# Teacher grader: what is the score?

An online EZ grader for teachers: turns the number of questions and the number a student got wrong into a percentage score, with the score for every other number wrong on a chart.

- Page: https://www.acalculator.org/education/ez-grader
- JSON spec: https://www.acalculator.org/education/ez-grader.json
- Version: 925f824a8c85

## Default answer

Example with the default inputs (Number of questions 20, Number wrong 3): 3 wrong out of 20 is a score of 85%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| n | Number of questions | The number of questions on the test, or its total points when each question is worth one point. |
| w | Number wrong | How many questions the student got wrong. Half points such as 2.5 are fine. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| score | Score | The share of the questions answered right: (questions − wrong) ÷ questions × 100. |
| right | Number right | Questions − wrong. |
| each | Each question is worth | The percentage points one question adds to the score: 100 ÷ questions. |

## Method

score = (questions − wrong) ÷ questions × 100; each question is worth 100 ÷ questions percentage points.

## Assumptions

- Every question is worth the same. For a test with points, enter the total points as the number of questions and the points lost as the number wrong.
- The number wrong may be a fraction (half credit); it cannot be more than the number of questions.
- Questions are whole numbers from 1 to 1,000. The score is shown to one decimal place, rounded half up from the exact fraction.

## Worked examples

1. n = 20, w = 3 gives score = 85%, right = 17, each = 5%. Source: OpenStax, Prealgebra 2e, §6.2 (percent = amount ÷ base × 100), https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent.
2. n = 30, w = 7 gives score = 76.666667%, right = 23, each = 3.333333%. Source: 23 ÷ 30 × 100 = 76.67 (percent method from OpenStax Prealgebra 2e §6.2, https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent).
3. n = 25, w = 2.5 gives score = 90%, right = 22.5, each = 4%.
4. n = 8, w = 1 gives score = 87.5%, right = 7, each = 12.5%.
5. n = 40, w = 0 gives score = 100%, right = 40, each = 2.5%.

## FAQ

### How does an EZ grader work?

It divides the number of questions answered right by the number of questions and multiplies by 100. On a 20-question test, 3 wrong means 17 right, and 17 ÷ 20 × 100 = 85%. A paper EZ grader is a slide chart with these answers printed for each test length; this one works for any length up to 1,000 questions.

### How do I grade a test with 30 questions?

Each question is worth 100 ÷ 30 = 3.33 percentage points. With 7 wrong, the student got 23 right: 23 ÷ 30 × 100 = 76.7%. The chart below the answer shows the score for every number wrong on the same test.

### Can I give half credit?

Yes. Type a half as .5 in Number wrong. A student who lost 2.5 questions on a 25-question test scores (25 − 2.5) ÷ 25 × 100 = 90%.

### What if the questions are worth different points?

Enter the total points as the number of questions and the points the student lost as the number wrong, as long as the total is a whole number. A 50-point test with 6 points lost scores 44 ÷ 50 × 100 = 88%.

### How are scores rounded?

The score is shown to at most one decimal place, rounded half up from the exact value, so 7 wrong out of 30 shows as 76.7% and 1 wrong out of 8 as 87.5%. Many teachers then round to a whole percent, which would make 87.5% into 88%.

### Which letter grade is my score?

That depends on your school’s grading scale. A common US scale gives an A for 90% to 100%, a B for 80% to 89%, a C for 70% to 79%, a D for 60% to 69% and an F below 60%, but many schools use other cut-offs, so the grader shows the percentage only.

## Sources

- OpenStax, Prealgebra 2e, §6.2 Solve General Applications of Percent (percent = amount ÷ base). https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent
- Wikipedia, Academic grading in the United States (common scale: A 90–100%, B 80–89%, C 70–79%, D 60–69%, F below 60%). https://en.wikipedia.org/wiki/Academic_grading_in_the_United_States