About this calculator
Percentages cause more everyday confusion than any other piece of arithmetic — usually because "percent" questions come in three different shapes that sound almost identical. "What is 15% of 200?", "45 is what percent of 180?" and "how much did it grow in percent?" each have their own formula, and mixing them up is how discounts, grades and statistics get misread. This calculator separates the three cleanly.
The most common real-world mistake is in the third shape: percentage change is always measured against the starting value, not the ending one. A price that rises from $80 to $100 rose 25%; if it then falls back to $80 it fell 20%. The asymmetry is real, and it is why "up 50%, then down 50%" does not bring you back to where you started.
How to use it
- Pick which of the three questions you are asking.
- Enter the two numbers (for "X% of Y", X is the percentage).
- Read the answer and the in-words line to confirm it matches the question you meant.
The formula
"Percent" literally means per hundred: a percentage is a fraction with denominator 100. Each formula converts between the fraction and the percent in the direction the question needs — and for change, the denominator is the original value, because that is what the change is relative to.
Worked example
What is 15% of 200? 0.15 × 200 = 30. What percent is 45 of 180? 45 ÷ 180 = 0.25, so 25%. And from 80 to 100: the change is +20 against a start of 80, so +25%. That last pair — 80 to 100 is +25%, 100 down to 80 is −20% — is the asymmetry worth remembering.
Frequently asked questions
What is the difference between percent and percentage points?
Percentage points measure the plain difference between two percentages. If an interest rate rises from 4% to 5%, that is +1 percentage point but a +25% increase in the rate. News reports mix these up constantly; when precision matters, say which one you mean.
How do I calculate a discount price?
Multiply the price by (100 − discount %) ÷ 100. A $80 item at 25% off: 80 × 0.75 = $60. Or use this page: the amount you save is "25% of 80" = $20. For our purposes the Tip Calculator's cousin, sales tax, works in the opposite direction: price × 1.08 for 8% tax.
Can a percentage be more than 100%?
Yes, whenever the part exceeds the whole or growth exceeds the starting value. A startup that grows revenue from $10k to $35k grew 250%. Percentages under 100% only apply when the result is a share of something it is part of.
Why doesn't "up 50% then down 50%" cancel out?
Because each percentage uses a different base. $100 up 50% is $150; $150 down 50% is $75. The loss applies to a bigger number than the gain did. To undo a +50% rise you need a fall of 33.3%; to undo a −50% fall you need a +100% rise.