Percentage Calculator
Solve any percentage problem in seconds. Find what X% of Y is, figure out what percent one number is of another, or calculate the percent change between two values. Three modes, one form, no math headaches.
Quick answer
X% of Y = (X / 100) × Y. X is what % of Y = (X / Y) × 100. Percent change = ((new − old) / old) × 100.
Percentage Calculator
How percentages work
A percentage is just a fraction where the denominator is 100. "50%" means 50 out of 100, or 1/2. The word comes from the Latin per centum — "per hundred." To find a percentage of a number, convert the percent to a decimal (divide by 100) and multiply. 15% of 200 = 0.15 × 200 = 30.
Going the other direction — finding what percent one number is of another — you divide the part by the whole and multiply by 100. If you got 30 out of 200 on a quiz, you scored (30 / 200) × 100 = 15%. Percent change uses the same division but against the original value: ((new − old) / old) × 100.
When to use it
Percentage math shows up everywhere: tipping (what's 18% of $47?), sales discounts (how much do I save at 30% off?), tax calculations, grade weighting, commission, polling results, investment returns, body fat, nutrition labels, and any comparison between "before" and "after." This calculator handles all three common forms, so you don't have to remember which formula applies.
Common mistakes
- Confusing percent change with percentage points. If a mortgage rate rises from 6% to 7%, that's a 1-percentage-point increase, but a 16.7% relative increase. Media outlets mix these up constantly.
- Stacking discounts wrong. 30% off followed by 20% off is NOT 50% off. It's 0.7 × 0.8 = 0.56, so you pay 56% of the original price — a 44% total discount.
- Reversing a percentage. If something increases by 25%, decreasing by 25% does not restore it. $100 → $125 → $93.75. To reverse a 25% increase you'd need a 20% decrease.
- Dividing by zero. "Percent change from 0" is undefined — there's no starting value to compare against.
Frequently asked questions
How do you calculate a percentage?
To find X% of Y, multiply Y by X/100. For example, 15% of 200 = 200 × 0.15 = 30.
How do you calculate percent change?
Percent change = ((new value − old value) / old value) × 100. A positive result is an increase; negative is a decrease.
What's the difference between percentage and percentage points?
Percentage points are an absolute change: 10% to 15% is a 5 percentage point increase. Percent change is relative: 10% to 15% is a 50% increase.
How do you calculate a 20% tip?
Multiply the bill by 0.20, or move the decimal one place left and double it. On a $45 bill: $4.50 × 2 = $9.
How do you subtract a percentage from a number?
Multiply by (1 − rate). To take 15% off $80: 80 × (1 − 0.15) = 80 × 0.85 = $68.