Math & General

Percentage Calculator

Solve all 8 types of percentage problems instantly. Basic percentage, percentage change, reverse percentage, increase/decrease, what % is X of Y, tip, profit margin, GST — with full working shown.

8 Calculation Types
Full Working Shown
Instant Results
100% Free

What Is a Percentage Calculator — And Why Eight Types of Percentage Problems Exist

Understanding the full scope of percentage mathematics before you calculate

One Number. Eight Different Questions. All Answered Instantly.

A percentage is a ratio expressed as parts per hundred. Simple enough. But the word "percentage" actually describes at least eight distinct mathematical operations that people encounter in daily life — and confusing one for another is one of the most common calculation errors in shopping, finance, business, and everyday reasoning. This calculator solves all eight types with full step-by-step working, so you understand the formula, not just the answer.

The most basic type — X% of Y — answers questions like "what is 18% GST on ₹12,500?" or "what is a 15% tip on a $68 restaurant bill?" This is straightforward multiplication: (X÷100) × Y. But when the question flips — "30 is what percentage of 200?" — the formula changes to (Part ÷ Whole) × 100. These look similar but are solved differently, and mixing them up produces wrong answers every time.

Percentage change is used constantly in investing, economics, and performance measurement: how much did a stock rise, how much did inflation change, how much did my salary increase? The formula — (New − Old) ÷ Old × 100 — is frequently misapplied when people use the wrong base value. A price rising from ₹80 to ₹100 is a 25% increase. A price falling from ₹100 to ₹80 is a 20% decrease. The absolute change is the same (₹20) but the percentage differs because the base changes.

Reverse percentage — finding the original value before a percentage was applied — is perhaps the most commonly mis-calculated type. If a product costs ₹840 after a 30% discount, the original is NOT ₹840 + 30% = ₹1,092. It is ₹840 ÷ 0.70 = ₹1,200. The same error appears in GST removal: a ₹11,800 GST-inclusive price at 18% GST has a base of ₹10,000, not ₹11,800 − 18% = ₹9,676. This calculator's reverse mode handles this correctly and shows why the common subtraction approach is wrong.

For businesses, profit margin vs markup is a critical distinction. Margin = (Sale − Cost) ÷ Sale. Markup = (Sale − Cost) ÷ Cost. On the same product, a 50% markup equals a 33.3% margin — and systematically confusing these two leads to chronic under-pricing that destroys profitability. The margin mode in this calculator shows both figures side by side.

Limitation to note: This calculator uses standard mathematical definitions for all eight percentage types. In some business contexts, "profit margin" may refer to net margin (after all costs) rather than gross margin (after cost of goods only). For GST, this calculator uses India's GST slabs as reference examples — always verify the applicable rate for your specific goods or service category with a qualified tax professional for compliance purposes.

💡 The Commutativity Trick: X% of Y always equals Y% of X. So 8% of 25 = 25% of 8 = 2. This means if you're struggling to calculate 8% of 25 in your head, flip it: 25% of 8 = 8 ÷ 4 = 2. Instant answer. This symmetry works for any pair of numbers and is one of the most useful mental math shortcuts available for percentage estimation.

Who Uses This Calculator — Six Real Percentage Scenarios

Concrete everyday situations where getting the percentage type right is the difference between a correct and wrong answer

Every Percentage Problem Has a Name. Use the Right Formula.
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Shopper Calculating Sale Prices
A jacket is "30% off ₹4,500" — use Basic % to find ₹1,350 discount and ₹3,150 final price. But if the tag reads "₹3,150 — was ₹4,500", use % Change to verify the real discount rate. And if you know the sale price and want the original before a discount, use Reverse % — not the wrong shortcut of adding the discount back to the sale price.
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Investor Tracking Portfolio Performance
Your SIP of ₹50,000 is now worth ₹62,000 — use % Change to find the 24% absolute return. But if a stock fell 40% and you want to know how much it needs to rise to recover, use Increase by % in reverse: a 40% loss requires a 66.7% gain to break even. These are different questions requiring different modes.
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Business Owner Calculating GST & Margins
You sell software at ₹23,600 inclusive of 18% GST — use the GST Remove mode to find your ₹20,000 base price and ₹3,600 GST liability. For pricing: if your product costs ₹800 and you want a 40% profit margin (not markup), use the Margin mode to find that selling price must be ₹1,333, not ₹1,120 (which is 40% markup).
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Student Checking Exam Scores
Scored 68 out of 85 on a test — use What % is X of Y to find 80%. Want to know what score you need to average 75% across three exams when the first two were 68% and 72%? Use Reverse % to find that you need 85% on the third. These are common exam-context calculations students mishandle by applying the wrong formula.
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HR Manager Processing Salary Revisions
Employee's salary is ₹45,000 and gets a 12% hike — use Increase by % to find new CTC of ₹50,400. But if the total revised budget is ₹50,400 and you need to find what percentage increase was applied from the ₹45,000 base, use % Change mode. Applying the wrong formula in payroll causes systematic under or over-payment.
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Healthcare Worker Reading Lab Results
A patient's HbA1c dropped from 8.2% to 7.1% — this is a 1.1 percentage point change but a 13.4% relative reduction. % Change mode shows the clinical significance. Blood counts, BMI changes, cholesterol reduction, and weight loss goals all involve percentage calculations where the base matters and the "percentage points vs percentage" distinction affects interpretation.

