Quick Answer
To find what percentage X is of Y, divide X by Y and multiply by 100: Percentage = (X ÷ Y) × 100. To find X% of a number, multiply the number by X and divide by 100.
What Is Percentage?
Percentages express a number as a fraction of 100, making it easy to compare proportions, calculate discounts, track changes over time, and interpret statistics across completely different scales. The word 'percent' literally comes from the Latin 'per centum,' meaning 'per hundred.'
There are three common percentage calculations people need: finding what percentage one number is of another (e.g. 'what percent of 80 is 20?'), finding a percentage of a number (e.g. 'what is 15% of 200?'), and calculating percentage change between two values (e.g. 'my salary went from $40,000 to $44,000, what's the percentage increase?'). Each uses a slightly different rearrangement of the same basic relationship.
Percentage change calculations are particularly prone to a common error: percentage increase and percentage decrease are not symmetric. A 50% increase followed by a 50% decrease does not return you to the original number, it results in a 25% net decrease, because the second percentage is calculated on a different (larger) base.
How to Use
- 1Choose the type of percentage calculation you need: 'X% of Y', 'X is what % of Y', or 'percentage change from X to Y'.
- 2Enter the relevant numbers into the fields.
- 3The calculator instantly returns the result with the formula used shown for transparency.
Formula
Result = (X ÷ 100) × YPercentage = (X ÷ Y) × 100% Change = ((New − Old) ÷ Old) × 100Example: Salary increased from $40,000 to $44,000, find the percentage increase
- Old Value = 40,000, New Value = 44,000
- Change = 44,000 − 40,000 = 4,000
- % Change = (4,000 ÷ 40,000) × 100
Tips & Things to Know
- Percentage increase and decrease are not reversible by the same percentage, a 20% increase followed by a 20% decrease on the new value does not return to the original number.
- When comparing percentage changes across different base values, always check what the 'whole' (denominator) actually is, a 10% increase on a small base is a very different real number than 10% on a large base.
- For repeated percentage changes (e.g. annual price increases over several years), each year's percentage applies to the previous year's already-adjusted value, similar to compound interest, not the original starting value.
- Negative percentage change values represent a decrease; always check the sign when interpreting percentage change results.