Percentage Calculator
The free Percentage Calculator handles the three most-common percentage calculations: "What is X% of Y", "X is what percent of Y", and "What is the percent change from X to Y". Instant results on input change, with step-by-step formulas shown.
The Three Percentage Modes
Mode 1 ("What is X% of Y"): multiplies X by Y and divides by 100. Example: 20% of 150 = 20 × 150 ÷ 100 = 30. Mode 2 ("X is what percent of Y"): divides X by Y and multiplies by 100. Example: 15 is what % of 60 = 15 ÷ 60 × 100 = 25%. Mode 3 (percent change): subtracts the old value from the new, divides by the old, and multiplies by 100. Example: change from 50 to 75 = (75-50) ÷ 50 × 100 = 50% increase.
Common Percentage Mistakes
The most common mistake is confusing "percent of" with "percent off". 25% off means you pay 75% of the original. A 25% increase followed by a 25% decrease does not return to the original: 100 × 1.25 × 0.75 = 93.75. Also, percentages do not add directly - a 50% increase and another 50% increase stacks to 125%, not 100%.
Real-World Uses
Percentages are used for: sales tax, discounts, tips, interest rates, grade calculations, markup, markdown, probability, population changes, scientific error reporting, and performance metrics.
Frequently Asked Questions
How do I calculate a percentage?
To find X% of Y: multiply X by Y and divide by 100. Example: 20% of 150 = 20 × 150 ÷ 100 = 30.
How do I calculate percentage change?
Subtract the old value from the new, divide by the old, multiply by 100. Example: change from 80 to 100 = (100-80) ÷ 80 × 100 = 25% increase.
What is the difference between percent of and percent off?
"25% of 100" is 25. "25% off 100" is 75 (the remaining 75%). These are different operations.
Can percentages exceed 100%?
Yes. A percentage increase can be any size. For example, if sales go from 100 to 300, that is a 200% increase.
Do successive percentage increases add up?
No. A 25% increase followed by another 25% increase stacks multiplicatively: 1.25 × 1.25 = 1.5625, which is a 56.25% total increase.
How do I calculate percentage decrease?
Same formula as percentage change, but the result will be negative. We show it as a positive number labeled "decrease".
What is a percentage point vs a percentage?
A percentage point is the arithmetic difference between two percentages. A change from 10% to 15% is 5 percentage points, but a 50% relative increase.
Can I use this for tax, tip, or discount calculations?
Yes - all of these are percentage operations. See our Tip Calculator at /calculator/tip-calculator for specialized tip math.