Table of Contents
What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word "percent" literally means "per hundred" — so 25% means 25 out of every 100.
Percentages are everywhere: shopping discounts, exam scores, interest rates, tax calculations, and statistical data. Understanding how to calculate them is an essential life skill.
Quick Definition
Percentage = (Part ÷ Whole) × 100
Example: 3 out of 4 = (3 ÷ 4) × 100 = 75%
Basic Percentage Formula
The fundamental formula for calculating what percentage one number is of another:
Part = The portion you're measuring
Whole = The total or original amount
Step-by-Step Example
Exam Score Example
Question: You scored 42 out of 50 on a test. What's your percentage?
Step 1: Divide part by whole: 42 ÷ 50 = 0.84
Step 2: Multiply by 100: 0.84 × 100 = 84%
Find Percentage of a Number
To find what a certain percentage of a number is, use this formula:
Examples
Shopping Discount
Question: A $80 shirt is 20% off. How much do you save?
Calculation: (20 / 100) × 80 = 0.2 × 80 = $16 saved
Final Price: $80 - $16 = $64
Restaurant Tip
Question: Your bill is $45. You want to leave a 15% tip.
Calculation: (15 / 100) × 45 = 0.15 × 45 = $6.75 tip
Percentage Increase
To calculate how much something has increased in percentage terms:
Example: Salary Raise
Salary Increase
Old Salary: $40,000
New Salary: $44,000
Calculation:
((44,000 - 40,000) / 40,000) × 100
= (4,000 / 40,000) × 100
= 0.1 × 100 = 10% raise
Percentage Decrease
To calculate how much something has decreased in percentage terms:
Example: Sale Price
Product Discount
Original Price: $120
Sale Price: $90
Calculation:
((120 - 90) / 120) × 100
= (30 / 120) × 100
= 0.25 × 100 = 25% off
Mental Math Tricks for Percentages
Calculate percentages quickly in your head with these shortcuts:
10% Trick
Move decimal one place left. 10% of 250 = 25
50% Trick
Just divide by 2. 50% of 84 = 42
25% Trick
Divide by 4. 25% of 100 = 25
15% Tip Trick
10% + half of 10%. 15% of $40 = $4 + $2 = $6
Pro Tip: The "1% Method"
To find any percentage, first find 1% (divide by 100), then multiply by the percentage you want.
Example: 17% of 300 → 1% = 3 → 17 × 3 = 51
Real-Life Uses of Percentages
| Situation | Formula | Example |
|---|---|---|
| Discount | Original × (1 - %/100) | 20% off $50 = $50 × 0.8 = $40 |
| Sales Tax | Price × (1 + Tax%/100) | 8% tax on $30 = $30 × 1.08 = $32.40 |
| Grade Average | (Points Earned / Total) × 100 | 85/100 = 85% |
| Profit Margin | ((Revenue - Cost) / Revenue) × 100 | ($150-$100)/$150 × 100 = 33.3% |
| Interest Earned | Principal × Rate × Time | $1000 × 5% × 1yr = $50 |
Quick Reference: Common Percentages
| Percentage | Decimal | Fraction | Quick Method |
|---|---|---|---|
| 1% | 0.01 | 1/100 | Divide by 100 |
| 10% | 0.1 | 1/10 | Move decimal left 1 |
| 20% | 0.2 | 1/5 | Divide by 5 |
| 25% | 0.25 | 1/4 | Divide by 4 |
| 50% | 0.5 | 1/2 | Divide by 2 |
| 75% | 0.75 | 3/4 | ¾ of the number |
Key Takeaways
- Percentage = (Part ÷ Whole) × 100 — memorize this!
- To find % of a number: convert % to decimal, then multiply
- Increase/decrease formulas help track changes over time
- Mental math tricks make everyday calculations faster
- Practice with real situations: tips, discounts, grades
Frequently Asked Questions
Q: What is 10% of 500?
10% of 500 = (10/100) × 500 = 0.1 × 500 = 50. Quick trick: Move decimal one place left → 500 → 50.
Q: How do I calculate percentage quickly?
Use the "1% method": Find 1% (divide by 100), then multiply by your target percentage. Example: 18% of 200 → 1% = 2 → 18 × 2 = 36.
Q: What's the difference between percentage and percentage points?
Percentage is a ratio (25% of something). Percentage points measure the difference between two percentages. If a rate goes from 10% to 15%, that's a 5 percentage point increase (but a 50% increase in relative terms).
Q: Can percentages be over 100%?
Yes! Percentages over 100% mean the part is larger than the whole. Example: If sales increased from $100 to $250, that's a 150% increase.
Calculate Percentages Instantly
Use our free percentage calculator for discounts, taxes, grades, and more — no math required!
Try the Percentage Calculator