Percentages are the universal language of comparison. Whether you're checking a discount, sizing up a salary hike, working through a tax problem, or sanity-checking a stat in the news, the answer almost always involves a percentage. This calculator handles every common percentage operation — percent of a number, percent one number is of another, percent change, percent increase, and percent decrease — with the formula shown alongside each result.
Below the calculator you'll find the three core percentage formulas, worked examples for each, a quick-reference table, and answers to the most-asked percentage questions.
What is a percentage?
A percentage is a number expressed as a fraction of 100. The symbol % stands for "per hundred" (Latin: per centum). 25% means 25 out of every 100, or one-quarter. The strength of percentages is that they're scale-independent — 25% of ₹100 and 25% of ₹100 crore both mean the same proportion.
Three forms come up over and over again in everyday life:
- Percent of a number — what's 18% of ₹2,000? (Answer: ₹360.)
- What percent one number is of another — what's 45 as a percent of 60? (Answer: 75%.)
- Percentage change — sales went from 200 to 260; what's the percent increase? (Answer: 30%.)
The three percentage formulas
Formula 1 — Find the part
Use this when you know the percent and the whole. Example: 15% of 200 = (15 ÷ 100) × 200 = 30.
Formula 2 — Find the percent
Use this when you know both numbers and want to express one as a percentage of the other. Example: 27 out of 60 students passed → (27 ÷ 60) × 100 = 45% pass rate.
Formula 3 — Find the whole
Use this when you know the percent and the part, and want the original total. Example: ₹300 is 20% of what? → 300 ÷ 0.20 = ₹1,500.
The percentage change formula
- Positive result → percent increase.
- Negative result → percent decrease.
- Absolute value bars ensure correct handling when the old value is negative.
Worked examples for every common case
Case 1 — Discount on a purchase
A shirt is marked ₹2,400 with a 25% discount. How much do you pay?
- Discount = 25% × 2,400 = ₹600
- Final price = 2,400 − 600 = ₹1,800
- Shortcut: 2,400 × (1 − 0.25) = 2,400 × 0.75 = ₹1,800
Case 2 — Marks and exam score
You scored 71 out of 90 in a maths test. What's your percentage?
- (71 ÷ 90) × 100 = 78.89%
Case 3 — Tip on a restaurant bill
The bill is $48 and you want to leave an 18% tip.
- Tip = 18% × 48 = (0.18) × 48 = $8.64
- Total = 48 + 8.64 = $56.64
Case 4 — Salary hike
Your CTC rose from ₹6,00,000 to ₹6,84,000. What percent increase?
- Change = 6,84,000 − 6,00,000 = 84,000
- (84,000 ÷ 6,00,000) × 100 = 14% hike
Case 5 — Original price from a sale
A product is listed at ₹1,275 after a 15% discount. What was the original price?
- Original = 1,275 ÷ (1 − 0.15) = 1,275 ÷ 0.85 = ₹1,500
Case 6 — Tax-inclusive vs exclusive
A bill shows ₹1,180 with 18% GST included. What was the pre-tax amount?
- Pre-tax = 1,180 ÷ 1.18 = ₹1,000
- GST portion = 1,180 − 1,000 = ₹180
How to use this calculator
- Pick the type of calculation from the tabs or input layout — "percent of a number," "what percent is X of Y," or "percent change."
- Enter your numbers into the two inputs.
- Read the result along with the formula the calculator used, so you can replicate it manually if needed.
Quick reference table
| Percent | Decimal | Fraction | 10% of 200 | This % of 1,000 |
|---|---|---|---|---|
| 5% | 0.05 | 1/20 | 10 | 50 |
| 10% | 0.10 | 1/10 | 20 | 100 |
| 12.5% | 0.125 | 1/8 | 25 | 125 |
| 20% | 0.20 | 1/5 | 40 | 200 |
| 25% | 0.25 | 1/4 | 50 | 250 |
| 33.33% | 0.3333 | 1/3 | 66.67 | 333.33 |
| 50% | 0.50 | 1/2 | 100 | 500 |
| 66.67% | 0.6667 | 2/3 | 133.33 | 666.67 |
| 75% | 0.75 | 3/4 | 150 | 750 |
| 100% | 1.00 | 1/1 | 200 | 1,000 |
| 150% | 1.50 | 3/2 | 300 | 1,500 |
| 200% | 2.00 | 2/1 | 400 | 2,000 |
Mental percentage shortcuts
- 10% of anything — move the decimal point one place left. 10% of 248 = 24.8.
