Explanation
How test scores are calculated
Turn correct answers into a percent, count the questions missed, or find the fewest correct answers that reach a target. Every question counts the same and is either right or wrong.
s = k ÷ n × 100
| s | Score (%) |
|---|---|
| k | Correct answers |
| n | Questions |
16 right out of 20
| Correct answers | 16 |
|---|---|
| Questions | 20 |
| Result | 80% |
s = k ÷ n × 100 = 16 ÷ 20 × 100 = 80%
m = n − k
| m | Questions missed |
|---|---|
| n | Questions |
| k | Correct answers |
20 questions, 16 right
| Questions | 20 |
|---|---|
| Correct answers | 16 |
| Result | 4 missed |
m = n − k = 20 − 16 = 4
k = ⌈T × n ÷ 100⌉
| k | Fewest correct answers that reach the target |
|---|---|
| T | Target score (%) |
| n | Questions |
An 80% target on 20 questions
| Target score | 80 |
|---|---|
| Questions | 20 |
| Result | 16 correct answers |
k = ⌈T × n ÷ 100⌉ = ⌈80 × 20 ÷ 100⌉ = 16
Diagram of this result
Under the answer, a grid draws one square per question when the test has 200 questions or fewer. Filled squares are correct answers, or the fewest correct answers that reach the target.
The same numbers appear in the answer and the steps, so the diagram is never the only place to read them.
Common mistakes
Round the correct answers needed up, never to the nearest whole number: a target can fall between two counts. Partial credit, negative marking and questions worth different points need the grade calculator instead.
Assumptions and limits
The test has 1 to 1,000,000 questions. Correct answers are a whole number from zero to the number of questions, and the target is 0 to 100%. Counts stay exact; percentages are not rounded in the steps.
How do the worked examples fit together?
16 right out of 20 is 80%, with 4 missed. An 80% target needs at least 16 right. A 75% target on a 7-question test needs 6 right, because 5 right is only 71.4%.
Sources
Percentage arithmetic as in OpenStax Prealgebra 2e, https://openstax.org/details/books/prealgebra-2e. Your teacher or institution decides pass marks and rounding; this calculator does not replace those policies.