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Percentage formulas explained: of, is-what-percent and percent change

"Percent" means per hundred, so 15% is 15 out of every 100, or 0.15. Almost every percentage question is one of the five below. The percentage calculator does each of them with your own numbers.

The five formulas

X% of Y              = X / 100 x Y          15% of 80  = 12
X is what % of Y     = X / Y x 100          12 of 80   = 15%
X is Y% of what      = X / (Y / 100)        12 is 15%  -> 80
percent change       = (new - old) / old x 100       40 -> 50 = +25%
new after Y% change  = old x (1 +/- Y / 100)         80 +25%  = 100

Mistake 1: percent versus percentage points

If an interest rate rises from 4% to 5%, it has risen by 1 percentage point. As a percent change it is up 25%, because 1 is a quarter of 4. News stories mix the two, so check which one is meant.

Mistake 2: a rise and a fall do not cancel

A percentage always applies to the current value. 100 falling by 50% is 50, and 50 rising by 50% is only 75. To get back to 100 from 50 you need a rise of 100%. This is why a share price that halves has to double to recover.

Mistake 3: adding discounts

Two discounts multiply. 20% off and then 10% off leaves 0.80 x 0.90 = 0.72 of the price, which is 28% off, not 30%. The percentage decrease calculator shows the result for one step at a time.

Mistake 4: using the wrong base

Percent change is measured against the starting value. From 40 to 50 is +25%, but from 50 to 40 is -20%. If neither value is the starting point, use percent difference, which divides by the average and gives the same answer both ways: 22.22% for 40 and 50. The percent change calculator shows both.

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