- 5% — half of 10%. 5% of 248 = 12.4.
- 1% — move the decimal two places left. 1% of 248 = 2.48.
- 15% (common tip) — 10% + 5%. 15% of 80 = 8 + 4 = 12.
- 20% — divide by 5. 20% of 175 = 35.
- 25% — divide by 4. 25% of 480 = 120.
- X% of Y = Y% of X. 18% of 50 is the same as 50% of 18, which is just 9 — much easier.
Where percentages show up in daily life
- Discounts and sales. Sticker price × (1 − discount %) = sale price.
- Taxes (GST, sales tax, VAT). Pre-tax amount × (1 + tax %) = total bill.
- Tips at restaurants. Bill × tip % = tip amount. Standard rates: 10% in India, 15–20% in the US.
- Interest rates and loans. Annual rate ÷ 12 gives the monthly rate used in EMI calculations.
- Investment returns. See our CAGR Calculator for annualized returns and SIP Calculator for compounding.
- Grades and exam scores. Marks scored ÷ total × 100.
- Statistics in news and reports. Confidence intervals, vote shares, opinion poll margins.
- Health metrics. Body fat %, hydration %, composition charts — see Body Fat Calculator.
Percentage vs percentage points
One of the most frequently confused distinctions in finance and news media:
- Percentage points measure the arithmetic difference between two percentages. A repo rate moving from 6.50% to 6.25% is a 0.25-percentage-point cut.
- Percentage change measures the relative difference. The same move is a 3.85% percentage decrease (0.25 ÷ 6.50 × 100).
"Rates fell 25 basis points" means 0.25 percentage points (1 basis point = 0.01 percentage point). See our Basis Point Calculator for the precise relationship.
Common percentage mistakes
- Adding successive percentages. 10% + 10% ≠ 20% on a compounding base. Multiply (1.10 × 1.10 = 1.21 → 21%) instead.
- Reversing an increase and decrease. A 25% increase followed by a 25% decrease does not return to the original — it gives 93.75% of the original.
- Using the wrong denominator. For percentage change, divide by the old value, not the new one.
- Mixing markup and margin. A 50% markup on a ₹100 cost gives a ₹150 selling price; the margin (profit ÷ selling price) is only 33.3%.
- Confusing percentages with percentage points. See the previous section.
- Dividing percentages directly. "50% ÷ 25% = 2" is mathematically correct but rarely the answer you want in everyday problems. Convert to a relative comparison instead.
Tips for working with percentages
- Always state the base. "Up 25%" is ambiguous without knowing the reference number.
- Round only at the end. Mid-calculation rounding compounds error.
- Reverse-check. Apply the result back to the base and see if it matches.
- For long-term growth, use CAGR, not simple percentage. Year-on-year increases compound — see CAGR Calculator.
- Be explicit about points vs percent. Especially in financial communication where the difference can mean lakhs of rupees over a long horizon.
Related calculators
- Percentage Increase Calculator — focused tool for upward changes.
- Percentage Decrease Calculator — for declines.
- Percentage Difference Calculator — comparing two values without a clear before/after.
- Percentage Change Calculator — handles both increase and decrease.
- Percent to Decimal Converter.
- Decimal to Percent Converter.
- Fraction to Percent Calculator.
- CAGR Calculator — for annualized long-term growth.
- Basis Point Calculator — finance-specific percentage units.
The bottom line
Percentages collapse the complexity of "ratios over a base" into a single number anyone can interpret. Master the three core formulas, watch out for the compounding trap and the percentage-points distinction, and you'll handle every percentage problem you encounter — from a restaurant tip to a loan EMI to a stock market return.