Percentage Calculator
Find percentages, work out percentage change, or solve for the missing number.
Try an example
30
About this calculator
What Is a Percentage?
A percentage is a number expressed as a fraction of 100, written with the % sign. The word comes from the Latin per centum, "by the hundred." Saying that 25% of a class passed an exam means 25 out of every 100 students — or, equivalently, one quarter. Percentages make it easy to compare parts of different-sized wholes, which is why they show up in discounts, interest rates, taxes, test scores, statistics and nutrition labels.
The Three Basic Percentage Questions
- What is X% of Y? Multiply Y by X ÷ 100. Example: 15% of 80 = 80 × 0.15 = 12.
- X is what percent of Y? Divide X by Y and multiply by 100. Example: 12 is 12 ÷ 80 × 100 = 15% of 80.
- X is Y% of what number? Divide X by Y ÷ 100. Example: 12 is 15% of 12 ÷ 0.15 = 80.
This calculator handles all three, so you only need to fill in the values you know.
The Three Modes, With Worked Examples
X% of Y — divide the percentage by 100 and multiply by the number. 20% of 150 is (20 ÷ 100) × 150 = 30.
X is what % of Y — divide the part by the whole, then multiply by 100. Scoring 42 out of 50 on a test is (42 ÷ 50) × 100 = 84%.
% change from X to Y — subtract the starting value from the ending value, divide by the starting value, then multiply by 100. A stock moving from $80 to $92 is ((92 − 80) ÷ 80) × 100 = 15% increase. A positive result means growth; a negative result means a decrease.
How to Calculate Percentage Change
Percentage change = (New value − Old value) ÷ Old value × 100. A price that rises from $50 to $60 has changed by (60 − 50) ÷ 50 × 100 = 20%. A negative answer means a decrease. Note that the starting value is always the base, which is why going up 20% and then down 20% does not bring you back to where you started: 100 → 120 → 96.
Percentage vs. Percentage Points
If an interest rate moves from 4% to 5%, it rose by one percentage point but by 25 percent (1 ÷ 4). The two phrases mean different things, and news headlines mix them up often. When you compare rates, be clear about which one you mean.
Everyday Uses
- Working out a sale price or a coupon (see the Discount Calculator).
- Figuring a tip or sales tax on a bill (Tip Calculator, Sales Tax Calculator).
- Comparing how much a salary, rent or grocery bill has gone up over time.
- Understanding grades, survey results and statistics.
Quick Mental Shortcuts
10% is the number with its decimal point moved one place left; 1% is two places left; 50% is half; 25% is a quarter. Combine them: 15% = 10% + half of 10%, and 35% = 25% + 10%. Those few tricks cover most day-to-day estimates.
Worked example
20% of 150 is (20 ÷ 100) × 150 = 30. Switch modes to answer the other two common percentage questions: what percent one number is of another, or the percent change between two values.
Frequently asked questions
What's the difference between the three modes?
"X% of Y" finds a portion of a value (20% of 150 = 30); "X is what % of Y" finds what share one number is of another (30 is 20% of 150); "% change" finds the percent increase or decrease between a starting and ending value.
How is percent change calculated?
(ending value − starting value) ÷ starting value × 100. A positive result is an increase, negative is a decrease.
Why does my percent change show a negative number?
The ending value is lower than the starting value — for example, going from 150 to 120 is a change of -20%, a 20% decrease.
Can I enter numbers over 100%?
Yes — percentages aren't capped at 100. "X% of Y" and "X is what % of Y" both accept values above 100 and calculate normally.
