Percentage Calculator
Calculate percentages in 5 different ways — find X% of a number, percentage change, what percent one number is of another, and more.
RESULT
100
10% of 1000 = 100
How to Calculate Percentages — A Complete Guide
Percentages are one of the most universally useful mathematical concepts in daily life. From calculating GST and discounts to understanding salary hikes, exam scores, and investment returns, percentages are the language of proportion. This guide explains the five key percentage calculation methods, shows step-by-step formulas, and covers real-world applications.
The 5 Percentage Calculation Modes — Explained
Mode 1 — What is X% of Y?
Formula: Result = (X ÷ 100) × Y. Used for GST, discounts, tips, interest. Example: 18% of ₹50,000 = ₹9,000. An item at ₹50,000 with 18% GST costs ₹59,000 total.
Mode 2 — X is what percent of Y?
Formula: Percentage = (X ÷ Y) × 100. Used for exam scores and proportions. If you scored 45 out of 60: (45 ÷ 60) × 100 = 75%.
Mode 3 — Percentage Change.
Formula: Change% = ((New − Old) ÷ Old) × 100. A product going from ₹80 to ₹100: ((100 − 80) ÷ 80) × 100 = 25% increase.
Mode 4 — Increase by X%.
Formula: New = Original × (1 + X/100). A ₹50,000 salary with 12% hike = 50,000 × 1.12 = ₹56,000.
Mode 5 — Decrease by X%.
Formula: New = Original × (1 − X/100). ₹80,000 laptop at 15% discount = 80,000 × 0.85 = ₹68,000.
Reverse Percentage Calculations
- Original before discount: Original = Final ÷ (1 − Discount%/100). A jacket at ₹850 after 15% off → 850 ÷ 0.85 = ₹1,000.
- Extract GST from inclusive price: GST = Total × Rate ÷ (100 + Rate). ₹59,000 with 18% GST → GST = 59,000 × 18/118 = ₹9,000.
- Original before markup: Original = Final ÷ (1 + Markup%/100). ₹1,200 price with 20% markup → 1,200 ÷ 1.20 = ₹1,000 original cost.
Stacked Discounts — The Common Shopping Trap
When an offer says "30% off + extra 20% off," shoppers assume 50% total. Wrong — discounts stack sequentially:
- Original: ₹1,000 → after 30% off: ₹700 → after 20% off ₹700 = ₹560.
- Effective discount: 44%, not 50%.
Formula: Final = Original × (1 − D1) × (1 − D2). Always verify with a calculator before assuming the advertised savings.
Percentage Points vs. Percentage Change
If the RBI repo rate rises from 6% to 6.5%, that is 0.5 percentage points (absolute arithmetic change). As a percentage change, it is (0.5 ÷ 6) × 100 = 8.33% relative increase. Headlines saying "inflation rose 2 percentage points" mean the rate moved from, say, 4% to 6% — not that it doubled.
Real-World Percentage Applications
| Scenario | Formula | Example |
|---|---|---|
| GST Calculation | Amount × Rate ÷ 100 | ₹10,000 × 18% = ₹1,800 |
| Salary Hike | Salary × (1 + Hike%/100) | ₹60,000 × 1.10 = ₹66,000 |
| Exam Score | (Marks ÷ Total) × 100 | 540/600 = 90% |
| Investment Return | ((End − Start) ÷ Start) × 100 | (₹13L − ₹10L) ÷ ₹10L = 30% |
| EMI-to-Income Ratio | (EMI ÷ Income) × 100 | ₹20K EMI / ₹60K salary = 33.3% |
| Body Weight Change | ((New − Old) ÷ Old) × 100 | 80kg → 72kg = −10% |
References
- CBSE Class 7–8 Mathematics — Percentage and Ratio chapters
- Reserve Bank of India (RBI) — Financial Literacy Program materials
- NISM — Investor Education: Percentage-based returns