Percentage Difference Calculator
The percentage difference calculator calculates the percentage when the direction of the change is unknown.
The formula
difference = |a − b| ÷ ((a + b) ÷ 2) × 100
Difference is not the same as change
Percentage change divides by the original value, so it has a direction and depends which number you start from. Percentage difference divides by the average, so it is symmetric — swapping the two inputs gives the same answer. Use difference when neither value is "the baseline".
What a percentage is
"Per cent" means "per hundred", so a percentage is just a fraction with 100 on the bottom. 15% is 15/100, which is 0.15 as a decimal. Every percentage calculation is therefore multiplication or division by a decimal — the percent sign is bookkeeping, not a new operation.
The three questions
Almost every percentage problem is one of three:
- What is P% of N? Multiply:
N × P/100 - A is what percent of B? Divide:
A/B × 100 - A is P% of what? Divide the other way:
A ÷ (P/100)
Recognising which one you have is most of the work; the arithmetic is straightforward once you do.