Percentage formulas
- X% of Y:
Y × X / 100. For example, 15% of 200 is 200 × 15 / 100 = 30. - X is what percent of Y:
X / Y × 100. 30 out of 120 is 25%. - Percentage change:
(new − old) / old × 100. Going from 80 to 100 is a 25% increase.
Everyday uses
Percentages show up when you work out a sale price, a tip, a tax amount, a grade, a pay raise or an investment return. A 20% discount on an $80 jacket takes off $16, leaving $64. A pay rise from $50,000 to $53,000 is a 6% increase.
Percent vs percentage points
If an interest rate rises from 4% to 5%, it went up by one percentage point but by 25 percent in relative terms. News stories mix these up often, so it is worth checking which one is meant.
Why a decrease followed by an increase does not cancel out
A 50% drop followed by a 50% rise leaves you at 75% of the original value, not 100%, because the rise is calculated on the smaller number. The same idea explains why investment losses are harder to recover from than they appear.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. So 25% of 80 is 80 x 25 / 100 = 20.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100.
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100.
How do I take a percentage off a price?
Multiply the price by (1 minus the discount as a decimal). For 30% off $50, calculate 50 x 0.70 = $35.