit, so you may take as long as necessary.

Do I need to take the diagnostic in a single sitting or can I leave and come back later?
The diagnostic is meant to be taken once and you should plan on completing it in one sitting. However, there is no time limit. Please see the front page of the diagnostic and review the “Basic Information” section for more information. Click here.

Will the placement diagnostic show up on my transcript?

How long will it take to enroll in a course once I complete the diagnostic?
You will receive an email within 7 days after you’ve completed the diagnostic indicating your eligibility to enroll. After receiving the email, you can enroll immediately in Axess. *Note: if you are an incoming student, although your prerequisite is now satisfied, you will still have an enrollment hold until you attend the New Student Orientation.

What topics are covered in the placement diagnostic?
Please see the front page of the diagnostic and review the “Basic Information” section. Click here. 

Do I need to study for the placement diagnostic?
The diagnostic aims to give an accurate sense of which Math course (19 through 51) would be the most appropriate starting point, based on your knowledge when you take it.

Whom do I contact if I have more questions?
Please see the front page of the diagnostic and review the “Basic Information” section. Click here.

Placement Recommendation Questions

Do I have to enroll in the course the placement diagnostic recommends me to take?
No, the purpose of the diagnostic is to suggest the appropriate first Math course based on your knowledge demonstrated in the diagnostic, but this is purely advisory.

I have AP credit, do I still need to take the placement diagnostic?
Yes, even if you have AP credit you are still required to take the diagnostic before enrolling in Math 51. Please note, if you do have AP credit and decide to take a calculus course, your units may be repeated.

If I want to go straight into 52 or higher, do I still need to take the placement diagnostic?
No, you can enroll directly into any course numbered higher than 51. If you choose to change enrollment from a higher course into Math 51 before the Final Study List deadline you will need to take the diagnostic to complete enrollment.

What are the differences between the Math 50 series and the CME 100 series?
The Math 50 series addresses real-world applications of the concepts it introduces; it does not involve any theoretical proofs, focusing on conveying an understanding of the principles relevant to all concepts where they may be used. The CME 100 series focuses more on engineering applications with the use of programming. The two course sequences teach material in very different orders; e.g., most of the linear algebra content of Math 51 is not covered in CME 100. The best preparation for taking Math 104 (Applied Linear Algebra), Math 52, or Math 53 is to take Math 51.

How do I decide which course sequence to take (Math 50 series or CME 100 series)?
It’s best to consider your future coursework and concentration plans. Both CS 229 and CS 230 specifically recommend Math 51 (or courses that rest on Math 51) for their math background; Math 51 is the only course at Stanford whose syllabus covers nearly all of the linear algebra and “matrix calculus” material used in CS 229 and CS 230. The Math 50-series provides multivariable calculus and linear algebra background that is relevant to students in all quantitative majors, both in the School of Humanities and Sciences as well as in the School of Engineering. The Mathematical and Computational Sciences (data science) and Physics majors accept only the Math 50 series to fulfill their math requirement, and the Engineering Physics major strongly recommends the Math 50-series for students who are likely to choose any of the Physics course options for depth. The Math 50 series is also strongly recommended if you may need to take more advanced courses in the Math or Statistics departments in the future.

Can you answer my additional question(s) about the CME 100 series?
No, since CME is housed under the ICME program at the engineering school, all further questions about regarding CME courses must be directed to ICME.  

What if I still want to talk to someone about where to be placed?
Please see the front page of the diagnostic and review the “Basic Information” section. Click here.



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