Percentage Calculations Explained: Scores, Increase, Decrease & More
Percentages appear in almost every part of student life, from exam marks to attendance. The calculator above covers seven common calculations. This guide explains each one, shows the formula and works through examples so you can check any answer by hand.
What Is a Percentage?
The word percent means "per hundred", and the % sign is shorthand for "out of 100". So 25% means 25 out of every 100, which is 25 ÷ 100 = 0.25. In the same way 50% is one half (0.5), 75% is three quarters (0.75) and 100% is the whole amount.
Because everything is rescaled to 100, percentages let you compare results of different sizes. A mark of 18 out of 20 and a mark of 72 out of 80 look unrelated, but both are 90%. That is why exam scores, assignment marks, attendance rates and grade weightings are usually compared as percentages.
How to Calculate a Percentage of a Number
Percentage of a Number = (Percentage ÷ 100) × Number
Divide the percentage by 100 to get a decimal, then multiply. For 30% of 200: 30 ÷ 100 × 200 = 0.30 × 200 = 60. For 15% of 240: 0.15 × 240 = 36. Decimal percentages work the same way: 7.5% of 80 is 0.075 × 80 = 6. Try your own numbers in the % of a Number mode.
How to Calculate an Exam or Assignment Percentage
Percentage = (Points Earned ÷ Total Points) × 100
Suppose you scored 43 out of 60. Step 1: divide 43 by 60 to get 0.71666… Step 2: multiply by 100 to get 71.67%, rounded to two decimals. Converting scores to percentages matters because assessments rarely share the same maximum. A 43/60 test and a 17/20 assignment can only be compared once both are percentages (71.67% and 85%). The Score / Exam mode does this instantly, and the Grade Calculator shows how those percentages combine into a course grade. For a step-by-step article, see How to Calculate Your Exam Percentage.
How to Convert a Score Into a Percentage
A raw score is what you earned, the total possible score is the maximum, and the percentage expresses the first as a share of the second on a scale of 100.
| Score | Working | Percentage |
|---|---|---|
| 18 / 20 | 18 ÷ 20 × 100 | 90% |
| 72 / 100 | 72 ÷ 100 × 100 | 72% |
| 37 / 50 | 37 ÷ 50 × 100 | 74% |
| 43 / 60 | 43 ÷ 60 × 100 | 71.67% |
A percentage is not the same thing as a letter grade. One institution may award its top letter from 70%, another from 90%, so the same percentage can mean different letters. Check your own grading boundaries. How to Convert a Score Into a Percentage covers more examples.
How to Calculate What Percentage One Number Is of Another
Percentage = (Part ÷ Whole) × 100
To find what percentage 30 is of 120: 30 ÷ 120 × 100 = 25%. This is a different question from "What is 25% of 120?", which asks for the part when you already know the percentage and gives 30. The three numbers are the same, but the unknown changes. In the first case you divide; in the second you multiply. See How to Calculate What Percentage One Number Is of Another for more.
How to Calculate Percentage Increase
Percentage Increase = ((New Value − Original Value) ÷ Original Value) × 100
Say your quiz score rises from 40 to 50. The change is 10, and 10 ÷ 40 × 100 = 25%. The original value is the reference point because the question is "how much bigger is the new value compared with where I started?" That is why direction matters: going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease, since the starting point differs. Learn more in How to Calculate Percentage Increase and Decrease.
How to Calculate Percentage Decrease
Percentage Decrease = ((Original Value − New Value) ÷ Original Value) × 100
Imagine your weekly study time falls from 12 hours to 9 hours. The drop is 3 hours, and 3 ÷ 12 × 100 = 25%. If the new value is higher than the original, the formula returns a negative number, which simply means the value increased. The calculator reports this in words so you are not left with a confusing negative.
Percentage Difference vs Percentage Change
These two are often confused. Percentage change compares a new value with an original or reference value. Percentage difference compares two values without treating either as the original, by dividing by their average.
