What is a Percentage?
The word percentage comes from the Latin per centum, meaning "by the hundred". A percentage is simply a ratio or fraction whose denominator is always 100. For example, 25% represents 25 parts out of 100, which is equivalent to the decimal 0.25 or the fraction 1/4.
The 3 Fundamental Percentage Formulas
Every percentage problem you encounter in school, work, taxes, or shopping falls into one of three mathematical patterns:
1. Finding X% of Y (The Amount)
When you know the percentage rate and the total, use this formula:
Result = (X ÷ 100) × Y
Worked Example: What is 20% of 150?
- Convert 20% to decimal: 20 ÷ 100 = 0.20
- Multiply by 150: 0.20 × 150 = 30
2. Finding What Percentage Y is of X (The Share)
When you have a part and a whole and want to know the percentage:
Percentage = (Y ÷ X) × 100%
Worked Example: What percentage is 25 out of 200?
- Divide the part by the total: 25 ÷ 200 = 0.125
- Multiply by 100: 0.125 × 100 = 12.5%
3. Percentage Change (Increase or Decrease)
To measure growth, inflation, price hikes, or investment gains:
Percentage Change = ((New Value – Old Value) ÷ Old Value) × 100%
Worked Example: If an item goes from ₹100 to ₹150:
- Difference: 150 – 100 = 50
- Divide by original: 50 ÷ 100 = 0.50
- Multiply by 100: +50% Increase
The Secret Mental Math Trick: Reversible Percentages
One of the most powerful mental math hacks that few people are taught in school is that percentages are reversible:
X% of Y = Y% of X
Suppose someone asks you to calculate 16% of 50. That feels tricky to compute in your head. Flip it: what is 50% of 16? That's just half of 16, which is 8! Therefore, 16% of 50 is also exactly 8.
Calculate Instantly Without Manual Math
Instead of punching numbers on paper, try our free Instant Percentage Calculator →. It features dedicated modes for X is what % of Y, X% of Y, and % Change, with real-time sliders and 1-click sharing.