Percentage Calculator
Three common percentage problems, solved instantly.
X% of Y
X is what % of Y
% Increase / Decrease
The three percentage formulas explained
A percentage is simply a fraction out of 100, and almost every real-world percentage question reduces to one of three patterns. The first, "X% of Y," answers questions like "what is 20% of 150?" by converting the percent to a decimal and multiplying: (X ÷ 100) × Y. This is the calculation behind discounts, tips, tax additions, and commission — if an item costs 150 and is 20% off, you're removing (20 ÷ 100) × 150 = 30 from the price.
The second pattern, "X is what percent of Y," flips the question around: instead of knowing the percentage, you know two actual numbers and want the relationship between them expressed as a percentage. The formula is (X ÷ Y) × 100. This is useful for grades (35 correct out of 50 questions), market share, or completion rates on a project.
The third pattern measures percentage change between two values: ((Y − X) ÷ |X|) × 100, where X is the starting value and Y is the ending value. A positive result means growth, a negative result means decline. This is the formula behind reported statistics like "sales grew 12%" or "prices fell 8%," and it's worth remembering that percentage changes aren't symmetric — a 50% increase followed by a 50% decrease does not return you to the original number, because the base amount changes between the two steps. Understanding which of these three patterns applies to your situation is usually the hardest part; the arithmetic itself is straightforward once you know which formula to reach for.
Frequently asked questions
What's the difference between percentage change and percentage points? A rate moving from 10% to 15% is a 5 percentage-point increase, but a 50% relative increase — the two describe the same change differently, and mixing them up is one of the most common percentage mistakes.
How do I calculate a discount price? Use the "% of" tool to find the discount amount, then subtract it from the original price — or use the increase/decrease tool directly with a negative percentage to get the final price in one step.
Why do percentage increase and decrease use different denominators? An increase is measured against the original (smaller) number, while reversing it back down is measured against the new (larger) number, which is why a 50% increase isn't undone by a 50% decrease.
Worked example
A $80 jacket is 25% off. Discount amount = 80 × 0.25 = $20, so the sale price is $60. Reversing it: if you paid $60 for something originally $80, you got a 25% discount — (80 − 60) ÷ 80 × 100 = 25%.
What's the difference between “percentage of” and “percentage change”? “What is 20% of 50?” is a direct multiplication (50 × 0.20 = 10). “By what percent did 50 increase to 60?” is a change calculation: (60 − 50) ÷ 50 × 100 = 20%. Mixing these up is the most common percentage mistake.
How do I calculate a tip using this tool? Enter the bill total and the tip percentage (commonly 15–20% in the US) — the result is the tip amount; add it to the bill for the total to pay.