The Barnard Grading & Academic Honors website explains all about honors:
College Honors
The Faculty awards honors to students who complete work for the degree with distinction (cum laude), with high distinction (magna cum laude), and with highest distinction (summa cum laude).
Honors are determined by a student’s final cumulative Barnard GPA, with the top 5 percent of the graduating class being awarded summa cum laude, the next 10 percent being awarded magna cum laude, and the remaining 20 percent awarded cum laude.
The minimum grade point averages that determine eligibility for each category of Latin Honors may change with each May’s graduating class. Those same criteria will be applied to the following February and October graduating classes. (For example, the criteria for each category of honors for the May 2024 class will also be applied to the October 2024 and February 2025 graduating classes.)
Beginning with the February and May 2022 graduating classes, study at other institutions (transfer, summer school, study leave) is not factored into a student’s Latin honors eligibility.
Latin honors appear on both the transcript and the diploma.
Departmental honors are awarded for distinguished work in the major to no more than 20% of graduates, as nominated by their major departments, and conferred by the Committee on Honors. Departmental honors display on student transcripts but not diplomas.
The Barnard section of the Columbia University chapter of Phi Beta Kappa was founded in 1901. Election to the national honor society is a recognition of scholarship, and Barnard students of exceptionally high standing are eligible. Junior election will require a minimum of 86 completed points, and senior election, 102. Students do not apply for membership; they are elected by Barnard faculty members who are themselves members of Phi Beta Kappa.