How to calculate grade equivalent scores

Because of the inherent psychometric problems associated with age and grade equivalents that seriously limit their reliability and validity, these scores should not be used for making diagnostic or placement decisions (Bracken, 1988; Reynolds, 1981).

The reliability of age- and grade-equivalent scores is limited by the relationship between the equivalents and the raw scores on which they are based. An age or grade equivalent is simply the median raw score for a particular age or grade level. Because the acquisition of skills measured by an instrument such as a vocabulary test occurs more rapidly during early ages, raw scores increase at a greater rate with younger examinees than with older examinees. Therefore, a similar change in raw scores of younger examinees and of older examinees will be represented quite differently in age equivalent scores.

For example, the age equivalent for a raw score of 50 on the PPVT-III is 4 years 0 months. The age equivalent for a raw score of 55 is 4 years 4 months. A change of 5 raw score points at this early age reflects a change of 4 months in terms of "age-equivalent" scores. However, the age equivalent for a raw score of 165 is 16 years 4 months, and for a raw score of 170 is 18 years 2 months. At the later age, a raw score change of 5 points results in almost 2 years' difference in terms of "age-equivalent" scores.

An age-equivalent score for a young examinee that reflects a 6-month delay actually may represent a greater difference in test performance than a 6-month delay in an older examinee. A greater difference in raw score points (and skills being measured) is represented by the younger examinee's 6-month delay. The older examinee is at a higher developmental level and is acquiring skills at a slower pace as he or she approaches competency. The 6-month delay may be caused by a difference of only 1 or 2 raw score points. Smaller changes in raw scores at these upper ages reflect larger and larger changes in age-equivalent scores as the ceiling of the assessment is reached.

Therefore, the reliability for age-equivalent scores is much poorer for advanced test-takers (McCauley & Swisher, 1984). This is why so many assessments do not report age or grade equivalents beyond a specified age or grade level. For example, in the OWLS Written Expression Scale, age-equivalent scores are not reported after age 12 and grade-equivalent scores are reported only up to grade 6. The acquisition of writing skills occurs most rapidly during the early years because writing mechanics are taught in the primary grades. The degree of discrimination among examinees with advanced writing skills is demonstrated by smaller changes in score points.

Standard scores are a more accurate representation of an examinee's ability because they are based not only on the mean at a given age level but also on the distribution of scores.

Standard scores also can be arithmetically compared and summarized. Age and grade equivalents are not a ratio or interval scale of measurement. They cannot be added, subtracted, or averaged.

Use this calculator to find out the grade of a course based on weighted averages. This calculator accepts both numerical as well as letter grades. It also can calculate the grade needed for the remaining assignments in order to get a desired grade for an ongoing course.

Final Grade Calculator

Use this calculator to find out the grade needed on the final exam in order to get a desired grade in a course. It accepts letter grades, percentage grades, and other numerical inputs.

The calculators above use the following letter grades and their typical corresponding numerical equivalents based on grade points.

Brief history of different grading systems

In 1785, students at Yale were ranked based on "optimi" being the highest rank, followed by second optimi, inferiore (lower), and pejores (worse). At William and Mary, students were ranked as either No. 1, or No. 2, where No. 1 represented students that were first in their class, while No. 2 represented those who were "orderly, correct and attentive." Meanwhile at Harvard, students were graded based on a numerical system from 1-200 (except for math and philosophy where 1-100 was used). Later, shortly after 1883, Harvard used a system of "Classes" where students were either Class I, II, III, IV, or V, with V representing a failing grade. All of these examples show the subjective, arbitrary, and inconsistent nature with which different institutions graded their students, demonstrating the need for a more standardized, albeit equally arbitrary grading system.

In 1887, Mount Holyoke College became the first college to use letter grades similar to those commonly used today. The college used a grading scale with the letters A, B, C, D, and E, where E represented a failing grade. This grading system however, was far stricter than those commonly used today, with a failing grade being defined as anything below 75%. The college later re-defined their grading system, adding the letter F for a failing grade (still below 75%). This system of using a letter grading scale became increasingly popular within colleges and high schools, eventually leading to the letter grading systems typically used today. However, there is still significant variation regarding what may constitute an A, or whether a system uses plusses or minuses (i.e. A+ or B-), among other differences.

An alternative to the letter grading system

Letter grades provide an easy means to generalize a student's performance. They can be more effective than qualitative evaluations in situations where "right" or "wrong" answers can be easily quantified, such as an algebra exam, but alone may not provide a student with enough feedback in regards to an assessment like a written paper (which is much more subjective).

Although a written analysis of each individual student's work may be a more effective form of feedback, there exists the argument that students and parents are unlikely to read the feedback, and that teachers do not have the time to write such an analysis. There is precedence for this type of evaluation system however, in Saint Ann's School in New York City, an arts-oriented private school that does not have a letter grading system. Instead, teachers write anecdotal reports for each student. This method of evaluation focuses on promoting learning and improvement, rather than the pursuit of a certain letter grade in a course. For better or for worse however, these types of programs constitute a minority in the United States, and though the experience may be better for the student, most institutions still use a fairly standard letter grading system that students will have to adjust to. The time investment that this type of evaluation method requires of teachers/professors is likely not viable on university campuses with hundreds of students per course. As such, although there are other high schools such as Sanborn High School that approach grading in a more qualitative way, it remains to be seen whether such grading methods can be scalable. Until then, more generalized forms of grading like the letter grading system are unlikely to be entirely replaced. However, many educators already try to create an environment that limits the role that grades play in motivating students. One could argue that a combination of these two systems would likely be the most realistic, and effective way to provide a more standardized evaluation of students, while promoting learning.

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