What is a Percentage?
A percentage is a number expressed as a fraction of 100. If you need to solve fractional equations or shifts, use our online percentage calculator to compute changes instantly. The symbol % comes from the Latin per centum meaning 'out of one hundred.' Percentages are used in discounts, taxes, exam scores, interest rates, statistics, and almost every area of daily life.
5 Essential Percentage Calculations
1. Find X% of a Number
FormulaResult = (Percentage ÷ 100) × Number
Example: 15% of 200 = (15 ÷ 100) × 200 = 30
Example: 15% of 200 = (15 ÷ 100) × 200 = 30
2. What Percentage is X of Y?
Formula% = (X ÷ Y) × 100
Example: 30 is what % of 200? = (30 ÷ 200) × 100 = 15%
Example: 30 is what % of 200? = (30 ÷ 200) × 100 = 15%
3. Percentage Increase
Formula% Increase = [(New − Old) ÷ Old] × 100
Example: Price goes from ₹80 to ₹100 = [(100−80) ÷ 80] × 100 = +25%
Example: Price goes from ₹80 to ₹100 = [(100−80) ÷ 80] × 100 = +25%
4. Percentage Decrease
Formula% Decrease = [(Old − New) ÷ Old] × 100
Example: Price drops from ₹100 to ₹80 = [(100−80) ÷ 100] × 100 = −20%
Example: Price drops from ₹100 to ₹80 = [(100−80) ÷ 100] × 100 = −20%
5. Reverse Percentage (Find Original)
FormulaOriginal = Amount ÷ (1 − Discount%/100)
Example: Sale price ₹800 after 20% off → 800 ÷ 0.8 = ₹1,000
Example: Sale price ₹800 after 20% off → 800 ÷ 0.8 = ₹1,000
Percentage vs Percentage Points
These two are frequently confused in news and finance:
- Interest rates rise from 4% to 6% — that is a rise of 2 percentage points, but a 50% increase relative to the original rate.
- Your exam score improves from 60% to 72% — that is 12 percentage points higher, or a 20% improvement.
💡 In financial news, "rates rose by 50 basis points" means 0.50 percentage points (1 basis point = 0.01%).
Real-World Percentage Examples
| Scenario | Calculation | Answer |
|---|---|---|
| 18% GST on ₹5,000 | 18% of 5,000 | ₹900 tax → ₹5,900 total |
| 25% off ₹2,000 | 25% of 2,000 | ₹500 off → ₹1,500 |
| Scored 72 out of 90 | (72÷90)×100 | 80% |
| Salary ₹40k→₹52k | (12÷40)×100 | 30% hike |
📊 Calculate any percentage in seconds — 3 modes in one tool
Open Percentage Calculator →📐 External Scientific References & Authoritative Sources
- Mathematical Association of America (MAA) — Statistical Averages, Ratios & Arithmetic Principles.
- NIST Digital Library of Mathematical Functions — Standard Mathematical Formulations & Algorithms.
- Wolfram MathWorld — Interactive Mathematical Formulas & Statistical Analysis Standards.