Introduction
Percentages describe a quantity as parts per hundred. They are useful for grades, discounts, growth rates, survey results and many everyday comparisons.
A percentage calculator removes repetitive arithmetic, but understanding which value is the whole and which value is the part is still essential.
Key concept
The word percent means per hundred. A result of 25% is equivalent to 25/100, 0.25 or one quarter of a whole.
- Identify the whole or reference value.
- Identify the part or rate being applied.
- Choose the formula that matches the question.
Formula and example
To find a percentage of a number, use result = number × percentage ÷ 100. For example, 18% of 250 is 250 × 18 ÷ 100 = 45.
To find what percentage one number is of another, use percentage = part ÷ whole × 100. If 45 of 250 items are selected, the percentage is 18%.
Common mistakes
A percentage increase and a percentage point increase are different. Moving from 20% to 25% is an increase of 5 percentage points, but the relative increase is 25%.
Reversing the part and whole produces a different answer. Also check whether a question expects the original value, the changed value or only the amount of change.
When a calculator helps
Use the calculator to check homework arithmetic, compare proportions or calculate a rate quickly. Keep enough decimal places during the calculation and round only the final answer when possible.