Percentage Calculator
Free Percentage Calculator — 6 Types of Percentage Calculations
Our free online percentage calculator solves six different types of percentage problems instantly, with step-by-step explanations and the formula used. From basic "what is 20% of 500" to reverse percentage (finding the original value before a discount), our tool covers all percentage calculations you need in daily life, business, academics, and finance.
What is Percentage?
A percentage is a number expressed as a fraction of 100. The word "percent" comes from the Latin "per centum" meaning "per hundred." Percentages are used everywhere — from calculating discounts while shopping to analysing stock market returns, from exam scores to bank interest rates. The symbol % represents "per hundred."
For example, 75% means 75 per 100, or 75/100, or 0.75. If you scored 75% on an exam with 200 marks, you got 75% × 200 = 150 marks. Percentages make it easy to compare numbers by expressing them on a common scale of 100.
The 6 Percentage Formulas Explained
1. Percentage of a Number (X% of Y)
This is the most basic percentage calculation — finding what X% of a number Y equals.
Formula: Result = (X ÷ 100) × Y
Example: What is 15% of ₹2,400? → (15 ÷ 100) × 2400 = 0.15 × 2400 = ₹360
Common uses: Calculating service charge on a bill, tip amount at a restaurant, commission on sales, interest on a loan for one period, GST amount on a product.
| % | Mental Math Trick | Example (of ₹1000) |
|---|---|---|
| 1% | Move decimal 2 places left | ₹10 |
| 5% | Divide by 20 | ₹50 |
| 10% | Move decimal 1 place left | ₹100 |
| 20% | Divide by 5 | ₹200 |
| 25% | Divide by 4 | ₹250 |
| 50% | Divide by 2 | ₹500 |
| 75% | Divide by 4, multiply by 3 | ₹750 |
2. X is What Percentage of Y?
Used when you know both values and need to find the percentage relationship between them.
Formula: Percentage = (X ÷ Y) × 100
Example: A student scored 360 marks out of 600. What percentage did they score? → (360 ÷ 600) × 100 = 0.60 × 100 = 60%
Common uses: Calculating exam percentage, market share analysis, expense as percentage of income, conversion rate in marketing, body fat percentage calculation.
3. Percentage Change (Increase/Decrease)
Measures how much a value has increased or decreased relative to its original value, expressed as a percentage.
Formula: % Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result = percentage increase. A negative result = percentage decrease.
Example: House price was ₹60 lakh, now ₹75 lakh. Change = ((75 - 60) ÷ 60) × 100 = (15 ÷ 60) × 100 = +25% increase
Common uses in India: Salary hike percentage, SIP/stock return calculation, inflation rate, property value change, discount from original price, GDP growth rate, population growth.
4. Add or Subtract a Percentage
Used to calculate the final value after adding (like GST) or subtracting (like discount) a percentage from a number.
Add: Final = N + (P% × N) = N × (1 + P/100)
Subtract: Final = N − (P% × N) = N × (1 − P/100)
Add example (GST): Product costs ₹1,000. Add 18% GST → 1000 × 1.18 = ₹1,180
Subtract example (Discount): Item MRP ₹2,000. 25% discount → 2000 × 0.75 = ₹1,500
5. Percentage Difference Between Two Values
Unlike percentage change (which has a clear starting and ending value), percentage difference treats both values equally. It is the absolute difference divided by the average, expressed as a percentage.
Formula: % Difference = (|V1 − V2| ÷ ((V1 + V2) ÷ 2)) × 100
Example: City A has 400 engineers; City B has 600. Difference = (|400 - 600| ÷ ((400 + 600) ÷ 2)) × 100 = (200 ÷ 500) × 100 = 40% difference
When to use: Comparing two measurements where neither is clearly the "original" — scientific experiments, price comparison between two products, comparing two candidates' scores.
6. Reverse Percentage (Finding Original Value)
Used when you know the final value after a percentage was applied and need to find the original value before the percentage change.
Before % increase: Original = Final ÷ (1 + P/100)
Before % decrease: Original = Final ÷ (1 − P/100)
Example (Remove GST): Invoice total including 18% GST = ₹1,180. Original price = 1180 ÷ 1.18 = ₹1,000
Example (Before discount): Sale price after 20% discount = ₹800. Original price = 800 ÷ 0.80 = ₹1,000
Common uses: Finding ex-GST price from inclusive price, finding original price before discount, finding pre-tax income from post-tax income, calculating CGPA from percentage.
