Percentage Calculator
Find a percentage of a number, what percent one number is of another, the percent change or percent difference between two values, or a number raised or lowered by a percent.
Last updated October 19, 2026
Result
30
20% of 150 is 30.
Show the work
20 / 100 x 150 = 30
How percentages are calculated
part = percent ÷ 100 × whole
percent = part ÷ whole × 100
change % = (new − old) ÷ |old| × 100
difference % = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
A percent is a fraction of 100. To find X% of a number, divide X by 100 and multiply by the number. To find what percent one number is of another, divide the part by the whole and multiply by 100.
Percent change compares a new value with an old one: subtract the old value from the new one, divide by the old value (ignoring its sign) and multiply by 100. A positive result is an increase and a negative result is a decrease. Results are rounded to four decimal places.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Grade Calculator, GPA Calculator and Fraction Calculator.
Discounts, tax and tips
A 25% discount on an 80 shirt takes off 25 ÷ 100 × 80 = 20, leaving 60. Adding 8% sales tax to that price multiplies by 1.08, which gives 64.80. Notice that the tax is worked out on the discounted price, not the original.
For a tip of 18% on a 45.50 bill, 0.18 × 45.50 = 8.19. A quick way to estimate is to find 10% by moving the decimal point (4.55), then add half of that for 15% (about 6.83) or double it for 20% (9.10).
Finding the original number
If a price after a 20% discount is 80, the original was not 80 plus 20%. The sale price is 80% of the original, so the original is 80 ÷ 0.8 = 100. In general, divide by 1 minus the discount, or by 1 plus the increase.
To check, use the percent-of mode on the result: 20% of 100 is 20, and 100 − 20 = 80.
Percentage points and repeated changes
A rate that moves from 4% to 6% has risen by 2 percentage points, which is a 50% increase on the old rate. Reports mix the two, so check which one is meant before comparing figures.
Repeated percentages multiply and do not add. Two increases of 10% make 1.1 × 1.1 = 1.21, a rise of 21%. Two discounts of 50% leave 0.5 × 0.5 = 0.25, which is 75% off in total, not 100%.
Percent of a number
To find 20% of 150, divide 20 by 100 to get 0.2 and multiply by 150: the answer is 30. This answers everyday questions such as the amount of a tip, the size of a discount or a share of a total.
What percent is one number of another
To find what percent 30 is of 120, divide 30 by 120 to get 0.25 and multiply by 100: 25%. The whole is always the number that comes after the word "of".
Percent change
Going from 80 to 100 is a change of 20 on a starting value of 80, which is +25%. Going back from 100 to 80 is a change of −20 on a starting value of 100, which is −20%. The two differ because each change is measured against its own starting value. The starting value cannot be zero.
Percentage difference between two values
Percentage difference compares two values when neither is the starting point, such as two prices or two measurements. The formula is |A − B| ÷ ((|A| + |B|) ÷ 2) × 100: the gap between the values divided by their average. For 80 and 100 the gap is 20 and the average is 90, so the difference is 20 ÷ 90 × 100 ≈ 22.22%. Swapping the values gives the same answer.
This is not percent change. Percent change treats the first value as the base, so 80 to 100 is +25% while 100 to 80 is −20%. Percent increase (the last mode) adds a given percent to a number. If the values are equal the difference is 0%. If one value is zero and the other is not, the result is always 200%, and two zeros give 0%.
Increase or decrease a number by a percent
To raise 200 by 15%, multiply by 1.15 to get 230. To lower it by 15%, multiply by 0.85 to get 170. Raising a number by a percent and then lowering it by the same percent does not return to the start: 200 up 15% is 230, and 230 down 15% is 195.5.
How to use the Percentage Calculator
- Choose the kind of percentage you want to find.
- Enter the two numbers.
- Read the result and the sentence that explains it.
- Open "Show the work", or use Copy, Print or Share.
Worked example
20% of 150 is 20 ÷ 100 × 150 = 30. 30 is 30 ÷ 120 × 100 = 25% of 120. From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. The percentage difference between 80 and 100 is |80 − 100| ÷ 90 × 100 ≈ 22.22%. Raising 200 by 15% gives 200 × 1.15 = 230. A quick check on the first result: 10% of 150 is 15, so 20% must be twice that, 30.
| Percent | Of 200 |
|---|---|
| 5% | 10 |
| 10% | 20 |
| 15% | 30 |
| 20% | 40 |
| 25% | 50 |
| 50% | 100 |
| 75% | 150 |
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percent by 100 and multiply by the number. For 20% of 150, that is 0.2 × 150 = 30.
Why is the change from 80 to 100 not the same as from 100 to 80?
Percent change is measured against the starting value. 20 on a base of 80 is +25%, while −20 on a base of 100 is −20%. Percentage difference, which divides the gap by the average of both values, gives about 22.22% in either order.
What happens if the starting value is zero?
A percent change from zero is undefined, so the calculator shows an error. In the "what percent" mode the whole cannot be zero either. Nothing you enter is stored or uploaded.
How do I add a percentage to a number?
Use the increase mode: multiply the number by 1 plus the percent as a decimal. Adding 15% to 200 is 200 × 1.15 = 230.
What is the difference between a percent and a percentage point?
A move from 4% to 6% is 2 percentage points but a 50% increase, because the change is measured against the old rate of 4%.