Percentage calculator

“Per cent” is Latin for “per hundred”, so a percentage is a fraction with 100 on the bottom. Every calculation on this page is that one idea rearranged.

X% of Y = X ÷ 100 × Y X is what % of Y = X ÷ Y × 100 percent change = (new − old) ÷ |old| × 100 reverse = value ÷ (percent ÷ 100)

Percent change is not symmetric

Going from 100 to 150 is a 50% rise. Going back from 150 to 100 is a 33% fall. The base changes, so the two directions never match — which is exactly why a stock that drops 50% needs to double just to break even.

Percent versus percentage point

If a rate moves from 4% to 6%, that is a rise of two percentage points and a rise of 50 percent. Both are true, and the difference is the most common way statistics get overstated in headlines.

Discounts do not stack the way people expect

“20% off, then another 10% off” is not 30% off. It is 0.8 × 0.9 = 0.72 of the original, so 28% off. The second discount applies to the already-reduced price.