This calculator handles four percentage operations that come up in everyday arithmetic — finding a portion of a number, expressing one number as a fraction of another, measuring growth or decline, and working backwards from a result to the original value.
How percentage calculations work
Every percentage is a ratio per 100. The four operations are derived from the same underlying relationship between three quantities: a whole, a part, and a rate (the percentage). Depending on which two quantities you know, you can solve for the third.
Finding X% of Y (part unknown)
Where percent is the rate you want to apply and whole is the base value.
Finding what percent X is of Y (rate unknown)
Where part is the value you have and whole is the reference total.
Percent change from X to Y
A positive result means the value increased; a negative result means it decreased.
Reverse percentage — finding the original whole
Use this when you know the result of applying a percentage but need to recover the base value.
Example: discount, test score, and price markup
Sale discount. A jacket costs $80 and is 15% off. The discount amount is 15% of 80 = $12. The sale price is $68.
Test score. You answered 48 out of 60 questions correctly. To find your percentage: 48 ÷ 60 × 100 = 80%.
Price markup. A product that costs $25 wholesale sells for $40 at retail. The markup: ((40 − 25) ÷ 25) × 100 = 60% markup.
Reverse: original price before tax. A receipt shows $135 as a total that includes 8% sales tax. What was the pre-tax price? $135 ÷ (108 ÷ 100) = $125.
When to use each operation
Use X% of Y when you know the rate and the base, and need the resulting amount — sale discounts, tip amounts, commission payments, percentage of a budget.
Use X is what % of Y when you have a part and a whole, and need the rate — test scores, completion percentages, what fraction of a goal you’ve reached.
Use % change when comparing two values over time — price increases, population growth, performance metrics, salary changes. The result shows direction (positive = up, negative = down) and magnitude.
Use Reverse % when you see the result of applying a percentage but need the original value — recovering the pre-tax price from a total, finding the full price before a discount, or working out the base salary behind a commission amount.
Common mistakes
Confusing percent of and percent change. “X is 25% more than Y” and “X is 25% of Y” are very different statements. The first uses the percent-change formula with X as the end value; the second uses the percent-of formula. Mixing them up can flip an answer by a factor of four.
Using the wrong base for percent change. Percent change always divides by the starting value, not the ending value and not the average. A price rising from $50 to $60 is a 20% increase (10 ÷ 50), not a 16.7% increase (10 ÷ 60). The latter would be the percentage-point change relative to the final price — a different concept.
Stacking percentages additively. A 10% increase followed by a 10% decrease does not return to the original. The second 10% applies to the inflated value, leaving you 1% below where you started. Use the percent-change tab twice in sequence, or compute: 1.10 × 0.90 = 0.99. For compounded growth over many periods, the exponent calculator handles the $(1+r)^n$ form directly; for the restaurant-tip special case, the tip calculator already bundles split-by-person.