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Math

Percentage Formula Explained – What is Percentage & How to Calculate It

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The percentage formula is the foundation of almost all mathematical calculations in daily life — from shopping discounts and GST computation to salary analysis and stock returns. This comprehensive guide explains every variation of the percentage formula with clear, practical examples using Indian contexts.

What is a Percentage?

A percentage is a ratio expressed as a fraction of 100. The word "percent" comes from the Latin "per centum" meaning "per hundred." When we say 25%, we mean 25 out of every 100. Percentages allow us to compare proportions on a standardised scale, making them invaluable in finance, education, statistics, and everyday commerce.

The Core Percentage Formulas

1. Find X% of a Number: Result = (X / 100) × Number

2. What % is A of B? % = (A / B) × 100

3. Percentage Change: % Change = ((New − Old) / Old) × 100

4. Find Original from Percentage: Original = Value / (1 + %/100)

Formula 1: Find X% of a Number

Question: What is 35% of ₹8,500?

  1. Result = (35 / 100) × 8,500
  2. Result = 0.35 × 8,500 = ₹2,975

Use this for: Discounts, tax calculations, commission, tips.

Formula 2: What Percentage is A of B?

Question: A student scored 72 marks out of 90. What percentage is this?

  1. % = (72 / 90) × 100
  2. % = 0.8 × 100 = 80%

Use this for: Grade calculation, success rates, market share analysis.

Formula 3: Percentage Change (Increase/Decrease)

Question: A flat's price rose from ₹45,00,000 to ₹54,00,000. What's the percentage increase?

  1. Change = ₹54,00,000 − ₹45,00,000 = ₹9,00,000
  2. % Change = (9,00,000 / 45,00,000) × 100 = 20%

Formula 4: Find Original Value from Percentage

Question: A TV is priced at ₹29,500 inclusive of 18% GST. What is the base price?

  1. Base Price = ₹29,500 / (1 + 18/100) = ₹29,500 / 1.18 = ₹25,000

Percentage Tips & Tricks

  • Swap trick: X% of Y = Y% of X. So 8% of 25 = 25% of 8 = 2. (Easier to calculate!)
  • 10% shortcut: Move the decimal one place left. 10% of 8,450 = 845.
  • 5% = half of 10%: 5% of 8,450 = 422.5.
  • 1% = move decimal two places: 1% of 8,450 = 84.5.

Common Mistakes to Avoid

  • Confusing "percentage of" with "percentage more than." 50% more than 100 = 150. 50% of 100 = 50.
  • Adding percentages directly: 20% off then 10% off is NOT 30% off. It's 28% off.
  • Using wrong base for percentage change calculation.

Frequently Asked Questions

What is the difference between percentage and percentile?

Percentage is a proportion out of 100. Percentile indicates what percentage of a population scored below a given value. Scoring 90th percentile means you scored better than 90% of test-takers.

How do I calculate percentage in Excel?

In Excel: =(A2/B2)*100 gives percentage of A of B. =A2*(1-B2/100) gives discounted price. Excel handles all percentage formulas natively.

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