Percentage Calculator
Calculate percentages in three modes: percentage of a number, what percent, and percentage change.
About the Percentage Calculator
This free percentage calculator solves the three most common percentage problems in one place: finding a percentage of a number, working out what percent one number is of another, and measuring the percentage change between two values. Enter your numbers and press Calculate to get the answer together with the exact formula used, so the tool doubles as a way to check homework, discounts, and business figures.
What is a Percentage?
A percentage is a number or ratio expressed as a fraction of 100, denoted by the symbol %. The word percent literally means "per hundred," so 45% is the same as 45/100 or the decimal 0.45. Because every percentage uses the same base of 100, they make it easy to compare values of very different sizes, which is why they appear everywhere: discounts, sales tax, interest rates, test scores, and tips.
How to Use
Select the tab that matches your problem, fill in the two fields, and press Calculate:
- What is X% of Y? finds the part, such as a discount amount or a tip.
- X is what % of Y? finds the rate, such as a test score or a market share.
- % Change finds the percentage increase or decrease between two values.
Every result box shows the formula with your numbers plugged in, so you can see exactly how the answer was derived.
The Three Core Percentage Problems
1. What is X% of Y?
Formula: Result = (X ÷ 100) × Y
- X — the percentage rate you want to apply
- Y — the whole, the number you are taking a percentage of
- Result — the part of Y equal to X percent
Worked example: What is 20% of 150? Convert 20% to a decimal (20 ÷ 100 = 0.2), then multiply by the whole: 0.2 × 150 = 30. So 20% of 150 is 30.
2. X is What Percent of Y?
Formula: Percentage = (X ÷ Y) × 100
- X — the part
- Y — the whole (must not be zero)
- Percentage — X expressed as a percent of Y
Worked example: 45 is what percent of 180? Divide the part by the whole: 45 ÷ 180 = 0.25. Then multiply by 100: 0.25 × 100 = 25%. So 45 is 25% of 180.
3. Percentage Increase and Decrease
Formula: Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100
- Original Value — the starting amount (must not be zero)
- New Value — the ending amount
- Percentage Change — positive for an increase, negative for a decrease
Worked example (increase): A price rises from $80 to $92. The change is ((92 − 80) ÷ 80) × 100 = (12 ÷ 80) × 100 = +15%. Worked example (decrease): A monthly bill drops from $250 to $200: ((200 − 250) ÷ 250) × 100 = (−50 ÷ 250) × 100 = −20%, a 20% decrease.
Percentage Difference vs. Percentage Change
These two measures sound alike but answer different questions. Percentage change is directional: it compares a new value to a specific original value, so the order of the numbers matters. Percentage difference is symmetric: it compares two values without treating either one as the starting point, by dividing the absolute difference by the average of the two values.
Formula: Percentage Difference = |A − B| ÷ ((A + B) ÷ 2) × 100
For example, the percentage difference between 80 and 100 is |80 − 100| ÷ 90 × 100 = 20 ÷ 90 × 100 ≈ 22.22%. Notice that this is not the same as the percentage change from 80 to 100, which is (20 ÷ 80) × 100 = 25%. Use percentage change for growth over time and percentage difference when comparing two independent measurements, such as the scores of two teams.
Converting Between Decimals, Fractions, and Percentages
Each form expresses the same proportion, and converting between them takes one step:
- Decimal → percentage: multiply by 100 (0.35 becomes 35%).
- Percentage → decimal: divide by 100 (7.5% becomes 0.075).
- Fraction → percentage: divide the numerator by the denominator, then multiply by 100 (5/8 = 0.625 = 62.5%).
- Percentage → fraction: write the percentage over 100 and simplify (85% = 85/100 = 17/20).
The most common conversions:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333 (repeating) | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 3/10 | 0.3 | 30% |
| 2/5 | 0.4 | 40% |
| 1/8 | 0.125 | 12.5% |
| 5/8 | 0.625 | 62.5% |
| 3/4 | 0.75 | 75% |
| 9/10 | 0.9 | 90% |
Everyday Uses of Percentages
Discounts and Sales
A jacket priced at $64 is marked 25% off. The discount is 25% of 64 = 0.25 × 64 = $16, so you pay $64 − $16 = $48.
Restaurant Tips
An 18% tip on a $45 meal is 0.18 × 45 = $8.10, bringing the total to $53.10.
Sales Tax
A 7% sales tax on an $85 purchase adds 0.07 × 85 = $5.95, for a checkout total of $90.95.
Grades and Test Scores
Scoring 42 out of 50 on a test works out to (42 ÷ 50) × 100 = 84%.
Frequently Asked Questions
How do I calculate percentage change?
Subtract the original value from the new value, divide by the original value, then multiply by 100: ((New Value − Original Value) ÷ Original Value) × 100. A positive result is an increase and a negative result is a decrease. For example, going from 80 to 92 is ((92 − 80) ÷ 80) × 100 = 15%, a 15% increase.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, to find what percent 45 is of 180, compute (45 ÷ 180) × 100 = 25%, so 45 is 25% of 180. The second tab above does this for you.
Can I calculate discounts with this tool?
Yes. In the first tab, enter the discount percentage as X and the original price as Y to get the discount amount, then subtract it from the price. For example, 25% of $64 is $16, so the sale price is $48.
What is the difference between percentage difference and percentage change?
Percentage change compares a new value to a specific original value, so the order matters. Percentage difference is symmetric: it divides the absolute difference of two values by their average, so neither value is treated as the starting point.
How do I convert a percentage to a decimal or a fraction?
Divide by 100 to get a decimal (7.5% = 0.075), or write the percentage over 100 and simplify to get a fraction (62.5% = 62.5/100 = 5/8). To convert a decimal back to a percentage, multiply by 100.
Are the results accurate?
Yes. All calculations run locally in your browser using standard JavaScript math operations for full precision, and every result is shown with the exact formula used.
Is this calculator free?
Yes, BestCalc's percentage calculator is completely free with no ads or registration required.