Percentage Formulas Explained

Each formula below matches a working calculator. Screen-reader text restates the expression in words. Percentage change and percentage difference are not the same formula.

1. Percentage of a number

R = (P / 100) × N

Readable: result equals percentage divided by one hundred, then multiplied by the number.

Example: 15% of 200 = 30, because 0.15 × 200 = 30.

Edge case: a percentage of zero is zero. Percentage of a number calculator

2. What percent one value is of another

P = (A / B) × 100

Readable: percentage equals part divided by total, times one hundred.

Example: 25 of 200 is 12.5%.

Edge case: total zero is undefined. What percent calculator

3. Percentage change

C = ((N − O) / O) × 100

Readable: subtract original from new, divide by original, multiply by one hundred.

Example: 80 to 100 is a 25% increase.

Edge case: original zero is undefined on this site. Change calculator

4. Percentage increase and decrease

N = O × (1 + R / 100) or N = O × (1 − R / 100)

Readable: multiply the start by one plus the rate to increase, or one minus the rate to decrease.

Example: 150 increased by 20% is 180.

Edge case: a 100% decrease is zero. Increase and decrease calculator

5. Reverse percentage

O = F / (P / 100), or F / (1 + R / 100), or F / (1 − R / 100)

Readable: divide the later value by the same multiplier the forward step used.

Example: 125 after a 25% increase came from 100.

Edge case: a 100% decrease cannot uniquely recover an original. Reverse calculator

6. Discount calculation

P1 = P0 × (1 − D1 / 100); P2 = P1 × (1 − D2 / 100)

Readable: apply each discount to whatever price remains. Optional tax is then the discounted price times the tax rate over one hundred.

Example: 20% then 10% off 100 is 72, not 70.

Edge case: adding 20 and 10 as if they were one 30% discount is the common error. Discount calculator

7. Percentage difference

D = |A − B| / ((|A| + |B|) / 2) × 100

Readable: absolute difference divided by the average of the absolute magnitudes, times one hundred.

Example: 40 and 60 differ by 40%.

Edge case: both zero is treated as 0% by a documented convention. Difference calculator