Percentage Calculator
Find a percentage of a number, or the percentage change between two numbers.
What this calculator does
Handles the three most common percentage questions: finding "X% of Y" (like calculating a tip or discount), finding the percent change between two numbers (like a price increase or a score improvement), and finding what percent one number is of another (like a test score or a completion rate). Pick the mode, enter your two numbers, and it returns the result instantly.
Who this is for
Anyone calculating a discount or tax, tracking a change in a metric (weight, sales, test scores, stock price), figuring out what share one number represents of another, or double-checking a percentage someone else has quoted before relying on it.
How this calculator works
"X% of Y" multiplies Y by X divided by 100. "X is what percent of Y" divides X by Y and multiplies by 100. Percent change is (new value minus old value) divided by old value, multiplied by 100; positive means an increase, negative a decrease.
Worked examples
X% of Y: 20% of 150 = 150 × (20/100) = 150 × 0.2 = 30.
X is what percent of Y: 30 is what percent of 150? 30 ÷ 150 × 100 = 20%. This is the reverse of the calculation above, and it's easy to confuse the two since they use the same three numbers.
Percent change: going from 150 to 180: (180 − 150) ÷ 150 × 100 = 30 ÷ 150 × 100 = 20% increase. Going the other way, from 180 to 150: (150 − 180) ÷ 180 × 100 = −30 ÷ 180 × 100 = −16.7% (a decrease), notice this isn't the same magnitude as the increase, because the base value is different each time.
Common mistakes
- Confusing percentage points with percent change. Going from 20% to 25% is a 5 percentage-point increase, but a 25% relative increase, these aren't the same thing, and mixing them up is a common source of confusion in statistics and news reporting.
- Using the wrong base for percent change. Percent change is always calculated relative to the original (old) value, not the new one; reversing this gives a different, incorrect answer.
- Forgetting the sign matters. A negative percent change means a decrease; don't drop the sign when reporting or comparing results.
- Assuming a percent increase and decrease of the same number cancel out. A 20% increase followed by a 20% decrease does not return you to the original value, because the second percentage is calculated on a different (larger) base.
Working Backward: Finding the Original Value
A common variation this calculator's three modes don't directly cover: if you know a sale price after a discount, what was the original price? If a $80 item is after a 20% discount, the $80 represents 80% of the original (100% − 20%), so original = 80 ÷ 0.80 = $100. The key mistake to avoid: don't just add 20% back to $80 (which gives $96, the wrong answer) — you need to divide by (1 − discount rate), not multiply by (1 + discount rate), since the discount was calculated on the larger original number, not the smaller sale price.
Related calculators
Related reading
Frequently Asked Questions
How do I find what percent one number is of another?
Divide the first number by the second, then multiply by 100. For example, 30 is what percent of 150? 30 ÷ 150 × 100 = 20%. This is different from "20% of 150," which asks the reverse question and gives 30 as the answer, it's easy to mix these two up since they share the same numbers.
What's the difference between percentage points and percent change?
If a rate goes from 20% to 25%, that's a 5 percentage-point increase, but a 25% relative increase (5 is 25% of the original 20). These describe different things and mixing them up is a common source of confusion.
Which number is the "old" value in percent change?
Always the starting value, not the ending one. Percent change = (new − old) ÷ old × 100, so reversing old and new gives an incorrect result.
Can percentage change be more than 100%?
Yes, if a value more than doubles, the percent increase exceeds 100%. For example, going from 10 to 25 is a 150% increase.
Does a 20% increase followed by a 20% decrease return you to the original number?
No. Increasing 100 by 20% gives 120, but decreasing 120 by 20% gives 96, not 100, because the second percentage is calculated on the new, larger base rather than the original value.
How do I find the original price before a discount?
Divide the sale price by (1 minus the discount rate), not multiply it by (1 plus the discount rate). An $80 price after a 20% discount means original = 80 ÷ 0.80 = $100, not 80 × 1.20 = $96.
Why can't I just add the percentage back to reverse a discount?
Because the discount percentage was calculated based on the original (larger) price, not the discounted (smaller) price — adding the same percentage back to the smaller number produces a different, incorrect result.