How to Calculate Percentages
Percentages are everywhere. You see them on price tags, nutrition labels, bank statements, school reports and news articles. Most people can recognise a percentage, but many are not fully sure how to calculate one quickly and confidently.
This guide walks through every type of percentage question you are likely to face. Each section shows the formula, a worked example and the fastest way to get the answer.
What Is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning per hundred. So 45 percent simply means 45 out of every 100.
Percentages are useful because they create a common scale. Saying a store offers 30 percent off is instantly comparable to another store offering 25 percent off, even though the actual prices are completely different.
The Three Core Percentage Questions
Almost every percentage problem falls into one of three categories. Identifying which one you are dealing with is the key to picking the right approach.
| Question | What you are finding |
|---|---|
| What is X percent of a number? | Find the part from the whole and the percentage |
| X is what percent of Y? | Find the percentage from the part and the whole |
| X percent of what number equals Y? | Find the whole from the part and the percentage |
Question Type 1: What Is X Percent of a Number?
This is the most common percentage question. Use it for sale prices, tips, commission and nutritional information.
Formula and Example
Formula: Result = (Percentage divided by 100) multiplied by Total
Example: What is 20 percent of 85?
Result = (20 divided by 100) multiplied by 85
Result = 0.20 multiplied by 85 = 17
So 20 percent of 85 is 17.
Quick mental shortcut: to find 10 percent of any number, move the decimal point one place to the left. Ten percent of 340 is 34. Twenty percent is double that, so 68.
Question Type 2: X Is What Percent of Y?
Use this when you want to express one number as a percentage of another. Useful for test scores, profit margins and comparing quantities.
Formula and Example
Formula: Percentage = (Part divided by Whole) multiplied by 100
Example: 36 is what percent of 90?
Percentage = (36 divided by 90) multiplied by 100
Percentage = 0.4 multiplied by 100 = 40 percent
So 36 is 40 percent of 90.
Question Type 3: X Percent of What Number Is Y?
Use this when you know the result and the percentage but need to find the original total. Common in reverse discount calculations.
Formula and Example
Formula: Whole = Part divided by (Percentage divided by 100)
Example: 15 percent of what number is 45?
Whole = 45 divided by (15 divided by 100)
Whole = 45 divided by 0.15 = 300
So 15 percent of 300 is 45.
Percentage Increase and Decrease
When a value changes, percentage change tells you how big that change is relative to the starting value.
Percentage Change Formula
Formula: Percentage change = ((New value minus Old value) divided by Old value) multiplied by 100
Example (increase): A price rises from 80 dollars to 100 dollars.
Change = ((100 minus 80) divided by 80) multiplied by 100
Change = (20 divided by 80) multiplied by 100 = 25 percent increase
Example (decrease): A price falls from 100 dollars to 75 dollars.
Change = ((75 minus 100) divided by 100) multiplied by 100 = minus 25 percent decrease
Use the Percentage Change Calculator to get this result instantly without doing the arithmetic yourself.
Percentage Difference
Percentage difference compares two values without treating either one as the starting point. It measures how far apart they are relative to their average.
Percentage Difference Formula
Formula: Percentage difference = (Absolute difference divided by Average of both values) multiplied by 100
Example: Compare 80 and 100.
Difference = 100 minus 80 = 20
Average = (80 plus 100) divided by 2 = 90
Percentage difference = (20 divided by 90) multiplied by 100 = 22.2 percent
Use the Percentage Difference Calculator for this type of comparison.
Percent Error
Percent error tells you how far off a measurement or estimate is from the true or accepted value. It is used heavily in science and engineering.
Percent Error Formula
Formula: Percent error = (Absolute value of (Measured minus Actual) divided by Actual) multiplied by 100
Example: You measure a plank as 98 cm. It is actually 100 cm.
Error = (Absolute value of (98 minus 100) divided by 100) multiplied by 100
Error = (2 divided by 100) multiplied by 100 = 2 percent error
Use the Percent Error Calculator for science and engineering measurements.
Common Percentage Mistakes
- Confusing percentage change with percentage difference. They use different formulas and answer different questions.
- Reversing the numerator and denominator. Always divide the part by the whole, not the other way around.
- Assuming two percentage increases add up. A 20 percent increase followed by a 20 percent decrease does not return you to the original value.
- Forgetting to multiply by 100 at the end when converting a decimal to a percentage.
Free Percentage Tools on CalConvs
- Percentage Calculator for all three core question types
- Percentage Change Calculator for increases and decreases
- Percentage Difference Calculator for comparing two values symmetrically
- Percent Error Calculator for scientific measurements
- All Math Calculators browse the full collection
Frequently Asked Questions
What is the easiest way to calculate a percentage?
Use the formula: Result = (Percentage / 100) × Total. For quick mental maths, find 10 percent first by moving the decimal point one place left, then adjust from there.
What is the difference between percentage change and percentage difference?
Percentage change has a direction and divides by the original value. Percentage difference has no direction and divides by the average of both values. Use change when comparing before and after; use difference when comparing two values that coexist at the same time.
How do I reverse a percentage to find the original number?
Divide the result by the percentage expressed as a decimal. If 60 is 75 percent of a number, divide 60 by 0.75 to get 80.
Can percentages exceed 100?
Yes. A 150 percent increase means the value grew by one and a half times the original. Percentages above 100 are very common in finance and growth rate comparisons.