Three percentage tools in one: find a percentage of a number, work out what percent one number is of another, or measure the percent change between two values. Pick a mode and go.
The three percentage formulas
Almost every percentage question is one of these three shapes:
X% of Y = (X × Y) ÷ 100
X as a % of Y = (X ÷ Y) × 100
% change = ((New − Old) ÷ Old) × 100
Worked examples
Tip on a bill: 18% of $64 = (18 × 64) ÷ 100 = $11.52.
Test score: 42 correct out of 60 questions = (42 ÷ 60) × 100 = 70%.
Price change: a $250 item now selling for $199 = ((199 − 250) ÷ 250) × 100 = −20.4%, a 20.4% discount.
A common trap: percent change is not symmetric
If a stock drops 50% and then rises 50%, it is not back where it started — it's down 25%. Percent change is always measured against the starting value, so a fall needs a bigger percentage rise to recover. A 50% loss needs a 100% gain to break even. Keep that in mind any time you chain percentage changes together.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 80 is (15 × 80) ÷ 100 = 12.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 120 is (30 ÷ 120) × 100 = 25%.
What's the difference between percent increase and percentage points?
Percent increase is relative to the starting value: going from 20% to 30% is a 50% increase. Percentage points measure the absolute gap: that same move is 10 percentage points. News reports mix these up constantly.
How do I calculate percent decrease?
Use the same percent change formula: ((New − Old) ÷ Old) × 100. If the result is negative, that's your percent decrease. Going from 50 to 40 is ((40 − 50) ÷ 50) × 100 = −20%, i.e. a 20% decrease.
How do I reverse a percentage (find the original number)?
Divide by the decimal form of the percentage. If 12 is 15% of some number, the number is 12 ÷ 0.15 = 80. You can check it with the "is what % of" mode of this calculator.