Percentage Calculator — All Types

Select a calculation type, enter your numbers, and get the answer with complete step-by-step working

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Basic %
X% of Y
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What % is
X of Y
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% Change
Old → New
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Reverse %
Find original
⬆️
Increase by
Add X%
⬇️
Decrease by
Subtract X%
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Profit Margin
Cost → Sale
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GST / Tax
Add or remove
💯 Find X% of a number
%
of
of
is
%
%
%
%
💯 RESULT
Formula applied
Result Summary
More Useful Results
Visual Breakdown
Step-by-Step Working
    Share This Result

    Why This Percentage Calculator Is Better Than a Basic % Tool

    Eight calculation modes, smart insights, full working shown — not just an answer box

    8 Types. Full Working. Real-World Context.
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    Smart Insights
    Every result includes a "What This Means" interpretation — practical context, real-world comparisons, and a nudge toward the next useful calculation for your situation.
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    8 Calculation Modes
    Basic %, What % is X of Y, % Change, Reverse %, Increase by %, Decrease by %, Profit Margin, GST/Tax — all eight types with dedicated input panels and correct formulas.
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    Full Step-by-Step Working
    Every calculation shows the exact formula used and each arithmetic step — not just the final answer. Ideal for students, verification, and understanding which formula applies.
    Live Calculation
    Results update as you type with no button press needed. Quick % chips (5%, 10%, 18%, 25%, 50%) fill common values instantly — perfect for GST, tip, and discount scenarios.
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    Visual Breakdown Bars
    Every result includes a proportional bar chart showing the relationship between the numbers — making abstract ratios immediately visible and intuitive.
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    100% Private
    All calculations run entirely in your browser. No number you enter is ever sent to a server. Works offline once the page loads. No accounts, no tracking.

    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 Universal Language for Proportions

    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.

    ⚠️ Common confusion: % vs percentage points. If inflation rises from 4% to 6%, it increased by 2 percentage points but by 50% (because 6 is 50% more than 4). Politicians and media often use these interchangeably — but they mean very different things. Always check which one is being cited when reading financial or economic news.

    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.

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    Basic Percentage
    X% of Y = (X/100) × Y. The most common use: 18% GST on ₹10,000 = (18/100) × 10,000 = ₹1,800. Or: 30% off ₹5,000 = ₹1,500 discount.
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    Percentage Change
    % Change = ((New − Old) / Old) × 100. Positive = increase. Negative = decrease. Used for salary hikes, market returns, price changes, score improvements.
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    Reverse Percentage
    Find the original value when you know the result after applying a percentage. E.g., a price after 20% discount is ₹800 — what was the original? Original = 800 / (1 − 0.20) = ₹1,000.
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    GST / Tax Calculation
    Adding GST: Price with GST = Amount × (1 + Rate/100). Removing GST from inclusive price: Original = GST-inclusive price / (1 + Rate/100). Critical for invoicing and reconciliation.

