Percentage Calculator

Four Percentage Problems, One Calculator

Percentages appear in almost every area of life — tax invoices, exam results, salary increases, investment returns, discounts, and data analysis. But there's more than one way to ask a percentage question:

• "What is 15% of ₹3,500?" → Basic percentage
• "₹840 is what percent of ₹3,500?" → Reverse percentage
• "Revenue went from ₹12 lakh to ₹16.8 lakh — what's the growth rate?" → Percentage change
• "₹8,500 plus 18% GST — what's the total?" → Add/subtract percentage

Each is a different formula. This calculator handles all four simultaneously as you type — no Calculate button needed.

The Four Problems and Their Formulas

1. What is X% of Y?

Result = (X ÷ 100) × Y

Example: 15% of ₹3,500 = (15 ÷ 100) × 3,500 = ₹525

Use cases: Commission on a sale, tip amount, tax on a value, discount amount

2. X is what percent of Y?

Percentage = (X ÷ Y) × 100

Example: 67 out of 80 = (67 ÷ 80) × 100 = 83.75%

Use cases: Exam scores, market share, completion percentage, error rate

3. Percentage Change (increase or decrease)

Change = ((New Value − Old Value) ÷ Old Value) × 100

Example: ₹12 lakh to ₹16.8 lakh = ((16.8 − 12) ÷ 12) × 100 = +40% Example: 100 employees to 72 employees = ((72 − 100) ÷ 100) × 100 = −28%

Use cases: Business growth metrics, year-over-year comparisons, weight loss tracking, price changes

4. Add or Subtract a Percentage from a Value

Add:      Result = Value × (1 + P ÷ 100)
Subtract: Result = Value × (1 − P ÷ 100)

Add example: ₹8,500 + 18% GST = ₹8,500 × 1.18 = ₹10,030 Subtract example: ₹3,200 − 25% discount = ₹3,200 × 0.75 = ₹2,400

Use cases: Tax-inclusive pricing, discount pricing, salary after deduction

Common Mistake: The Percentage Trap

A 20% increase followed by a 20% decrease doesn't return you to the original value:

• Start: 100
• +20%: 100 × 1.20 = 120
• −20%: 120 × 0.80 = 96

You've lost 4% overall, even though the percentage rises and falls were identical. This catches people off guard in investment return discussions and is worth checking with a calculator before presenting numbers.

Percentage Point vs. Percentage Change (a Common Confusion)

If a tax rate rises from 5% to 6%, two descriptions are both technically valid but describe different things:

• 1 percentage point increase — the rate went up by one unit
• 20% increase in the rate — the rate increased by 20% of its previous value (1 ÷ 5 = 0.20)

News articles and financial reports often use these interchangeably, which creates confusion. When precision matters (financial reporting, research), always specify which measure you mean.

Practical Applications

Retail: "Original price ₹2,400, discount 35%, what's the final price?" → 2,400 × 0.65 = ₹1,560

Finance: "I invested ₹50,000 and got back ₹61,500 — what's my return?" → (61,500 − 50,000) ÷ 50,000 × 100 = 23%

HR/Payroll: "Salary increase from ₹45,000 to ₹52,200 — what percentage?" → (52,200 − 45,000) ÷ 45,000 × 100 = 16%

Students: "I scored 54 out of 65. What percentage?" → (54 ÷ 65) × 100 = 83.08%

Health: "Starting weight 90kg, now 82kg. Percentage lost?" → (90 − 82) ÷ 90 × 100 = 8.9%

Related Finance Tools

• GST/VAT Calculator — Add or extract tax specifically, with jurisdiction rates
• Discount Calculator — Specialized discount and savings calculation
• ROI Calculator — Calculate investment return percentages
• Compound Interest Calculator — Multi-period percentage growth modeling
• Salary Tax Calculator — Percentage-based income tax calculation

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