"What is X% of Y" and "X is what % of Y" are opposite calculations — using the wrong mode gives a technically-valid but completely different answer to the question you meant to ask.
For a discount or tax, use the dedicated tool
This calculator handles the underlying percentage math, but the Discount Calculator and GST/VAT Calculators add the comparison tables and business context those specific tasks need.
Percentage change has a direction
A positive result means an increase, negative means a decrease — don't drop the sign when reporting a percentage change figure.
Select calculation type — What is X% of Y? X is what % of Y? What is the % change from X to Y?
Enter your values — fill in the known numbers for your chosen calculation type.
Read the result — the answer appears instantly with the calculation shown.
Use multiple modes — run different types of percentage calculations without clearing — each mode is independent.
Copy the result — use the copy button for use in documents, spreadsheets, or messages.
📊 Three essential percentage calculations: 1) 'What is 15% of 200?' = 30 (tip calculation, discount amount). 2) '45 is what % of 180?' = 25% (test score, market share). 3) 'What is the % change from 80 to 100?' = +25% (price increase, growth rate). These three types cover 95% of real-world percentage needs.
Understanding Percentages
📊 Percentage Basics
Percent means 'per hundred' (Latin per centum). 25% = 25/100 = 0.25. To find X% of Y: multiply Y × (X/100). 15% of 200 = 200 × 0.15 = 30. To convert fraction to %: divide numerator by denominator, multiply by 100. 3/4 = 0.75 = 75%. Percentages express parts of a whole on a 0–100 scale.
📈 Percentage Change
(New − Old) / Old × 100. Positive = increase, negative = decrease. Price from $80 to $100: (100−80)/80 × 100 = 25% increase. From $100 to $80: (80−100)/100 × 100 = −20% decrease. Note asymmetry: a 25% increase followed by a 20% decrease does NOT return to start — it ends at $96.
🔢 Percentage Points vs Percent
Critical distinction: interest rate rising from 2% to 3% is a 1 percentage point increase but a 50% relative increase. 'Interest rates rose 1%' is ambiguous — does it mean 1 percentage point (3%) or 1% of 2% (2.02%)? Always specify 'percentage points' when discussing absolute changes to avoid misinterpretation.
💰 Tip Calculation
Shortcut for 20%: double the price, move decimal left one place. $45.00 → $90 → $9.00 tip. For 15%: take 10% (move decimal) + half of that. $45 → $4.50 + $2.25 = $6.75 tip. For 18%: 10% + 8% (which is 10% minus 2%). These mental shortcuts eliminate the need for a calculator in restaurants.
📊 Percentage in Statistics
Percentages describe proportions in data: market share (Apple has 57% of US smartphone market), poll results (64% approve), growth rates (GDP grew 3.2%). Always ask: percentage of what? A '20% increase in crime' means nothing without knowing the base rate and what counts as 'crime.' Context and base numbers are as important as the percentage itself.
🔄 Successive Percentages
Two percentage changes are not simply added. A 20% increase followed by a 20% decrease: 100 → 120 → 96. Net result: −4%, not 0%. This mathematical fact has important implications for investment returns — a 50% loss requires a 100% gain to recover. Percentage changes compound multiplicatively, not additively.
Percentages in Daily Life
Tax and discount calculations
Percentage calculations are essential for financial decisions. Sales tax: multiply price by (1 + tax rate). $50 item with 8% tax: $50 × 1.08 = $54. Discount: multiply price by (1 − discount rate). 30% off $80: $80 × 0.70 = $56. Comparing discounts: 25% off a $120 item ($90) vs 20% off a $100 item ($80) — the lower discount is better value. Always calculate final prices rather than comparing discount percentages when the original prices differ.
Interest and investment percentages
Annual Percentage Rate (APR) for loans and credit cards. Annual Percentage Yield (APY) for savings accounts — includes compound interest effect. A credit card with 20% APR actually costs more than 20% annually when compounded monthly (APY = 21.9%). Mortgage rates are quoted as APR but amortised monthly. Investment returns quoted as annualised percentages for comparison — a 5-year investment showing 50% total return is approximately 8.45% annualised, not 10% (50%/5 years).
Percentage in data analysis
Percentages make different-scale data comparable. A department with 10 errors out of 100 transactions (10% error rate) has worse performance than one with 50 errors out of 1,000 transactions (5% error rate) — the absolute number is higher but the rate is better. Converting to percentages enables fair comparison. However, be aware of small sample size issues: a 100% error rate from 1 out of 1 transactions is statistically meaningless compared to 5% from 1,000 transactions.
📊 Percentage mental math shortcuts: 1% of any number: move decimal 2 places left (1% of 450 = 4.50). 10%: move decimal 1 place left (10% of 450 = 45). 5%: half of 10% (5% of 450 = 22.5). 25%: divide by 4 (25% of 450 = 112.5). 50%: divide by 2 (50% of 450 = 225). 75%: three-quarters = 50% + 25% (75% of 450 = 337.5). These shortcuts handle most everyday percentage calculations instantly.
Percentage Formulas
X% of Y = (X ÷ 100) × Y. X is what % of Y = (X ÷ Y) × 100. % change from X to Y = ((Y − X) ÷ |X|) × 100.
Worked example
What is 15% of 300? = (15 ÷ 100) × 300 = 45. 45 is what % of 300? = (45 ÷ 300) × 100 = 15% — the same relationship, calculated in the opposite direction.
Assumption: "X is what % of Y" and "% change" both require a non-zero denominator (Y and X respectively) — these calculations are mathematically undefined at zero, not just unusual.
Common Mistakes
Confusing percentage points with percentage change
Going from 20% to 25% is a 5 percentage-point increase, but a 25% relative increase (5 ÷ 20 × 100) — these are different numbers and mixing them up is a common source of confusion.
Using the wrong calculation mode
"X% of Y" and "X is what % of Y" answer different questions — double-check which one matches what you're actually trying to find before reading the result.
Comparing discount percentages instead of final prices
A bigger percentage off a higher original price isn't automatically the better deal — always compare the actual final price, not just the discount rate.
Averaging percentages incorrectly
The average of a 10% increase and a 10% decrease is not 0% in absolute terms — a 10% increase followed by a 10% decrease on the new value ends below the starting point.
Frequently Asked Questions
How do I find what % X is of Y?
Divide X by Y and multiply by 100. Formula: (X / Y) × 100. Example: 25 is what % of 200? = (25/200) × 100 = 12.5%