Exam Score Calculator

How an exam score is built from question points

A raw exam score is points added up. Every question on the paper carries a value: usually 1 point for a multiple choice item, 2 to 4 points for a short answer, and 5 to 10 points for a long response or a proof. Add the values of every question and you have the points possible. Add the values of the questions the student answered correctly and you have the points earned. Divide earned by possible, multiply by 100, and the result is the percentage that goes in the grade book.

Two details trip people up. First, points possible includes every question on the paper, including the ones left blank, so a student who skips the back page is not scored out of a smaller exam. Second, a point is not a fixed amount of the grade. On a 60 point exam each single point is worth 1.67 percent, and on a 40 point quiz each point is worth 2.5 percent. That is why the same 5 missed points can be a small dent or a letter grade drop.

Partial credit changes the arithmetic without changing the method. If a 5 point question earns 3 of its 5 points, it adds 3 to the earned total and 5 to the possible total, exactly as if it had been a 5 point question answered correctly and then docked 2. The calculator on this page works in whole questions, so add any partial credit to the earned figure by hand when you compare with a real marked paper.

Worked example: 60 points possible, 45 earned

Take an exam with 20 multiple choice questions at 1 point each, 10 short answers at 2 points each, and 4 long responses at 5 points each. The points possible are 20 plus 20 plus 20, or 60. A student answers 16 multiple choice correctly for 16 points, 7 short answers for 14 points, and 3 long responses for 15 points. The earned total is 45.

Forty five out of 60 is 0.75, so the percentage is 75.0 percent and the letter grade is a C under the cutoffs most US schools use. The student missed 15 points, which is 25 percent of the exam. That 25 percent gap is worth knowing, because it is the amount a curve has to close.

Now count questions instead of points and a different number appears. The student got 26 of 34 questions right, which is 76.5 percent. The grade book says 75.0 percent, and the grade book is correct, because the long responses carry more weight per question. This is the single most common reason a student thinks a score is wrong when it is not: the question count and the point count give different percentages, and only the point count matters.

What each question group is worth

The table lays out the example above the way a teacher's answer key does. Fill in the same columns for a real exam and the score falls out without any guessing.

One missed long response costs 8.3 percentage points. One missed multiple choice costs 1.7. A student who runs out of time and leaves two long responses blank loses 16.7 points of percentage before touching anything else, which is usually the whole difference between a B and a C. When a paper comes back lower than expected, check the point values before checking the answers.

Weighted sections: when one part of the exam counts more

Some exams are scored in parts that do not carry the same weight. A typical world language final puts 40 percent on the multiple choice section and 60 percent on the speaking and writing section, even when the multiple choice section has more raw points. The weights are set in the syllabus, and they override the raw point counts.

To combine weighted parts, multiply each part's percentage by its weight as a decimal, then add the results. Part A at 82 percent with a 0.40 weight contributes 32.8 points. Part B at 71 percent with a 0.60 weight contributes 42.6 points. The exam grade is 75.4 percent, which is a C. Notice that Part B pulled the grade down even though its score of 71 is close to the overall result, because it carries more of the weight.

The weights have to add to 100 percent. When a syllabus lists 40 and 60, or 30, 30 and 40, the math is clean. When a teacher lists three parts at 40 percent each, ask which one is capped, because the total cannot exceed 100. A weighted exam can also differ from the raw point total: if Part A holds only 20 of the 60 raw points but carries 40 percent of the grade, each Part A point is worth three times a long response point.

Four curve methods and what each does to a 75%

A curve is a rule for raising scores after the exam is marked. Four methods cover almost every curve a US teacher uses, and each one treats a 75 percent differently.

• Flat add. Add the same number of points to every paper. Adding 5 points turns 75 into 80. It is easy to explain and easy to check, and it can push a strong paper over 100, which most teachers cap.
• Square root curve. Multiply the square root of the percentage by 10. A 75 becomes 86.6, a 36 becomes 60, and a 100 stays at 100. It lifts low scores hard and high scores barely, which is why it shows up in classes with a wide spread.
• Half the missed points. Give back half of what the student lost. A 75 has 25 points missing, so the score becomes 87.5. This one is popular because it can never push anyone past 100.
• Top score to 100. Find the best paper and add the gap between it and 100 to every paper. If the best score was 88, everyone gains 12 points and the 75 becomes 87.

The square root curve is the one that surprises people. It is not linear: the lower the score, the bigger the gain. A 25 percent paper moves to 50, a gain of 25 points, while a 90 percent paper moves to 94.9, a gain of 4.9. That shape is the point of the method, and it is also why some departments do not allow it.

Letter grades and the 89.5 problem

Most US schools map percentages to letters with the same cutoffs: A from 90 to 100, B from 80 to 89.9, C from 70 to 79.9, D from 60 to 69.9, and F below 60. Districts set their own policy, and a few use 93 for an A or add plus and minus bands at 87 and 77. The state assessment pages published by education agencies show how much the cutoffs vary from one system to the next.

The 89.5 problem comes from rounding. A score of 89.5 is a B if the school truncates and an A if the school rounds to the nearest whole percent. A score of 89.4 is a B either way. Some grade books round each assignment and then average, which can move a term grade by a point or two in either direction. If a report card looks off by half a point, the cause is usually the rounding rule, not the arithmetic.

Colleges and testing companies publish their own scales that have nothing to do with classroom percentages. Advanced Placement exams run 1 to 5, and the College Board score page explains how a raw score maps to that 5 point scale. The ACT reports 1 to 36 per section with a composite average, described on the ACT scoring page. A 75 percent on a classroom exam and a 75th percentile on a national test are unrelated numbers that happen to share digits.

Half points, extra credit and partial credit

Real exams are messier than whole questions. Three adjustments come up often enough to plan for.

• Half points. A 1 point question marked 0.5 adds half a point to earned and a full point to possible. Twenty such questions can shift a percentage by several points, so keep the decimals until the final division and round once at the end.
• Extra credit. Extra credit usually adds to earned without adding to possible, which lets a total exceed 100 percent. A 45 out of 60 paper with 5 points of extra credit becomes 50 out of 60, or 83.3 percent, not 50 out of 65.
• Dropped questions. When a question is thrown out, both the earned and the possible totals drop by that question's value. Removing a missed 5 point question from the 60 point exam leaves 45 out of 55, which is 81.8 percent, a gain of 6.8 points for the student who missed it.

Each of these changes the denominator or the numerator, and the order matters when more than one applies. Throw out the bad question first, then add extra credit, then apply the curve. Doing it in the other order gives a different number, and the difference can be a letter grade on a small exam.

Checking the math before you ask for a regrade

Before a conversation with a teacher, rebuild the score from the answer key. Write down the point value of every question, mark each one correct or not, and total both columns. If your total matches the paper, the score is arithmetic and the only remaining question is whether a specific answer deserved credit. If it does not match, you have found a real error and you can point at the exact question.

Check the easy things first: a question marked wrong that was answered on the back of the page, a page that was never scored, a point value that changed between the review sheet and the exam, or a total that was added by hand. Adding errors are common on long exams and they run in both directions, so a regrade can lower a score as easily as raise it.

Keep the percentage and the letter separate in the conversation. A 79.4 percent that the teacher rounds to 79 is a C, and the request is about rounding policy, not about the answers. A 75 percent with a square root curve is an 86.6, and the request is about whether the curve applies to this exam. Naming which of the two you are asking about gets a faster answer than asking why the grade is low.

Grading scales and curve policies are set by each school and each teacher. Use this calculator to check the arithmetic, then confirm the policy with the course syllabus.