Percentage Calculator
Choose the percentage calculation you need. The tool shows the result, substituted formula and interpretation without combining different questions into separate pages.
Percentage formulas
- X% of Y: (X ÷ 100) × Y.
- X as a percentage of Y: (X ÷ Y) × 100.
- Percentage change: ((new − original) ÷ |original|) × 100.
- Increase by Y%: original × (1 + Y ÷ 100).
- Decrease by Y%: original × (1 − Y ÷ 100).
- Percentage difference: |X − Y| ÷ ((|X| + |Y|) ÷ 2) × 100.
Six checked examples
| Question | Calculation | Answer |
|---|---|---|
| What is 20% of 150? | (20 ÷ 100) × 150 | 30 |
| 30 is what percent of 120? | (30 ÷ 120) × 100 | 25% |
| Change from 80 to 100 | ((100 − 80) ÷ 80) × 100 | 25% increase |
| Increase 200 by 15% | 200 × 1.15 | 230 |
| Decrease 200 by 15% | 200 × 0.85 | 170 |
| Difference between 80 and 100 | 20 ÷ 90 × 100 | 22.222222% |
How to choose the correct calculation
Use “X% of Y” when a rate and base number are known. Use “X is what percent of Y” when comparing a part with a whole. Percentage change has a defined starting value and direction; percentage difference is symmetric and is appropriate when neither value is the baseline.
Limits and interpretation
A zero comparison value cannot be used as a denominator. Percentage change from zero is undefined in this calculator. A reduction above 100% can produce a negative result, which may be mathematically valid but unsuitable for quantities that cannot be negative. Results retain full numeric precision internally and are formatted to at most ten decimal places on screen.
Frequently asked questions
Are percentage change and percentage difference the same?
No. Change uses the original value as its denominator and has a direction. Difference uses the average magnitude of both values and is symmetric.
How do I add a percentage to a number?
Choose “Increase X by Y%.” The calculator multiplies the original number by 1 plus the percentage expressed as a decimal.
Can percentages be greater than 100?
Yes. For example, 150% of 40 is 60. Whether that result makes sense depends on the quantity being modeled.
Related calculators
Bowling handicap: Use the Bowling Handicap Calculator to turn a league average, base and percentage into game or series handicap and adjusted scratch scores.
- Fraction Calculator
- Ratio Calculator
- Dilution Calculator
- Probability Calculator
- Weighted Average Calculator
- Standard Deviation Calculator
- Ramp Percentage and Slope Calculator
- Time Card Calculator
- Significant Figures Calculator
Salary increase: Convert a percentage or fixed raise into hourly, paycheck and annual pay with the Pay Raise Calculator.
\n
Related financial tool: Project long-term growth with the Compound Interest Calculator.
Investment percentage: Calculate net return, return multiple and annualized performance with the ROI Calculator.
Business pricing: Calculate selling price, unit profit, margin and markup with the Margin Calculator.
Shopping discounts: Use the Discount Calculator for stacked percent-off offers, fixed coupons, tax, shipping and reverse price calculations.
Need a practical gratuity calculation? Use the Tip Calculator to calculate a tip and split the final bill evenly.
Sales tax: Use the Sales Tax Calculator to add tax, remove tax from an inclusive price, or calculate the effective tax rate.
Sports records: Use the Win Percentage Calculator for wins, losses, ties, future records and a target winning percentage. For baseball and softball batting power, use the Slugging Percentage Calculator.
Blood alcohol percentage: Estimate BAC from beverage volume, ABV, body weight and elapsed time with the safety-limited Blood Alcohol Calculator.
Pool concentration changes: Use the Pool Chemistry Calculator to convert a measured ppm increase into liquid chlorine, dry chlorine or salt and to scale a manufacturer label dose.