Percentage Change = ((New − Original) ÷ Original) × 100
Percentage Difference = |A − B| ÷ ((A + B) ÷ 2) × 100
With 80 and 100: the change from 80 to 100 is 20 ÷ 80 × 100 = 25%. The percentage difference is 20 ÷ 90 × 100 = 22.22%, because the average of 80 and 100 is 90. Use change for before-and-after comparisons, such as your score this term against last term. Use difference when neither number is the starting point, such as two classes' average marks. The article Percentage Difference vs Percentage Change: What's the Difference? explores this further.
How to Calculate a Reverse Percentage
A reverse percentage works backwards from a final value to the original.
After an increase: Original = Final ÷ (1 + increase ÷ 100)
After a decrease: Original = Final ÷ (1 − decrease ÷ 100)
A value is now 120 after a 20% increase: 120 ÷ 1.20 = 100. A value is now 80 after a 20% decrease: 80 ÷ 0.80 = 100. You cannot simply take 20% off 120, which gives 96, because the 20% was added to the original value, not to the final one. A 100% decrease cannot be reversed at all, since the final value would be zero whatever the original was.
Percentage Points vs Percent Change
A percentage point is the arithmetic gap between two percentages. A percent change is the relative size of that gap. If a pass rate moves from 60% to 70%, that is an increase of 10 percentage points, but also a relative increase of 10 ÷ 60 × 100 = 16.67%. Both statements are true, but they describe different things, so do not use them interchangeably.
Weighted Percentages and Academic Results
When assessments carry different weights, percentages cannot simply be averaged. Suppose an assignment scores 80% and is worth 30% of the course, while the exam scores 70% and is worth 70%. The contributions are 80 × 0.30 = 24 and 70 × 0.70 = 49, so the weighted result is 24 + 49 = 73%. A plain average would give 75%, which overstates the result because the lower score carries more weight. This is a weighted grade calculation, and the Grade Calculator handles it. A simple average is only correct when every item counts equally, and the Average Calculator covers that case. If your institution converts percentages into grade points, the GPA & CGPA Calculator lets you enter your own scale.
Common Percentage Calculation Mistakes
- Forgetting to divide by 100: 15% must become 0.15 before multiplying.
- Dividing by the wrong number: the whole, or the original value, is the denominator.
- Confusing "X% of Y" with "X is what percentage of Y?": one multiplies, the other divides.
- Using the new value for percentage change: the original value is the reference.
- Confusing percentage points with percent change: 60% to 70% is 10 points, not 10%.
- Treating percentage difference as percentage increase: they use different denominators.
- Rounding too early: round only the final answer.
- Ignoring decimal percentages: 7.5% is not 7% or 8%.
- Assuming a percentage determines a letter grade: boundaries vary by institution.
- Reversing a percentage increase incorrectly: divide by 1.20, do not subtract 20%.
Worked Student Examples
- Exam score: 43 out of 60 → 43 ÷ 60 × 100 = 71.67%.
- Assignment percentage: 17 out of 20 → 17 ÷ 20 × 100 = 85%.
- Percentage of a number: 15% of 240 → 0.15 × 240 = 36.
- Percentage increase: 80 to 100 → 20 ÷ 80 × 100 = 25%.
- Percentage decrease: 100 to 75 → 25 ÷ 100 × 100 = 25%.
- Percentage difference: 80 and 100 → 20 ÷ 90 × 100 = 22.22%.
- Reverse percentage: 120 after a 20% increase → 120 ÷ 1.20 = 100.
- Weighted result: 80% at 30% and 70% at 70% → 24 + 49 = 73%.
How Percentages Are Used in Academic Life
Percentages turn up wherever students need to compare or track numbers:
- Exam scores and assignment results
- Attendance rates
- Grade weighting across assessments
- Progress tracking from term to term
- Comparing results between assessments with different totals
- Measuring improvement or decline in scores
- Meeting score thresholds in scholarship or admission requirements, where an institution sets them
The requirements themselves belong to each institution, so check the official source for any threshold that applies to you.
Understanding Your Result
A percentage is a number, not a verdict. Before drawing conclusions, ask what weight the assessment carries, what the grading boundaries are, whether your institution applies its own rounding rules, and whether your figure is a raw score or a weighted result. BioScribe provides mathematical calculations and does not determine anyone's official grade.