Course Sequencing and Placement

Stanford gives you a significant degree of freedom and flexibility to choose among a wide range of courses offered. The Stanford curriculum is not strictly divided into upper and lower divisions, so you may enroll in any course for which you are prepared. If you are in doubt about an appropriate match between your background and a particular class, talk to the instructor.

Some foundational courses are taken as a sequence over multiple quarters, with the first course serving as a prerequisite for the second course, and so on. Common course sequences that begin Autumn Quarter are explained in more detail below. Consider the following guidance for determining when and where you should begin and consult with your Academic Advising Director. Depending on your interests, it may be a good idea to start a course sequence Autumn Quarter freshman year or it may be a good idea to wait.

Calculus Sequences and Placement

If you are interested in Economics, Engineering, or Natural Sciences, you will need calculus. The Mathematics Department offers three calculus sequences: MATH 19-20-21, MATH 41-42, and MATH 51-52-53. The MATH 19-20-21 sequence forms the basic single variable calculus course. The MATH 41-42 sequence is an accelerated version of the Math 19-20-21 sequence. When deciding whether to take MATH 19 or 41, you should consider how comfortable you are with high school trigonometry, advanced algebra, and analysis of elementary functions, including exponentials and logarithms. If you do not have a strong background in some portion of these topics then it is recommended that you take MATH 19. If you have not taken precalculus, or wish to brush up before starting calculus at Stanford, consider using the summer online module at

After completing or placing out of MATH 21 or MATH 42, you will be prepared to take the multivariable calculus course, MATH 51. The MATH 51-52-53 sequence integrates several topics in multivariable mathematics and is recommended for students who scored a 5 on the AP Calculus AB exam or a 4 or 5 on the BC exam. The MATH 51H-52H-53H sequence is the honors version and requires either a 5 on the AP Calculus BC exam or the instructor’s permission.

The CME 100-102-104-106 sequence of computational mathematics courses covers important areas of engineering mathematics, including partial differential equations, probability & statistics, and numerical methods, and focuses on applications and computation. The sequence can be used as an alternative to the MATH 50 series to satisfy the general mathematics requirement for the School of Engineering.

Math Department Placement Guidelines

Chemistry Sequences and Placement

Chemistry is a prerequisite for the Biology Core, typically taken in the sophomore year. Students interested in health-related careers such as Medicine, Earth Systems and other Earth, Energy & Environmental Sciences, as well as certain Engineering majors should also consider taking Chemistry during their first year. The Department of Chemistry offers the following introductory courses: CHEM 31A-31B, 31X, and 33.

The CHEM 31A-31B sequence, which begins in Autumn Quarter, is for students with moderate or no background in high school chemistry. It covers all the essential topics in general chemistry that are required to prepare students for the subsequent courses in the curriculum and emphasizes problem solving. CHEM 31X, offered only in Autumn Quarter, is an accelerated course for students with a strong high school chemistry background. To enroll in CHEM 31X, you must either pass the Chemistry Placement exam during NSO or receive a score of 5 on the AP Chemistry exam. CHEM 31X covers the more advanced portions of the same topics in CHEM 31A-31B and moves at a faster pace.

CHEM 33 is the next course in the chemistry sequence after CHEM 31A-31B or CHEM 31X and is the first organic chemistry course in the introductory sequence. Students who scored a 5 on the AP Chemistry exam may be able to start their study of chemistry with CHEM 33 beginning Winter Quarter.

If you are planning on taking a chemistry lab at Stanford, be sure to bring your eyeglass prescription with you to request customized protective eyewear provided by the Chemistry Department.

Chemistry Department Placement Guidelines

Physics Sequences and Placement

There are three different Physics sequences: the algebra-based Physics 20 track and the calculus-based Physics 40 and Physics 60 tracks. See the Physics Department website for more information on the differences among these three sequences.

Most students interested in Physics or Engineering take Physics in their first year, often starting with either Physics 41 in Winter Quarter or Physics 61 in Autumn Quarter. Students interested in life science or health-related careers typically take the Physics 20 series after their first year, although some take the Physics 40 series.

If you are considering Physics 40 or Physics 60, you should take the Physics Placement Diagnostic given during NSO. The diagnostic is designed to help students calibrate their readiness and identify the Physics course sequence in which they will be challenged but not overwhelmed. It helps students determine whether they should complete further studies in Math and/or Physics before entering one of the calculus-based Physics sequences. More details are online at Physics Placement Diagnostic. The Physics teaching staff will provide advice to each student based on the results of his or her placement diagnostic.

Physics Department Placement Guidelines

Language Sequences and Placement

If you plan to continue studying a language at Stanford that you speak at home or studied in high school, you must take a placement test to determine the level in which to enroll at Stanford. Students with any background in a language (study or home background) may not self-place, even into beginning-level courses. Students who have fulfilled the language requirement through advanced placement (AP), SAT II, or International Baccalaureate (IB) testing must take the placement test if they wish to continue taking courses in that language at Stanford.

A language placement test is not required if you plan to start a new language. There are many reasons to begin learning a new language, such as your personal, academic, or research interests, or plans to study abroad. The Stanford Language Center offers courses in over 40 different languages.

Most language placement tests have two parts: oral and written. The written portions are offered online during the summer according to the schedule below. In the case of Spanish only: if you scored a 4 or 5 on the AP Spanish Language Exam or a 630 or above on the Spanish SAT II and have sent your score to Stanford, you do not need to take the online portion of the Spanish placement test; simply take the oral test on campus during NSO.

The oral portions of the Chinese, French, German, Italian, Japanese, Korean, Russian, and Spanish placement tests are administered on campus during NSO. Please note that there are no online written tests for Arabic, Classical Greek, Hebrew, Hindi, Latin, Portuguese, Tagalog, or Vietnamese. Full placement tests (written and oral, if applicable) in these languages are administered on campus during NSO. For languages not listed above, placement tests may be arranged by appointment. More information about placement tests is available on the Language Center website. Contact the Language Center if you have questions or difficulty meeting the schedule below. The schedule for the on-campus placement tests will be announced in your NSO calendar when you arrive on campus. You are welcome to take placement tests in multiple languages.

For course placement purposes, placement test results are valid for one year.

Language Online Written Test Dates

Online written tests offered for: Chinese, French, German, Italian, Japanese, Korean, Russian, and Spanish.

Last name begins with:

A–C                 June 8 - 28

D–F                 June 29 - July 9

G–J                 July 10 - 20

K–M                July 21 - 29

N–Q                July 30 - August 6

R–U                 August 7 - 17

V–Z                 August 18 – 29

Language Center Placement Testing