Percentage Calculator — All Types
Select a calculation type, enter your numbers, and get the answer with complete step-by-step working
X% of Y
X of Y
Old → New
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Add X%
Subtract X%
Cost → Sale
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Result Summary
More Useful Results
Visual Breakdown
Step-by-Step Working
What Is a Percentage?
The core concept behind percentages, why they matter and how all the different types of percentage problems relate to each other
A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum meaning "by the hundred." When we say 45%, we mean 45 out of every 100 — or equivalently, 45/100 = 0.45 as a decimal. Percentages are the most universal way to compare proportions because they normalise everything to the same denominator (100), making comparisons immediate and intuitive.
Percentages appear in every area of daily life: bank interest rates, exam scores, discount offers, tax rates (GST 18%, income tax 30%), salary hikes, inflation figures (7% per year), nutrition labels (% daily value), battery levels, polling data and sports statistics. Misunderstanding percentages — especially percentage change and percentage points — leads to widespread confusion in how data is communicated and interpreted.
The three core percentage relationships are: (1) Part = Percentage × Whole, (2) Percentage = Part ÷ Whole × 100, and (3) Whole = Part ÷ Percentage × 100. Every percentage question — however complex it looks — is a rearrangement of these three fundamental equations.
All Percentage Formulas — Reference Table
Every percentage formula you'll ever need, with example, use case and direction of calculation
| Type | Formula | Example | Used For |
|---|---|---|---|
| X% of Y Most common | Result = (X/100) × Y | 15% of 200 = 30 | Discount, tax, tip, interest |
| What % is X of Y | % = (X/Y) × 100 | 30 of 150 = 20% | Score, market share, completion |
| % Increase / Decrease | % = ((New−Old)/Old) × 100 | (1200−1000)/1000×100 = +20% | Salary hike, price change, returns |
| Reverse Percentage | Original = Value / (P/100) | 60 is 40% of 150 | Find original before discount/tax |
| Increase Value by X% | New = Old × (1 + X/100) | 1000 + 15% = 1150 | Hike, markup, compound growth |
| Decrease Value by X% | New = Old × (1 − X/100) | 5000 − 20% = 4000 | Discount, depreciation, loss |
| Profit Margin | Margin% = ((Sale−Cost)/Sale) × 100Markup% = ((Sale−Cost)/Cost) × 100 | Cost 800, Sale 1200 → Margin 33.3% | Business pricing, retail, gross margin |
| GST / Tax | With GST: Amount × (1 + Rate/100)Remove GST: Incl / (1 + Rate/100) | ₹10,000 + 18% = ₹11,800 | Invoicing, reconciliation, pricing |
Discount & Sale Price
Final price = Original × (1 − Discount%/100). A 30% discount on ₹2,000 = ₹2,000 × 0.70 = ₹1,400. To find what discount was applied: Discount% = ((Original − Sale) / Original) × 100. Retailers often stack discounts — 20% off and then 10% off is NOT 30% off; it's 20% + 8% = 28% total.
Sale pricingExam Score & Pass %
Score% = (Marks obtained / Total marks) × 100. If you scored 68/80: 68/80 × 100 = 85%. To find marks needed for a passing %: Marks needed = (Pass% / 100) × Total. For a 40% pass in 80-mark exam: 40/100 × 80 = 32 marks minimum. Percentile ≠ percentage — percentile ranks you against others.
EducationSalary Hike & CTC
New salary = Current × (1 + Hike%/100). A 12% hike on ₹50,000 = ₹50,000 × 1.12 = ₹56,000. To find the hike%: Hike% = ((New − Old) / Old) × 100. Companies sometimes quote "% increase in CTC" when the in-hand amount increases by a different % due to variable pay or PF changes — always calculate both.
HR / FinanceGST in India (5/12/18/28%)
India's GST slabs: 5% (essentials), 12% (standard goods), 18% (most services, electronics), 28% (luxury/sin goods). To add: Amount × (1 + Rate/100). To remove from GST-inclusive price: Price / (1 + Rate/100). CGST = SGST = half the GST rate. IGST = full rate for inter-state supply.
TaxationInvestment Returns
Absolute return% = ((Current − Invested) / Invested) × 100. CAGR = (Final/Initial)^(1/Years) − 1. A ₹1L investment worth ₹1.6L after 4 years: CAGR = (1.6)^(0.25) − 1 = 12.47%. Mutual fund fact sheets often show point-to-point returns — these are simple % changes, not CAGR unless stated.
InvestingReverse % — Find Original
If a price after 20% discount is ₹960, the original was ₹960 / 0.80 = ₹1,200. Never subtract 20% to find original — that gives ₹768, which is wrong! Original = Discounted / (1 − Discount%). Same for GST removal: if price includes 18% GST, original = Price / 1.18. This is the most commonly mis-calculated percentage type.
