About This Tool
Percentages are one of the most practical math concepts used in daily life. From figuring out how much tip to leave at a restaurant to analyzing quarterly revenue growth, percentage calculations show up constantly. This percentage calculator handles four distinct types of percentage problems, so you always get the right answer regardless of how the question is phrased. The first mode answers "What is X% of Y?" -- useful for tips, taxes, discounts, and commissions. The second mode solves "X is what percent of Y?" -- perfect for grading, test scores, and comparing parts to wholes. The third mode calculates the percentage increase or decrease between two values, which is essential for tracking price changes, salary raises, and investment returns. The fourth mode finds the percentage difference between two values relative to their average, commonly used in scientific measurements and comparing competing products. Each mode provides a clear result along with supplementary data. The percentage change mode, for instance, also shows the absolute change and the multiplier factor. All calculations update in real time as you adjust the inputs, and your data stays private -- nothing is stored or shared.
How to Use This Percentage Calculator
Select the calculation type that matches your question using the four buttons at the top of the tool. Each mode provides tailored input fields:
- "What is X% of Y?" -- Enter the percentage and the base number. Example: What is 15% of 85? Enter 15 and 85 to get 12.75.
- "X is what % of Y?" -- Enter the part and the whole. Example: 35 is what % of 140? Enter 35 and 140 to get 25%.
- "% Increase / Decrease" -- Enter the original value and the new value. Example: A price went from $60 to $75. Enter 60 and 75 to see a 25% increase.
- "% Difference" -- Enter two values to compare. Example: Compare test scores of 72 and 88. The tool shows the relative percentage difference based on the average of both numbers.
Results appear instantly below the inputs. Each result includes a primary answer and relevant supplementary values like the remaining portion, absolute difference, or multiplier.
Understanding the Four Percentage Formulas
Each calculation mode uses a specific mathematical formula:
1. Finding a Percentage of a Number: Multiply the base number by the percentage expressed as a decimal. For instance, 20% of 150 equals 150 multiplied by 0.20, which is 30.
2. Finding What Percent One Number Is of Another: Divide the part by the whole and multiply by 100. If 45 students passed out of 60 total, that is (45 / 60) * 100 = 75%.
3. Percentage Change (Increase or Decrease): Subtract the original value from the new value, divide by the absolute value of the original, and multiply by 100. A stock going from $40 to $52 is ((52 - 40) / 40) * 100 = 30% increase.
4. Percentage Difference: Find the absolute difference between the two values, divide by their average, and multiply by 100. Comparing 200 and 250: |200 - 250| / ((200 + 250) / 2) * 100 = 22.2%. This formula treats neither value as the "original" and is symmetric.
Percentage Change vs. Percentage Difference
These two calculations answer fundamentally different questions, and mixing them up is a common source of errors.
Percentage change measures how much a value has grown or shrunk relative to its starting point. It requires a clear "before" and "after." The order matters: going from 50 to 100 is a 100% increase, but going from 100 to 50 is a 50% decrease.
Percentage difference measures the relative gap between two values when neither is inherently the "starting" value. It is always positive and symmetric -- comparing 50 to 100 gives the same percentage difference as comparing 100 to 50. Scientists use it to compare two measurements. Shoppers use it to compare prices between two stores.
Rule of thumb: use percentage change when you have a clear time sequence (before/after). Use percentage difference when you are comparing two independent measurements side by side.
Real-World Applications
Percentages appear across nearly every field and profession:
- Shopping and Sales: A store marks an item 30% off its $89.99 price tag. Using "What is 30% of $89.99?" gives $27.00, meaning you pay $63.00.
- Grades and Testing: You scored 42 out of 50 on a test. Using "42 is what % of 50?" gives 84%.
- Finance and Investing: Your portfolio grew from $10,000 to $12,500 over a year. The percentage change is 25%.
- Health and Fitness: You weighed 185 lbs and now weigh 172 lbs. The percentage change is -7.03%, meaning you lost about 7% of your body weight.
- Business Reporting: Revenue was $1.2M last quarter and $1.38M this quarter. The percentage increase is 15%.
- Cooking: A recipe calls for 200g of flour but you want to make 75% of it. 75% of 200g is 150g.
Common Percentage Mistakes to Avoid
Even experienced professionals make percentage errors. Here are the most frequent pitfalls:
- Adding and subtracting percentages directly: A 50% increase followed by a 50% decrease does NOT return you to the original value. $100 + 50% = $150, then $150 - 50% = $75. You lost $25.
- Confusing percentage points with percentages: If an interest rate goes from 2% to 3%, it increased by 1 percentage point but by 50% in relative terms.
- Reversing the direction of change: Going from 200 to 300 is a 50% increase, but going from 300 to 200 is a 33.3% decrease. The base number matters.
- Using the wrong denominator: Margin uses selling price as the base; markup uses cost as the base. Same profit, different percentages.
Frequently Asked Questions
How do I calculate a percentage of a number without a calculator?
Break the percentage into easier parts you can do mentally:
- 10% of any number: Move the decimal point one place left. 10% of 350 = 35.
- 5%: Find 10%, then halve it. 5% of 350 = 17.50.
- 1%: Move the decimal two places left. 1% of 350 = 3.50.
- 25%: Divide by 4. 25% of 200 = 50.
- Any other percentage: Combine the above. 15% = 10% + 5%. So 15% of 350 = 35 + 17.50 = 52.50.
What is the difference between percentage change and percentage difference?
Percentage change has a direction -- it measures growth or decline from a specific starting value. It can be positive (increase) or negative (decrease). Percentage difference compares two values without assigning either one as the baseline. It uses the average of both values as the denominator, is always positive, and gives the same result regardless of which value comes first. Use change for time-based comparisons (last month vs. this month). Use difference for side-by-side comparisons (Brand A vs. Brand B).
Why does a 50% increase followed by a 50% decrease not equal the original?
Because the two percentages are calculated from different base numbers. Start with $100. A 50% increase adds $50 (50% of $100), making it $150. A 50% decrease then removes $75 (50% of $150), leaving $75. The second percentage applies to the already-increased amount, not the original. To reverse a 50% increase, you need a 33.3% decrease: $150 minus 33.3% of $150 = $150 - $50 = $100.
How do I convert a fraction to a percentage?
Divide the numerator (top number) by the denominator (bottom number), then multiply by 100. For example:
- 3/4 = 0.75 * 100 = 75%
- 7/8 = 0.875 * 100 = 87.5%
- 1/3 = 0.3333 * 100 = 33.33%
- 2/5 = 0.40 * 100 = 40%
You can also use the "X is what % of Y?" mode on this calculator. Enter the numerator as the part and the denominator as the whole to get the percentage instantly.
What does "percentage points" mean versus "percent"?
A "percentage point" is the arithmetic difference between two percentages. A "percent" refers to the relative change. If unemployment drops from 8% to 6%, it fell by 2 percentage points but decreased by 25% in relative terms (because 2 is 25% of 8). Financial news often uses percentage points when discussing interest rates, tax rates, and approval ratings. Mixing up the two leads to significant misinterpretation of data.
How do I calculate percentage increase for a raise or salary bump?
Use the "% Increase / Decrease" mode. Enter your current salary as the "Original Value" and your new salary as the "New Value." The tool will show the exact percentage increase. For example, going from $55,000 to $60,000 is an increase of approximately 9.09%. If you know the percentage raise and want the new salary, use "What is X% of Y?" with your current salary, then add the result to your current salary.