Percentage Calculations for India — Practical Examples
GST Calculation
GST (Goods and Services Tax) is applied on most goods and services in India. Under GST 2.0 (from 22 September 2025) the main rates are 5% and 18%, with a special 40% rate for luxury and sin goods. The old 12% and 28% slabs were removed.
| GST Rate | On ₹1,000 | GST Amount | Total (incl. GST) |
|---|---|---|---|
| 5% | ₹1,000 | ₹50 | ₹1,050 |
| 12% | ₹1,000 | ₹120 | ₹1,120 |
| 18% | ₹1,000 | ₹180 | ₹1,180 |
| 28% | ₹1,000 | ₹280 | ₹1,280 |
Board Exam Percentage Calculation
To calculate board exam percentage: (Total marks obtained ÷ Total marks) × 100. For CBSE students, CGPA to percentage conversion: CGPA × 9.5 = percentage.
| CGPA (CBSE) | Percentage Equivalent | Grade |
|---|---|---|
| 10.0 | 95% | A1 |
| 9.0 | 85.5% | A2 |
| 8.0 | 76% | B1 |
| 7.0 | 66.5% | B2 |
| 6.0 | 57% | C1 |
Salary Hike Calculation
Annual salary increments in India typically range from 8–15% for most sectors. Here's how to calculate your new salary after a hike:
- New Salary = Current Salary × (1 + Hike% ÷ 100)
- Hike Amount = Current Salary × (Hike% ÷ 100)
- Example: ₹45,000/month with 12% hike → New = ₹45,000 × 1.12 = ₹50,400. Hike = ₹5,400
Discount and Sale Price Calculation
Sale price = Original Price × (1 − Discount% ÷ 100). Discount amount = Original Price × (Discount% ÷ 100).
| Discount | On ₹2,000 | Savings | You Pay |
|---|---|---|---|
| 10% | ₹2,000 | ₹200 | ₹1,800 |
| 20% | ₹2,000 | ₹400 | ₹1,600 |
| 30% | ₹2,000 | ₹600 | ₹1,400 |
| 50% | ₹2,000 | ₹1,000 | ₹1,000 |
Common Percentage Mistakes to Avoid
- Confusing percentage change and percentage difference: Percentage change requires a clear starting point (from 100 to 120 = 20% increase). Percentage difference treats both values equally (between 100 and 120 = 18.18% difference based on average).
- Adding/subtracting percentages incorrectly: A 20% increase followed by a 20% decrease does NOT return to the original value. 100 → +20% → 120 → -20% → 96 (not 100). This is because the second percentage is applied to a different base.
- Forgetting reverse percentage when removing GST: If an invoice shows ₹1,180 inclusive of 18% GST, the base price is NOT 1180 - 18% = 967.6. The correct calculation is 1180 ÷ 1.18 = ₹1,000.
- Mixing up percentage points and percentages: If interest rates go from 5% to 7%, that is a 2 percentage point increase, but a 40% increase in the interest rate itself ((7-5)/5 × 100 = 40%).
Percent vs Percentage Points
When a rate changes, be careful with the words you use. If a bank's interest rate rises from 6% to 8%, it has gone up by 2 percentage points – but by 33.3 percent of its original value, because 2 is a third of 6. News reports and loan offers often mix these up. Use percentage points for the simple difference between two percentages, and percent for the relative change. This calculator's % Change mode gives the relative change; subtract the two percentages yourself to get the points.
Why a 50% Loss Needs a 100% Gain
Percentage changes are not symmetrical. If an investment of ₹10,000 falls by 50%, it is worth ₹5,000. To get back to ₹10,000 it must now rise by ₹5,000 – which is 100% of ₹5,000. In the same way, a price that goes up by 20% and then down by 20% does not return to where it started: ₹100 → ₹120 → ₹96. Always apply each percentage to the current value, not the original one.
| Fall of | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 25% | 33.3% |
| 33.3% | 50% |
| 50% | 100% |
| 75% | 300% |
Converting Fractions, Decimals and Percentages
A percentage is simply a fraction out of 100. To turn a decimal into a percentage, multiply by 100 (0.375 = 37.5%). To turn a fraction into a percentage, divide the top by the bottom and multiply by 100 (3/8 = 0.375 = 37.5%). To go back, divide the percentage by 100. Knowing a few common equivalents makes mental maths much faster: 1/2 = 50%, 1/3 = 33.3%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5% and 1/10 = 10%. For exact fraction work, use our fraction calculator.
Read our guide: How to calculate percentage – formulas, marks and examples.