Percentage Calculator
Versatile percentage calculator handling four common calculations: (1) What is X% of Y, (2) X is what % of Y, (3) Increase X by Y%, and (4) Decrease X by Y%. Select the calculation type, enter the required values, and get instant results with formulas and explanations. Perfect for calculating discounts, tips, sales tax, interest rates, grade calculations, or any percentage-based applications. The calculator shows the mathematical formulas used and provides practical examples for common use cases. All calculations happen instantly in your browser with complete privacy—no data is stored or transmitted.
Percentage Calculator
How it works: This calculator handles four common percentage calculations: (1) What is X% of Y, (2) X is what % of Y, (3) Increase X by Y%, and (4) Decrease X by Y%. Select the calculation type, enter the required values, and get instant results with formulas and explanations. Perfect for calculating discounts, tips, sales tax, interest, or any percentage-based calculations.
What Is a Percentage Calculator?
A percentage calculator solves the three core percent problems: finding what percentage one number is of another, calculating a percentage of a number, and computing percentage change between two values. These three operations cover virtually every everyday percentage question — from figuring out a tip to calculating a salary raise to evaluating investment returns.
The word "percent" comes from the Latin per centum, meaning "per hundred." Every percentage is simply a fraction with 100 in the denominator. 25% = 25/100 = 0.25. Understanding that makes every percent calculation a multiplication or division problem.
How to Use This Percentage Calculator
- Choose the type of percentage calculation you need.
- For "X% of Y": enter the percentage and the base number to find the result.
- For "X is what % of Y": enter both numbers to find the percentage.
- For percentage change: enter the original and new values to see the increase or decrease.
- Results appear instantly with the full calculation shown.
Essential Percentage Formulas with Worked Examples
| Calculation Type | Formula | Worked Example | Answer |
|---|---|---|---|
| Find X% of Y | (X ÷ 100) × Y | What is 18% of $250? | $45.00 |
| X is what % of Y | (X ÷ Y) × 100 | 45 is what % of 250? | 18% |
| Percentage increase | ((New − Old) ÷ Old) × 100 | $50,000 → $55,000 salary | +10% |
| Percentage decrease | ((Old − New) ÷ Old) × 100 | $200 item → $160 sale price | -20% |
| Find original value | Result ÷ (X ÷ 100) | $45 is 18% of what? | $250 |
Sarah’s salary went from $50,000 to $55,000 after a promotion. The increase: ($55,000 − $50,000) ÷ $50,000 × 100 = 10%. The raise amounts to $5,000 in dollar terms — but the percentage is what matters for comparing across different salary levels.
Common Percentage Applications
- Tips: 18% of $85 bill = $15.30 tip. Quick mental shortcut: 10% of $85 = $8.50, then add 8% ($6.80) = $15.30.
- Discounts: 30% off $120 = $36 off, final price $84. Always apply percentage discounts before subtracting flat coupons.
- Tax: 8.5% sales tax on $499 item = $42.42, total $541.42.
- Investment returns: Portfolio up from $10,000 to $11,350 = 13.5% return.
- Grade calculations: 42 correct out of 50 questions = 42 ÷ 50 × 100 = 84%.
- Pay cuts / raises: A 10% pay cut on $70,000 = −$7,000. Getting a 10% raise after doesn’t restore original salary: $63,000 × 1.10 = $69,300, not $70,000.
Key Percentage Concepts to Know
- Percent vs. percentage point: If interest rates go from 4% to 6%, that’s a 2 percentage point increase, but a 50% increase in the rate itself. These are frequently confused in news reporting.
- Asymmetry of gains and losses: Losing 50% requires a 100% gain to recover. A 20% loss requires a 25% gain. This is why protecting against downside matters more than chasing upside in investing.
- Base rate matters: "20% off" means different things depending on the original price. $20 off $100 vs. $20 off $1,000 is the same dollar amount but a very different percentage savings.
- Compounding percentages: Applying 10% then 20% doesn’t equal 30%. It equals: 1.10 × 1.20 − 1 = 32% total increase.
Tips for Quick Mental Percentage Math
- 10% shortcut: Move the decimal left one place. 10% of $340 = $34. Then scale: 5% = half of $34 = $17; 20% = $68; 15% = $51.
- 1% then multiply: For any percentage, find 1% first (divide by 100), then multiply by the desired percent. 7% of $850: $8.50 × 7 = $59.50.
- Flip the numbers: X% of Y = Y% of X. 16% of 25 = 25% of 16 = 4. Often one direction is easier to compute mentally.
- Percentage increase shortcut: Multiply by (1 + rate). 15% increase on $200 = $200 × 1.15 = $230. No need to calculate $30 separately then add.
Frequently Asked Questions About Percentages
How do I calculate what percentage one number is of another?
Divide the part by the whole, then multiply by 100. Example: 30 is what percent of 120? 30 ÷ 120 = 0.25 × 100 = 25%.
What’s the formula for percentage change?
(New Value − Old Value) ÷ Old Value × 100. A positive result is an increase; negative is a decrease. Always divide by the original value, not the new one.
How do I find the original price before a percentage discount?
Divide the sale price by (1 − discount rate). If something costs $85 after 15% off: $85 ÷ 0.85 = $100 original price. Equivalently: the sale price is 85% of the original.
Are percentages the same as decimal fractions?
Yes — a percentage is a decimal multiplied by 100. 0.35 = 35%. To convert from decimal to percent, multiply by 100. To convert from percent to decimal, divide by 100.
Why does a 10% gain after a 10% loss not return to the original value?
Because the base changes. $1,000 − 10% = $900. Then $900 + 10% = $990, not $1,000. The gain is applied to a smaller base, so you need an 11.1% gain to recover from a 10% loss.
Related Calculators
- Percentage Increase Calculator — dedicated to percent change calculations
- Percentage Difference Calculator — compare two values symmetrically
- Discount Calculator — sale price and percent off calculations
- Tip Calculator — tip percentage and split bill