    All Percentage Formulas — Reference Table

    Every percentage formula you'll ever need, with example, use case and direction of calculation

    8 Types of Percentage Calculations
    TypeFormulaExampleUsed For
    X% of Y Most commonResult = (X/100) × Y15% of 200 = 30Discount, tax, tip, interest
    What % is X of Y% = (X/Y) × 10030 of 150 = 20%Score, market share, completion
    % Increase / Decrease% = ((New−Old)/Old) × 100(1200−1000)/1000×100 = +20%Salary hike, price change, returns
    Reverse PercentageOriginal = Value / (P/100)60 is 40% of 150Find original before discount/tax
    Increase Value by X%New = Old × (1 + X/100)1000 + 15% = 1150Hike, markup, compound growth
    Decrease Value by X%New = Old × (1 − X/100)5000 − 20% = 4000Discount, depreciation, loss
    Profit MarginMargin% = ((Sale−Cost)/Sale) × 100
    Markup% = ((Sale−Cost)/Cost) × 100
    Cost 800, Sale 1200 → Margin 33.3%Business pricing, retail, gross margin
    GST / TaxWith GST: Amount × (1 + Rate/100)
    Remove GST: Incl / (1 + Rate/100)
    ₹10,000 + 18% = ₹11,800Invoicing, reconciliation, pricing
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    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 pricing
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    Exam 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.

    Education
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    Salary 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 / Finance
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    GST 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.

    Taxation
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    Investment 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.

    Investing
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    Reverse % — 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 skill

    How This Calculator Works

    Step-by-step: how each of the 8 calculation modes processes your inputs and generates the full working

    From Raw Numbers to Full Breakdown
    • 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.

    • 3
      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.

    • 4
      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.

    • 5
      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.

    All formulas used in this calculator:
    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

    Percentages Are Full of Surprises
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    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.

    Common Percentage Mistakes That Lead to Wrong Answers Every Time

    The exact errors that produce incorrect results in shopping, finance, business, and everyday calculation

    Wrong Formulas for the Right Intentions
    Adding the Discount Back to the Sale Price to Find the Original
    If an item costs ₹840 after a 30% discount, the most common error is calculating ₹840 + 30% = ₹1,092 as the original price. This is wrong. 30% of ₹840 is not the same as 30% of the original price — they have different bases. The correct method: ₹840 ÷ (1 − 0.30) = ₹840 ÷ 0.70 = ₹1,200. Use the Reverse % mode to avoid this error. It catches thousands of people in the same trap every day across every country.
    Subtracting a Percentage to Remove GST from an Inclusive Price
    A software licence costs ₹11,800 inclusive of 18% GST. The wrong method: ₹11,800 − 18% = ₹9,676 (this is actually 82% of the inclusive price, not the base). The correct method: ₹11,800 ÷ 1.18 = ₹10,000. The GST is 18% of the base price, not of the GST-inclusive price. This distinction costs small business owners thousands in incorrect invoicing and tax reporting every year.
    Adding Consecutive Percentage Discounts Together
    "20% off, then an extra 10% off" sounds like 30% off. It is 28% off. First: ₹1,000 × 0.80 = ₹800. Then: ₹800 × 0.90 = ₹720. Total: ₹280 off, not ₹300. Formula: Combined effect = 1 − (1 − d₁)(1 − d₂). Retailers deliberately stack discounts this way because "20% + 10%" sounds more generous than "28% off." Similarly, a 50% loss followed by a 50% gain = ₹75, not ₹100 back. Percentages applied sequentially compound; they do not simply add.
    Confusing Margin with Markup
    A product costs ₹600 and sells for ₹1,000. The markup is 66.7% (profit ÷ cost). The margin is 40% (profit ÷ selling price). Both are correct descriptions of the same transaction — but they are not interchangeable. A supplier who says "we work on 40% margin" and a buyer who hears "40% markup" will negotiate to completely different prices. In retail, margin is standard. In manufacturing and wholesale, markup is more common. Always clarify which is meant before pricing or budgeting.
    Using the Wrong Base for Percentage Change
    A salary goes from ₹40,000 to ₹50,000. The percentage increase is (50,000 − 40,000) ÷ 40,000 × 100 = 25%, using the original as the base. But if the same salary drops from ₹50,000 back to ₹40,000, the decrease is (50,000 − 40,000) ÷ 50,000 × 100 = 20%, using the new original as base. A 25% increase is not reversed by a 25% decrease — it requires a 20% decrease. Always identify the correct base (the starting value) before computing percentage change.
    The Right Approach: Identify the Question Type First
    Before calculating, name the question: (1) Basic % — "What is X% of Y?" → (X÷100) × Y. (2) What % is X of Y? → (X÷Y) × 100. (3) % Change → (New−Old)÷Old × 100. (4) Reverse % → Final ÷ (1 ± Rate). (5) Increase/Decrease by % → Value × (1 ± Rate). (6) Margin → Profit ÷ Sale. (7) GST add/remove → Multiply or divide by (1 + Rate). Selecting the right formula before entering numbers eliminates the vast majority of percentage errors.
    Verified Tool — KeeHelper by Keeroot Solutions
    About This Percentage Calculator
    This calculator is built and maintained by KeeHelper, a product of Keeroot Solutions. All eight percentage formulas follow standard mathematical definitions as used in NCERT mathematics (Class 7–10), CBSE and ICSE syllabi, and internationally accepted business mathematics. GST slabs (5%, 12%, 18%, 28%) are as defined by India's Central Board of Indirect Taxes and Customs (CBIC). Profit margin formula uses the standard gross margin definition (Profit ÷ Revenue). All calculations run entirely in your browser — no input is ever transmitted to a server.
    NCERT Math Standards CBIC GST Slabs Standard Business Math 8 Calculation Modes Client-Side Only Free Forever
    ⚠️ Disclaimer: This tool is for educational and general-purpose use. GST rates shown are for reference only — actual applicable rates vary by goods/service category and change periodically. For tax compliance, invoicing, and financial reporting, always verify the current applicable rate with a qualified CA or tax professional and the official CBIC portal.

