How to Calculate Percentage: Formulas, Percentage Increase & Reverse Discount Math Explained
Learn how to calculate percentage of a number, percentage increase/decrease, reverse discount pricing, and exam marks scores with step-by-step arithmetic examples.
What is a Percentage?
A **percentage** (from Latin *per centum*, meaning "by the hundred") is a fraction or ratio expressed with a denominator of 100. It is denoted using the percent sign **"%"**.
Percentages are used universally across retail sales discounts, GST and income tax rates, financial returns, salary appraisals, and student exam grades.
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Master Formula Cheat-Sheet
| Calculation Goal | Mathematical Formula | Practical Example | | :--- | :--- | :--- | | **Find $X$% of $Y$** | $$\text{Value} = \left(\frac{X}{100}\right) \times Y$$ | 18% GST on ₹2,500 = $$(18 \div 100) \times 2500 = \mathbf{450}$$ | | **$X$ is what % of $Y$?** | $$\text{Percentage (\%)} = \left(\frac{X}{Y}\right) \times 100$$ | 480 marks out of 600 = $$(480 \div 600) \times 100 = \mathbf{80\%}$$ | | **Percentage Increase / Decrease** | $$\text{Change (\%)} = \left(\frac{\text{Final} - \text{Initial}}{\text{Initial}}\right) \times 100$$ | Salary hike from 50k to 65k = $$\left(\frac{15000}{50000}\right) \times 100 = \mathbf{+30\%}$$ | | **Reverse Discount (Find Original Price)** | $$\text{Original Price} = \frac{\text{Sale Price}}{1 - \left(\frac{\text{Discount \%}}{100}\right)}$$ | Paid ₹800 after 20% off = $$800 \div 0.80 = \mathbf{₹1,000}$$ |
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Step-by-Step: Solving Everyday Percentage Problems
#### 1. How to Calculate Percentage Increase Suppose your electricity bill was ₹1,200 last month and increased to ₹1,500 this month. - **Difference:** $$1500 - 1200 = 300$$ - **Divide by Original:** $$300 \div 1200 = 0.25$$ - **Multiply by 100:** $$0.25 \times 100 = \mathbf{+25\% \text{ increase}}$$
#### 2. How to Calculate Exam Score Percentage If you scored 482 marks out of 600 in your semester exams: - **Divide score by total:** $$482 \div 600 = 0.8033$$ - **Multiply by 100:** $$0.8033 \times 100 = \mathbf{80.33\%}$$
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Instant Online Calculations with DocuDev
Save time doing manual math using our free **[DocuDev Percentage Calculator](https://www.docudev.site/tools/percentage-calculator)**: - Switch between 5 dedicated calculation modules. - Copy answers in one click. - Download verified PDF math solution worksheets.