Percentages turn up everywhere: discounts, tips, test scores, interest, and growth rates. A percentage is simply a fraction of 100, so 25% means 25 out of 100, or 0.25. Once you know the three core calculations, every percentage problem becomes straightforward.
The three core percentage formulas
Most everyday questions fall into one of three patterns: finding a percentage of a number, finding what percentage one number is of another, and finding the percentage change between two numbers.
X% of Y = (X / 100) * Y X is what % of Y = (X / Y) * 100 percentage change = (new - old) / |old| * 100
Working out a percentage, step by step
- Pick the calculation you need: percent of a number, what percent, or percentage change
- Enter your two values in the labeled fields
- Read the result instantly, with no rounding errors to chase
- Switch modes to answer a related question without retyping
Worked examples
- 20% of 150 = (20 / 100) * 150 = 30
- 45 is what percent of 180? (45 / 180) * 100 = 25%
- A price rises from 80 to 100: (100 - 80) / 80 * 100 = 25% increase
- A price falls from 100 to 80: (80 - 100) / 100 * 100 = 20% decrease
Avoid common mistakes
When measuring change, always divide by the original (old) value, not the new one. Using the absolute value of the old number keeps the sign of the change meaningful even when the starting value is negative. And remember that percentage points are not the same as percent: moving from 10% to 15% is a 5 percentage-point rise but a 50% relative increase.
With the Percentage Calculator handling the arithmetic, you can focus on interpreting the numbers correctly and making better decisions.
Percentage points vs percent, clarified
Moving from 5% to 10% is a rise of 5 percentage points but a 100% relative increase — two true statements. Growth rates and interest discussions quote the relative change (“we grew 100%!”) while risk and margin discussions use points (“margin up 2 points”). Swap one for the other and the headline inflates 20×. The calculator keeps both readings straight, which is the whole point of a dedicated percent tool rather than back-of-envelope math.
- A percent of a percent multiplies, not adds: 50% of 10% is 5%.
- Percent change on a percentage must be qualified (points vs %).
- Always say which base the percentage refers to when numbers look alarming.
