📖 What is a Percentage?
A percentage is a way to express a number as a fraction of 100. The word "percent" comes from Latin "per centum" meaning "by the hundred".
1% = 1/100 = 0.01
🔧 The Basic Percentage Formula
Percentage = (Part / Whole) × 100%
📝 Common Percentage Calculations
1. Finding a Percentage of a Number
Formula: Result = (Percentage ÷ 100) × Number
Example: What is 20% of 200?
= (20 ÷ 100) × 200 = 0.2 × 200 = 40
= (20 ÷ 100) × 200 = 0.2 × 200 = 40
2. Finding What Percentage One Number is of Another
Formula: Percentage = (Part ÷ Whole) × 100%
Example: 40 is what percent of 200?
= (40 ÷ 200) × 100% = 0.2 × 100% = 20%
= (40 ÷ 200) × 100% = 0.2 × 100% = 20%
3. Percentage Change (Increase/Decrease)
Formula: Percentage Change = [(New - Original) ÷ Original] × 100%
Example: From 100 to 120 (increase)
= [(120 - 100) ÷ 100] × 100% = (20 ÷ 100) × 100% = 20% increase
= [(120 - 100) ÷ 100] × 100% = (20 ÷ 100) × 100% = 20% increase
4. Adding Percentage to a Number
Formula: Result = Original × (1 + Percentage ÷ 100)
Example: 100 + 10% = 100 × 1.10 = 110
5. Subtracting Percentage from a Number
Formula: Result = Original × (1 - Percentage ÷ 100)
Example: 100 - 10% = 100 × 0.90 = 90
Pro Tips:
- To find 10% of any number, just move the decimal one place left (10% of 250 = 25)
- To find 1% of any number, move the decimal two places left (1% of 250 = 2.5)
- For discounts: Final Price = Original Price × (1 - Discount% ÷ 100)
- For tips: Tip Amount = Bill Amount × (Tip% ÷ 100)
💡 Real-Life Applications
- Shopping: Calculating discounts and sales tax
- Restaurants: Figuring out tips
- Finance: Interest rates, investment returns
- Statistics: Data analysis and comparisons
- Grades: Calculating test scores
Ready to calculate? Use the calculator above to solve any percentage problem with step-by-step explanations!