Critical skillHow This Calculator Works
Step-by-step: how each of the 8 calculation modes processes your inputs and generates the full working
- 1
Select Your Calculation Type
Click the type that matches your question — Basic %, What % is X of Y, % Change, Reverse %, Increase/Decrease, Profit Margin, or GST. The input fields, equation display and formula all update instantly to match your selection. The equation box at the top always shows what you're solving for.
- 2
Enter Your Numbers (Live Preview)
As you type, the result box above the Calculate button updates in real time — no button click needed. This live feedback lets you see the answer immediately and adjust your numbers. Quick-preset buttons (e.g., 5%, 10%, 18%, 25%) speed up entry for the most common percentage values.
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Click Calculate for Full Breakdown
The full Calculate button generates: the hero result with colour coding, 6 summary cards, a "More Useful Results" panel with related calculations, a visual bar breakdown, and a complete step-by-step working list showing every formula, substitution and intermediate value — just like a textbook solution.
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See Related Calculations Automatically
Each mode automatically computes and shows related useful results. For example: Basic % also shows the complement (what % remains), the fraction equivalent, and what multiple percentages of the same number are. % Change shows the multiplier, reverse change, and absolute difference. These extras save you from doing follow-up calculations.
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Share or Copy Results
Use the Copy, WhatsApp or Tweet buttons to share the complete result with working. The shared text includes the calculation type, inputs, formula used, the answer and all related results — useful for sharing billing breakdowns, negotiation data, school homework or financial summaries with colleagues.
Basic% : Result = (P/100) × N
What% : P% = (Part/Total) × 100
%Change : C% = ((New−Old)/Old) × 100
Reverse : Original = Value / (P/100)
Increase : New = Old × (1 + P/100)
Decrease : New = Old × (1 − P/100)
Margin : Margin = ((Sale−Cost)/Sale) × 100
GST Add : With GST = Amount × (1 + Rate/100)
GST Remove: Original = Incl / (1 + Rate/100)Percentage Tricks, Shortcuts & Fun Facts
Mental math shortcuts, common misconceptions and fascinating facts about percentages
X% of Y = Y% of X (Always!)
A surprisingly useful identity: 8% of 25 is the same as 25% of 8. Both equal 2. This means if you need 8% of 25, just compute 25% of 8 (÷4) = 2, which is far easier mentally. This works because (X/100)×Y = (Y/100)×X — they're both just XY/100.
10% Trick: Just Move the Decimal
10% of any number = shift decimal one place left. 10% of 8,340 = 834. Then: 5% = half of 10%, 20% = double 10%, 15% = 10% + 5%, 1% = 10% ÷ 10. With these anchors, you can calculate any "round" percentage in seconds without a calculator.
-50% Then +50% ≠ Zero
If a stock falls 50% and then rises 50%, you've lost 25% overall. Starting at ₹100: after −50% = ₹50, after +50% = ₹75, not ₹100. This asymmetry is why losses hurt more than equivalent gains. A 50% loss requires a 100% gain to recover. A 90% loss requires a 900% gain — the math of drawdowns is brutal.
Stacked Discounts Are Not Additive
Two consecutive discounts of 20% and 10% do not equal 30% off. First discount: ₹100 → ₹80. Second: ₹80 → ₹72. Total effective discount = 28%, not 30%. Formula: Combined = 1 − (1−d1)(1−d2). Retailers use stacked discounts deliberately because they sound more generous than they are.
Percentage Points vs Percentages
Party A gets 40% of votes; in the next election it gets 52%. This is +12 percentage points, but a +30% increase in vote share. News reports regularly confuse these. In finance: a fund's expense ratio going from 1% to 1.5% is a 50% increase in cost, but only 0.5 percentage points higher. Always clarify which is being stated.
The 72 Rule for Doubling
To estimate how long it takes money to double at a given interest rate, divide 72 by the rate. At 8% annual return: 72 ÷ 8 = 9 years to double. At 12%: 72 ÷ 12 = 6 years. At 6%: 72 ÷ 6 = 12 years. This "Rule of 72" is one of the most useful mental math tools in personal finance.
100% ≠ Everything in Some Contexts
You can give "110% effort" as an expression but not literally. However, prices and returns can exceed 100% — a ₹1,000 investment that grows to ₹5,000 has gained 400%. Percentage change has no upper limit for gains but has a floor of −100% (you can only lose everything once, but gains are unbounded).
GST: India's Most-Calculated Percentage
India's GST replaced 17 different indirect taxes in 2017. The four main slabs — 5%, 12%, 18%, 28% — affect everything from groceries to cars. Most service invoices carry 18% GST. Removing GST from an inclusive price: divide by 1.18 (not subtract 18%). Confusing these two methods is one of the most common billing errors in small business invoicing.
Frequently Asked Questions
Common questions about percentage calculations, reverse percentage, GST, margins and percentage change