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    Frequently Asked Questions

    Common questions about percentage calculations, reverse percentage, GST, margins and percentage change

    What is the difference between percentage change and percentage points?
    Percentage points measure the arithmetic difference between two percentages. Percentage change measures how much one percentage changed relative to its starting value. If a tax rate goes from 10% to 15%, it increased by 5 percentage points — but by 50% (since 15 is 50% more than 10). Financial news and political reporting often use these interchangeably, which causes significant misunderstanding. When in doubt, use percentage change (relative) for measuring growth or returns, and percentage points for measuring shifts in rates or proportions.
    How do I find the original price before a discount was applied?
    Use the reverse percentage formula: Original = Final Price / (1 − Discount%/100). For example, if a product costs ₹840 after a 30% discount, the original price = 840 / (1 − 0.30) = 840 / 0.70 = ₹1,200. A very common mistake is to add 30% to ₹840 (getting ₹1,092) — this is wrong because 30% of the discounted price is not the same as 30% of the original price. Always divide by (1 − rate) to reverse a percentage reduction.
    What is the difference between profit margin and markup?
    Margin and markup both describe the relationship between cost and selling price, but their denominators differ. Profit Margin = (Sale − Cost) / Sale × 100 — expressed as a percentage of the selling price. Markup = (Sale − Cost) / Cost × 100 — expressed as a percentage of the cost price. On a product costing ₹800 and selling for ₹1,200: Margin = 400/1200 = 33.3%. Markup = 400/800 = 50%. Retail typically uses margin; manufacturing often uses markup. Confusing them leads to systematic mis-pricing.
    How do I add and remove GST correctly?
    Adding GST: Price with GST = Amount × (1 + Rate/100). For 18% GST on ₹10,000: 10,000 × 1.18 = ₹11,800. GST amount = ₹1,800. Removing GST from a GST-inclusive price: Original = Inclusive Price / (1 + Rate/100). For a ₹11,800 GST-inclusive price: 11,800 / 1.18 = ₹10,000 original; GST = ₹1,800. The common wrong method — subtracting 18% from ₹11,800 = ₹9,676 — is incorrect because 18% of the inclusive price is not the same as the GST that was added.
    Why doesn't a 50% loss and 50% gain cancel out?
    Because percentage changes are calculated on different base values. A 50% loss on ₹1,000 leaves you with ₹500. A 50% gain on ₹500 brings you to ₹750 — not back to ₹1,000. To recover from an X% loss, you need a gain of X/(1−X) × 100%. To recover a 50% loss: 50/(1−0.5) × 100% = 100% gain required. To recover a 90% loss: 90/0.10 × 100% = 900% gain required. This asymmetry is why capital preservation is so important in investing.
    Is this calculator private? Is any data stored?
    Yes, completely private. All calculations happen entirely in your browser using JavaScript — no number you enter is ever sent to a server, stored in a database, or logged anywhere. This page works fully offline once loaded. Your inputs disappear when you close or refresh the tab. There are no accounts, no sign-ups and no data collection of any kind.