Test Score Calculator

How to use this tool

Choose what to calculate. "My score and letter grade" takes the questions you got right and the total, or points earned and points possible, with optional bonus points. If wrong answers cost points, enter the penalty as 0.25 or 1/4 and the number you left blank. "Questions I can miss" takes the test size and a target percent or letter. "A curved score" takes your raw score and the class high score. "A score table" lists every score on a test of any size.

The input people most often get wrong is Left blank. On a penalty test a blank costs nothing and a wrong answer costs the penalty, so every question that is neither correct nor blank counts as wrong. With no penalty, leave it empty. The second is the scale: open "Grading scale and rounding" to set your own cutoffs, drop the plus and minus, or choose a rounding policy.

What the calculation is doing

The percent is points earned divided by points possible, times 100, where points earned are the correct answers, minus the penalty times the wrong answers, plus any bonus. So 18 of 20 is 18 ÷ 20 = 0.90, or 90%. The letter comes from cutoffs, by default A from 90, B from 80, C from 70 and D from 60. Plus and minus take the top and bottom three tenths of each band: A minus from 90, A from 93, A plus from 97, and the same pattern down the scale.

Target mode works backwards. The fewest right answers is the target percent times the questions ÷ 100, rounded up to a whole question, and the most you can miss is the total minus that: 90% of 25 questions is 22.5, so 23 right and 2 misses. On a test with unequal marks, work in points, where 90% of 100 lets you lose 10. The curves are a flat curve that adds 100 minus the top score to everyone, scaling by 100 ÷ top score, and the square root curve, which turns a raw x into 10 × √x. All comparisons use exact fractions, so a score exactly on a cutoff gets the higher letter.

A percent is a ratio, not a verdict

Eighteen out of twenty is 90 percent whatever the test, and that is all the arithmetic says. A 90 on an exam where the class median was 60 is exceptional; a 90 where the median was 88 is about average. With the class mean and spread, a z score puts two tests on one footing: (90 − 60) ÷ 15 = 2.0 on a hard test with a standard deviation of 15, and (90 − 85) ÷ 5 = 1.0 on an easy one. A curve says something about the test, not about you.

Rounding at a letter boundary

Most arguments about letter grades happen within half a point of a cutoff. Take 224 out of 250, which is 89.6%. Graded exactly it is a B plus. Rounded to the nearest whole percent it is 90, an A minus. Neither is wrong until the syllabus says which policy applies, and some instructors round while others never do. The tool grades the exact percent by default and offers whole percent or one decimal rounding, half up. Try 179 out of 200, exactly 89.5%: a B plus without rounding and an A minus with it.

Penalty scoring and blind guessing

Some tests subtract a fraction of a point for each wrong answer, with blanks costing nothing. The standard design sets the penalty to 1 ÷ (choices − 1), so a blind guess has an expected gain of zero; the National Council on Measurement in Education writes the formula score as right minus wrong ÷ (choices − 1). The old SAT took a quarter point with five choices: a guess wins 1 point one time in five and loses 0.25 four times in five, so 0.2 − 0.2 = 0.

The numbers change with the choices. With four choices and a quarter point penalty a blind guess is worth 0.25 − 0.75 × 0.25 = +0.0625 points, slightly positive, and it takes a penalty of 1/3 to make it zero. If you can rule out one choice on a four choice question, a guess is worth 1/3 − 2/3 × 1/4 = +0.17. A blank is not the safe answer, only the neutral one. If the penalty pushes a score below zero, the tool counts it as zero.

What curves actually do

A curve is instructor policy, not a rule, and many courses have none. A Johns Hopkins laboratory guide to curving grades describes two families, shifting every score by a fixed number of points and scaling every score by a constant factor, and the CUNY Hostos guide describes the difference method, where the gap between 100% and the top score is added to everyone. A bell curve that grades by rank cannot be worked out from one score, so this tool does not try.

The three methods treat the same score very differently. Adding points lifts a 50 and a 90 equally. Scaling multiplies every score by the same factor, so it gives more points to higher scores and leaves the top student at exactly 100. The square root curve does the opposite and lifts low scores most: a raw 25 becomes 50, its biggest gain at 25 points, a raw 1 becomes 10, and a raw 90 becomes only 94.9.

Most questions you can miss, by test size

Most questions you can miss and still reach the percent, with no rounding. On 25 questions each miss costs 4 points, so 90 percent allows 2 misses and lands on 92.

A worked example you can check on paper

Use the tool's starting values: 18 correct out of 20. 18 ÷ 20 = 0.90 and 0.90 × 100 = 90%, exactly on the A minus line of 90. The next letter, an A, starts at 93%, and 0.93 × 20 = 18.6 points, so you are 0.6 of a point short. One more correct answer, 19 of 20, would be 95%, an A.

