Percentages show up everywhere: discounts, test scores, tips, interest, and statistics. Once you know three simple formulas, you can work out almost any percentage in seconds. This guide covers the three most common cases with clear examples, plus a free calculator to check your answers.
What is a percentage?
A percentage is just a fraction of 100. "Per cent" means "per hundred", so 25% is the same as 25/100, or 0.25. To turn a percentage into a decimal, divide by 100. To turn a decimal back into a percentage, multiply by 100.
1. Percentage of a number
Formula: (percentage ÷ 100) × number
Example: What is 20% of 150?
(20 ÷ 100) × 150 = 0.20 × 150 = 30.
2. What percentage is X of Y?
Formula: (X ÷ Y) × 100
Example: You scored 42 out of 60 on a test. What percentage is that?
(42 ÷ 60) × 100 = 70%.
3. Percentage increase or decrease
Formula: ((new − old) ÷ old) × 100
Example: A price rises from $80 to $100.
((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase.
If the result is negative, it is a decrease instead.
Skip the maths and use a calculator
Our free Percentage Calculator handles all three cases, percentage of a number, X of Y, and percentage change, instantly and with no sign-up.
Where you will use percentages
- Shopping: work out sale prices with our Discount Calculator.
- Business: set prices and margins with the Markup Calculator.
- School: turn scores into grades and GPA with the GPA Calculator.
- Dining: split the bill and add a tip with the Tip Calculator.
Frequently asked questions
How do I calculate a percentage quickly in my head?
Find 10% first by moving the decimal one place to the left, then scale it. For 30% of 50: 10% is 5, so 30% is 15.
What is the difference between a percentage and percentage points?
If a rate goes from 20% to 25%, that is a 5 percentage point rise, but a 25% increase relative to the starting value.
How do I reverse a percentage?
To find the original amount before a percentage change, divide by (1 + rate). If $120 is the price after a 20% increase: 120 ÷ 1.20 = $100.
Want to check your work? Open the free Percentage Calculator, or explore all our free calculators and tools.