A percentage calculator answers the three percent questions people ask most: what is X% of a number, what percentage one number is of another, and the percentage change between two values. Percentages express a part of a whole in terms of 100, which makes quantities of very different sizes easy to compare.
Pick the question you want answered, enter your two numbers, and the calculator applies the correct formula instantly. Each result also shows the formula with your numbers plugged in, so you can see exactly how the answer was reached — useful for checking homework, tips, discounts, taxes, and statistics.
The Three Percentage Formulas
Each mode of this calculator uses one core formula:
- What is X% of Y? — Answer = (X ÷ 100) × Y. Example: 25% of 200 = 0.25 × 200 = 50.
- X is what % of Y? — Answer = (X ÷ Y) × 100. Example: 50 is what % of 200? 50 ÷ 200 = 0.25, so 25%.
- % change from X to Y — Answer = ((Y − X) ÷ |X|) × 100. Example: from 200 to 250 is (50 ÷ 200) × 100 = a 25% increase.
All three come from the same idea: a percent is simply a fraction with 100 as the denominator, so 25% means 25/100 or 0.25. Converting between the percent form and the decimal form is what makes each calculation work.
Where Each Formula Shows Up in Real Life
Knowing which formula to reach for is half the battle:
- Percent of a number: sales tax (8% of a $60 purchase), tips (20% of a restaurant bill), commissions, and interest for one period.
- What percent X is of Y: test scores (42 correct out of 50 = 84%), completion rates, market share, and budget breakdowns.
- Percentage change: price increases, salary raises, stock returns, and population growth.
A quick mental shortcut: 10% of any number is that number with the decimal point moved one place left, so 10% of 84 is 8.4. From there, 5% is half of that (4.2) and 20% is double (16.8) — enough to sanity-check most everyday calculations.
Worked Example: A Price Increase
Suppose a gym membership rises from $48 to $60 per month. Which formula applies? You are comparing an old value to a new value, so use percentage change.
Step 1: Find the difference: 60 − 48 = 12. Step 2: Divide by the original value: 12 ÷ 48 = 0.25. Step 3: Multiply by 100: 0.25 × 100 = 25%.
The membership increased by 25%. Now reverse-check it with the percent-of formula: 25% of 48 is (25 ÷ 100) × 48 = 12, and 48 + 12 = 60. Both formulas agree, which is a reliable way to verify any percentage answer.
Frequently Asked Questions
How do I calculate a percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. For example, 15% of 80 is 0.15 × 80 = 12. Equivalently, multiply the two numbers and divide by 100: (15 × 80) ÷ 100 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If you scored 42 out of 50 on a test, compute 42 ÷ 50 = 0.84, then 0.84 × 100 = 84%. The order matters: the number after "of" always goes in the denominator.
How is percentage change calculated?
Percentage change = (new value − old value) ÷ |old value| × 100. Going from 200 to 250 gives (250 − 200) ÷ 200 × 100 = 25% increase. A negative result means a decrease. The original (older) value is always the divisor.
What is the difference between percentage and percentage points?
Percentage points measure the arithmetic difference between two percentages, while percent change measures relative change. If an interest rate rises from 4% to 5%, that is 1 percentage point, but a 25% relative increase — because 1 is 25% of the original 4.
Can a percentage be greater than 100?
Yes. A value more than double the original represents a change above 100%. For example, growing from 50 to 150 is a 200% increase, and 150 is 300% of 50. Percentages over 100 simply mean the part exceeds the whole you are comparing against.