Percentage Formula Explained: Every Calculation You'll Actually Need
There's more than one "percentage formula" — depending on what you're actually trying to find, you need a slightly different version of the equation. This guide covers all of them: the basic formula, increase and decrease, reverse percentages, and percentage-of-a-percentage, each with a worked numeric example.
01. What a Percentage Actually Is
The word "percent" comes from the Latin per centum, meaning "by the hundred." A percentage is just a way of expressing a part of something as if the whole were exactly 100 — which makes it easy to compare two things that started out on completely different scales. A score of 45 out of 60 and a score of 90 out of 120 look different at first glance, but they're both exactly 75%, which is the entire point of converting to a percentage in the first place.
02. The Four Formulas You'll Actually Use
Which formula you need depends on what you already know and what you're trying to find:
| Type | Formula | When to Use It |
|---|---|---|
| Basic Percentage | Percentage = (Part ÷ Whole) × 100 | Finding what a score, mark, or portion is out of 100. |
| Percentage Increase | ((New − Old) ÷ Old) × 100 | Tracking growth — a rising score, salary, or measurement. |
| Percentage Decrease | ((Old − New) ÷ Old) × 100 | Tracking a drop — a falling score, a discount, an error rate. |
| Reverse Percentage | Whole = Part ÷ (Percentage ÷ 100) | Finding the total when you only know a part and its percentage. |
03. Worked Examples for Each One
Formulas make more sense with real numbers plugged in. Here's each one in action:
Basic
You scored 68 out of 80 on an exam.
(68 ÷ 80) × 100
= 85%
Increase
Your GPA moved from 3.0 to 3.6.
((3.6 − 3.0) ÷ 3.0) × 100
= 20% increase
Decrease
Attendance fell from 90% to 72%.
((90 − 72) ÷ 90) × 100
= 20% decrease
Reverse
42 marks is 70% of the total paper.
42 ÷ (70 ÷ 100)
= 60 total marks
04. Percentage of a Percentage (Weighted Grading)
This one trips people up the most, and it's exactly the math behind weighted grading. To find a percentage of a percentage, convert both to decimals and multiply them together, then convert back if you want a percentage as the answer.
50% of 40% = 0.50 × 0.40 = 0.20 = 20%
Practical example: if one chapter makes up 40% of your final exam, and the final exam is worth 50% of your overall course grade, that single chapter is actually worth 20% of your final grade — even though neither of the original numbers said "20%" anywhere.
05. Where This Shows Up in School and University
Percentages are the bridge between raw marks and almost everything else on your transcript — letter grades, GPA, and class rank are all ultimately built on top of a percentage calculation somewhere. Attendance eligibility works the exact same way, as covered in our attendance percentage guide. If you're converting a raw percentage into a letter grade or GPA point value, our letter grade conversion chart covers that directly.
Frequently Asked Questions
Q: What is the basic percentage formula?
Percentage = (Part ÷ Whole) × 100. If you scored 45 out of 60 on a test, that's (45 ÷ 60) × 100 = 75%.
Q: How do you calculate percentage increase?
((New Value − Old Value) ÷ Old Value) × 100. If your marks went from 60 to 75, that's ((75 − 60) ÷ 60) × 100 = 25% increase.
Q: How do you calculate percentage decrease?
((Old Value − New Value) ÷ Old Value) × 100. Dropping from 80 to 60 is ((80 − 60) ÷ 80) × 100 = 25% decrease.
Q: What's the difference between a percentage point and a percentage?
A percentage point is the plain arithmetic gap between two percentages — going from 40% to 50% is a 10 percentage point jump. A percentage change describes that same move relative to the starting number, which here is actually a 25% increase (10 ÷ 40 × 100). News headlines mix these up constantly, and it changes the meaning a lot.
Q: How do you find the whole number when you only know the percentage and the part?
This is a reverse percentage: Whole = Part ÷ (Percentage ÷ 100). If 30 marks represent 60% of a test, the total is 30 ÷ 0.60 = 50 marks.
Q: How do you find a percentage of a percentage?
Convert both to decimals and multiply. 50% of 40% is 0.50 × 0.40 = 0.20, or 20%. This comes up in weighted grading — if a chapter is 40% of the final exam, and the final exam is 50% of your grade, that chapter alone is worth 20% of your final grade.
Q: Why do schools use weighted percentages instead of a simple average?
A weighted percentage assigns different importance to different categories — say 40% exams, 30% assignments, 20% quizzes, 10% participation — so a strong final exam counts for more than a single quiz, rather than every graded item being treated as equally important.
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