Percentage calculation: four basic formulas and common mistakes

September 30, 2026 · 2 min read

Percentages come up all the time: discounts, raises, interest, grade averages. Knowing four formulas and spotting one or two traps solves most calculations.

1. A percentage of a number

Multiply the number by the percentage and divide by 100.

Result = number × percent / 100
18% of 250 = 250 × 18 / 100 = 45

2. What percent is one number of another?

Divide the part by the whole and multiply by 100.

Percent = part / whole × 100
45 is what percent of 180? 45 / 180 × 100 = 25%

3. Percentage increase and decrease

Divide the difference between the new and the old value by the old value. If the result is positive it is an increase, if negative a decrease.

Change = (new − old) / old × 100
80 to 100: (100 − 80) / 80 × 100 = 25% increase
100 to 80: (80 − 100) / 100 × 100 = 20% decrease

4. Add or subtract a percentage

To add a percentage to a number multiply by (1 + percent/100), to subtract multiply by (1 − percent/100).

Add 15% to 500  : 500 × 1.15 = 575
Take 15% off 500: 500 × 0.85 = 425

Trap 1: an increase and a decrease do not cancel out

If you raise 100 by 20% you get 120. Lowering that by 20% gives 96, not 100, because the second percentage is now taken of 120. To get from 120 back to 100 you need a 16.67% decrease.

Trap 2: going from a discounted price back to the original

If the price after a 20% discount is 80, the original is not 80 × 1.20 = 96 but 80 / 0.80 = 100. The discounted price is 80% of the original, so you divide by 0.80.

Trap 3: percent versus percentage points

If an interest rate goes from 10% to 12% that is a rise of "2 percentage points", but the rate itself grew by 20% (2 / 10). News stories and contracts mix these two up.

Quick calculation

To do these four calculations on one page with results that update as you type, use the percentage calculator. You can type decimals with a comma or a dot, and your numbers never leave your browser.