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Math Placement

chalkboard with math equations

The Placement Diagnostic for the 2024-25 academic year will open on August 1. Please check back then.

Placement Diagnostic

The placement diagnostic is required of everyone (regardless of AP Calculus credit) to enroll in the courses listed in the chart below unless you’ve already successfully completed the prerequisite course at Stanford.  The diagnostic is only to be taken at most once in an academic year, and not after enrollment in a first Math course at the level of Math 51 (or CME 100) or below.

The placement diagnostic will recommend the initial math course in which to enroll, and this recommendation is purely advisory. The recommended placement does not itself constitute the fulfillment of any requirements at Stanford (for majors or prerequisites). 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.

The Precalculus Refresher in Canvas, consists of videos and associated exercises that are available for use at any time. It goes through the core skills in algebra, graphing, functions, and trigonometry that are necessary for learning and using calculus. It is recommended for anyone who needs to brush up on some of these skills or has background gaps. It is best to do this enough in advance so that you have worked through all relevant parts prior to enrollment in a calculus course here.

CoursePlacement DiagnosticFurther Information
Math 18Only offered in the Fall quarter. Please see the FAQ below: Should I take Math 18 before or alongside Math 19?
Math 19n/a
Math 20Math 19 or equivalent is the recommended prerequisite.
Math 21Math 20 or equivalent is the recommended prerequisite. Math 21 is an enforced prerequisite for Math 51. See the Math 21 before Math 51? page for further information.
Math 51Either 5 on AP Calculus BC exam or Math 21 is an enforced prerequisite. Please see the FAQ below: The Placement Diagnostic recommended Math 51 for me, can I take Math 51 without Math 21 or 5 on Calc BC?

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, 2023 and July 3, 2024 gives you permission to enroll in Math 18, 19, 20, 21, and 51 for the 2023-24 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 2024-25 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 University 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 PlacementFallWinterSpring
Math 18 (offered only in the Fall quarter)Math 18Math 19Math 20
Math 19 (offered only in the Fall and Winter quarters)Math 19Math 20Math 21
Math 20 (offered Fall, Winter, and Spring)Math 20Math 21Math 51
Math 21 (offered Fall, Winter, and Spring)Math 21Math 51Math 52 or 53*
Math 51 (offered Fall, Winter, and Spring)Math 51Math 52 or 53*Math 52 or 53*

*Math 52 and 53 are independent of each other, but should be taken after completing Math 51. Math 53 is offered in every quarter of the academic year. Math 52 is offered only in the Winter and Spring quarters.

Frequently Asked Questions

The Placement Diagnostic recommended Math 51 for me, can I take Math 51 without Math 21 or 5 on Calc BC?

The Placement Diagnostic helps to identify topics you may need to brush up on before taking your first math course at Stanford.  The recommendations are purely advisory.   

You need a strong foundation to ensure a successful experience in more advanced math courses such as Math 51 as well as courses in other quantitative majors. See the Math 21 before Math 51? page for further information. If you have mastered the material in Math 21 but do not have credit for this showing on your transcript, please fill out this google form.

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.

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 for more information.

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.

Should I take Math 18 before or alongside Math 19?

If your score on the PreCalculus portion of the Placement Diagnostic is below 20, we strongly suggest that you take Math 18 (offered only in the fall quarter) to strengthen your mathematical skills before embarking on Calculus courses at Stanford.  It is possible to take Math 18 concurrently with Math 19 in the fall quarter.

Whom do I contact if I have more questions?

Please see the front page of the diagnostic and review the “Basic Information” section for more information.

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 Chemistry, Data Science, Physics, and Symbolic Systems 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 CMEcourses 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 for more information.