Percentage Change Calculator
The percentage change calculator determines the value difference and the percent change from the original value to the new value.
The formula
change = (new − old) ÷ |old| × 100
Why reversing is not symmetric
A 50% rise followed by a 50% fall does not return you to the start: 100 becomes 150, then 75. Each percentage is taken of a different base, which is why the "to reverse it" figure above is not simply the negative of the change.
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.