With a penalty: 50 questions, 42 right, 4 wrong, 4 blank, and a 1/4 point penalty. The penalty is 4 × 0.25 = 1, so points earned are 42 − 1 = 41 and the percent is 41 ÷ 50 = 82%, a B minus. For a 90% target on 25 questions: 0.90 × 25 = 22.5, rounded up to 23 right, so you can miss 2, and 23 of 25 is 92%. To curve a raw 72 with a class high score of 88: adding points gives 72 + 12 = 84, scaling gives 72 × 100 ÷ 88 = 81.82, and the square root gives 10 × √72 = 84.85.

Mistakes that catch people out

Counting blanks as wrong, or the reverse. On a penalty test they differ: a blank costs nothing and a wrong answer costs the penalty. Enter them separately, and leave Left blank empty when there is no penalty.

Rounding up in your head. 89.6% is not 90% unless your instructor rounds. Check the policy before you plan around a near miss.

Counting on a curve. Nothing obliges an instructor to curve, and the method varies. Treat curved figures as a scenario until the course announces how it works.

Using question counts on a weighted test. If questions carry different marks, 18 of 20 questions is not 90%. Switch the test to points and enter the points earned and possible.

Forgetting that bonus can pass 100. Extra credit can take a score above 100%, and some instructors cap it. The tool does not, so apply your instructor's rule.

Popular calculations

Each opens the calculator with its own address, and every value can be changed once it is open.

Score a test

Penalty, bonus and rounding

How many questions can I miss

Curve a score

Score tables

How this was checked

The letter scale was compared with the Randolph College physics department grade scale, 97 to 100 for A plus down to 60 to 62 for D minus and 0 to 59 for F. The engine reproduces it for all 101 whole percents. Other institutions differ: Hobart and William Smith Colleges start A plus at 98 and Eastern Illinois University has no D minus, which is why the cutoffs here are editable. The 90, 80, 70 and 60 bands match the common US scale in the Wikipedia article on US academic grading, which also says schools differ.

The target answer was checked by brute force: for every test size from 1 to 200 questions, every target from 50 to 100 percent in half percent steps and all three rounding modes, an independent integer routine tried every number of misses and kept the largest that met the target. It matched in all 60,600 cases. Exact fractions matter: 17.4 of 20 points is exactly 87%, but floating point division gives 86.99999999999999. The penalty rule matches the NCME formula score example, 10 right and 30 wrong on 40 four choice items giving 10 − 30 ÷ 3 = 0, and the old SAT quarter point rule described by The Princeton Review. The flat curve matches the CUNY Hostos difference method, and the square root matches the published 10 × √75, about 87, and 10 × √25 = 50. No university teaching center page states the square root formula, so it rests on the definition and an educator source. Every address above was opened and checked for a distinct title, the right answer and clean exports.

Common questions

How do I calculate a test score as a percent?

Divide the points you earned by the points possible and multiply by 100. For 42 correct answers out of 50, 42 ÷ 50 = 0.84, so 84%. Add any bonus points first, and subtract any wrong answer penalty before dividing.

What is 18 out of 20 as a percent and a letter grade?

18 ÷ 20 = 0.90, so exactly 90%. On the common US scale with plus and minus that is an A minus, and one more correct answer, 19 of 20, is 95% and an A. If your school uses whole letters with an A from 90, it is simply an A.

How many questions can I miss and still get an A?

With an A cutoff of 90%, you can miss 2 of 20 questions, 5 of 50 or 10 of 100. If you need a plain A rather than an A minus, the line is usually 93%, which allows 1 miss on 20 questions, 3 on 50 and 7 on 100.

How do you score a test that takes points off for wrong answers?

Points earned = right answers − penalty × wrong answers, and blank answers count for nothing. With 42 right, 4 wrong and 4 blank out of 50 and a 1/4 point penalty, the score is 42 − 4 × 0.25 = 41, which is 82%. The percent is taken against the points possible, here 50.

How does the square root curve work?

It replaces each raw percent with 10 times its square root. A raw 25 becomes 50, a raw 50 becomes 70.7, a raw 81 becomes 90 and a raw 100 stays 100. It lifts low scores far more than high ones, and no score can go above 100 because the square root of 100 is 10.

Does my instructor have to curve a test?

No. Curving is a choice each instructor makes, and many never do it. Some add points, some scale, some use a square root, and some lower the letter cutoffs instead. Until the syllabus says how a curve will work, treat any curved figure as an estimate.

Related Calculators and Reference

• Final Grade Calculator: the score you need on the final exam to reach a target course grade.
• GPA Calculator: turn the letter grades you earn into a grade point average.
• Percentage Calculator: percent of a number, change and difference for any other percentage question.
• Weighted Average Calculator: combine tests, homework and exams that count for different amounts.
• Z Score Calculator: compare a score with the class mean and spread, not just the percent.
• To Curve or Not to Curve, Johns Hopkins Innovative Instructor: why instructors curve, and the alternatives.