Percentage Calculator

Calculate percentages in 4 modes — find X% of Y, reverse percentage, percentage change, or percentage difference.

What is X% of Y?

Number

20% of 500

100

500 × 0.20 = 100

Calculation History

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Percentage Formulas Explained

A percentage is a fraction expressed as parts per hundred. The symbol % means "out of 100." Understanding the four core percentage operations covers 95% of everyday percentage problems.

1. What is X% of Y? (Most Common)

Result = Y × (X ÷ 100)

Example: What is 15% of ₹800? → 800 × 0.15 = ₹120. Used for: calculating tips, tax amounts, commission, discount savings.

2. Y is What Percentage of X? (Reverse)

Percentage = (Y ÷ X) × 100

Example: 45 is what % of 180? → (45÷180)×100 = 25%. Used for: test scores, market share, completion percentage.

3. Percentage Increase / Decrease

% Change = [(New − Old) ÷ |Old|] × 100

Positive result = increase, negative = decrease. Example: Price rose from ₹200 to ₹250 → (50÷200)×100 = +25%. Used for: inflation, profit/loss, performance comparison.

4. Percentage Difference

% Difference = [|A − B| ÷ ((A + B) ÷ 2)] × 100

Unlike % change, this is symmetric — it doesn't matter which value is "old" or "new." Used when comparing two values without a clear before/after relationship.

Common Percentage Shortcuts

10% of any number: move decimal point one left (10% of ₹1,250 = ₹125)
5%: half of 10% (₹62.50 in the example above)
1%: move decimal point two places left (₹12.50)
20%: double the 10% value (₹250)
25%: divide by 4 (₹312.50)
50%: divide by 2 (₹625)
To find original from a discounted price: Original = Sale ÷ (1 − discount%)

Frequently Asked Questions

What is the formula for percentage increase?

% Increase = [(New Value − Old Value) ÷ Old Value] × 100. If the result is negative, it's a percentage decrease instead.

How do I find original price from discounted price?

Original = Discounted Price ÷ (1 − Discount% ÷ 100). Example: ₹680 after 15% off → 680 ÷ 0.85 = ₹800 original price.

What is the difference between percentage change and percentage difference?

Percentage change measures the change from a starting value to an ending value (directional). Percentage difference compares two values symmetrically (non-directional) — useful when there's no clear "before" and "after."

How do I calculate compound percentage growth?

For compound growth over N periods: Final = Initial × (1 + Rate)^N. Example: ₹1,000 at 10% for 3 years = 1000 × 1.1³ = ₹1,331. This is the basis of SIP and compound interest calculations.

What is a percentage point vs a percentage change?

A percentage point is an absolute difference between two percentages. If inflation rises from 5% to 7%, it increased by 2 percentage points, but by 40% as a relative percentage change [(7−5)÷5×100 = 40%]. These are very different and commonly confused in news reporting.

How do I calculate what percentage one number is of another?

Divide the part by the whole and multiply by 100. Example: 36 out of 48 = (36÷48)×100 = 75%. This is the "Y is what % of X" formula — useful for test scores, completion rates, and market share calculations.

Real-World Percentage Calculations — Practical Guide

Percentages appear in almost every financial, academic, and professional context. From calculating GST on an invoice to finding your exam score percentage, from computing profit margin to working out a salary hike — mastering percentage calculation is one of the most practical everyday math skills.

Percentage in Finance and Business

Profit margin: (Profit ÷ Revenue) × 100. A business selling at ₹500 with ₹350 cost has 30% profit margin.
GST calculation: Amount × Rate ÷ 100. ₹10,000 goods with 18% GST = ₹1,800 tax. To extract GST from inclusive price: (Price × Rate) ÷ (100 + Rate).
Salary hike: New Salary = Current × (1 + Hike% ÷ 100). ₹50,000 with 12% hike = 50,000 × 1.12 = ₹56,000.
EMI interest component: Monthly interest = Outstanding Principal × (Annual Rate ÷ 12 ÷ 100).
Portfolio return: (Current Value − Invested) ÷ Invested × 100. ₹1,20,000 from ₹1,00,000 = 20% return.

Percentage in Academics and Exams

Exam percentage: (Marks Obtained ÷ Total Marks) × 100. 420 out of 500 = 84%.
CGPA to percentage (CBSE): CGPA × 9.5. CGPA 8.5 = 80.75%.
Pass percentage: (Passed Students ÷ Total Students) × 100.
Grade boundaries: A = 90%+, B = 75%+, C = 60%+, D = 45%+, F = below 35% (varies by institution).

Percentage in Daily Shopping

Discount calculation: Savings = MRP × Discount% ÷ 100. Sale price = MRP × (1 − Discount% ÷ 100).
Additional discount on already-discounted item: Sequential, not additive. 20% then 10% off = 28% total (not 30%).
Effective discount: 100 − (final price ÷ original × 100). Useful when discount% is not shown directly.
Comparing unit prices: Price per unit = Total Price ÷ Quantity. Then calculate % difference to decide which pack size is cheaper per unit.

Common Percentage Mistakes to Avoid

Reversibility error: A 50% increase followed by a 50% decrease does NOT return to the original. 100 → 150 → 75 (a 25% net loss). Percentage changes are not reversible.
Base confusion: "10% off, then another 10% off" = 10% off the original, then 10% off the reduced price. Result: 19% total discount, not 20%.
Percentage point vs percentage: Inflation going from 5% to 6% rose by 1 percentage point, but by 20% relative to its previous value.
Mixing absolute and relative: "Sales increased by ₹5,000" is absolute. "Sales increased by 10%" is relative. Both can describe the same event.

Who Uses This Calculator?

Students checking exam scores and CGPA conversions. Shoppers calculating final prices after discount. Business owners computing GST, profit margins, and markups. Job seekers calculating salary hike percentages. Investors computing portfolio returns. Teachers grading and scaling marks. Data analysts computing growth rates and percentage contributions. Anyone who needs quick, accurate percentage math without a pen and paper.