What is X% of Y?
20 ÷ 100 × 150 = 30
20% of 150
Everyday numbers, explained
Percentage calculator
Find a percentage, compare a change, reverse a discount, or turn a rate difference into basis points. Ten useful calculations with the formula behind every answer.
A quick starting point
20% of 150 is 30. Divide 20 by 100, then multiply by 150. Change the example values to solve your own question.
Updates as you type · 10 calculation types
Your answer
20% of 150
Calculation20 ÷ 100 × 150 = 30
Choose the right percentage formula
First identify what is known and what is missing. A percentage of a number, a relative change and a rate difference answer different questions. These examples use the same calculation engine as the interactive tool.
X is what percent of Y?
30 ÷ 200 × 100 = 15%
30 as a percentage of 200
Percentage increase or decrease
(100 − 80) ÷ |80| × 100 = 25%
Increase from 80 to 100
Percentage difference between two values
|80 − 100| ÷ ((80 + 100) ÷ 2) × 100 = 22.22222222%
Difference relative to the average of both values
Increase a value by a percentage
100 × (1 + 25 ÷ 100) = 125
Value after a 25% increase
Decrease a value by a percentage
100 × (1 − 20 ÷ 100) = 80
Value after a 20% decrease
X is Y% of what? (find the whole)
30 ÷ (20 ÷ 100) = 150
The whole: 30 is 20% of this value
Original price before a discount
80 ÷ (1 − 20 ÷ 100) = 100
Original value before the percentage adjustment
Original value before an increase
120 ÷ (1 + 20 ÷ 100) = 100
Original value before the percentage adjustment
Percentage points & basis points
5% − 4% = 1 pp
1 percentage points = 100 basis points; 25% relative change
Reverse percentage calculator: find the original
There are two common reverse-percentage questions. If you know a part and the percentage it represents, divide by the decimal percentage: 30 is 20% of 30 ÷ 0.20 = 150. Choose “X is Y% of what?” to find this whole.
If you know a price after a discount, divide by the fraction that remains. An 80 price after 20% off represents 80% of the original, so the original is 80 ÷ 0.80 = 100. Adding 20% back to 80 gives 96, which is why simply reversing the sign is incorrect.
After an increase, use the corresponding multiplier. A value of 120 after a 20% increase came from 120 ÷ 1.20 = 100. The same arithmetic can remove an included percentage charge when the rate and the applicable base are known. For jurisdiction-specific tax handling, use the VAT calculator and check its assumptions.
Percentage change versus percentage difference
Use percentage change for a before-and-after question: a salary, price or measurement moves from one value to another. It needs a non-zero starting value. Use percentage difference to compare two non-negative measurements on equal terms, dividing their absolute difference by their average.
For 80 and 100, the absolute difference is 20. Relative to the starting 80 it is 25%; relative to their average of 90 it is approximately 22.22%. Both calculations can be correct, but they describe different comparisons. State the denominator when reporting the result.
Percentage points and basis points calculator
A rate changing from 4% to 5% rises by 1 percentage point, also called 100 basis points. Relative to the original rate, that is a 25% increase. Saying only “a 1% increase” would be ambiguous. The rate-difference mode displays the point change, basis points and relative change together.
One basis point is 0.01 percentage point. A change from 5% to 4.75% is −0.25 percentage points, or −25 basis points. This notation is useful for comparing interest rates, margins and other percentages without confusing an absolute rate difference with a relative change.
Rounding and edge cases
Answers display up to ten significant digits and keep greater precision internally. A zero starting value makes relative change undefined. Two zeros also have no percentage difference under the average-denominator formula. The calculator explains these cases rather than showing infinity or keeping an old result.
Signed values are allowed where the formula supports them. For negative starting values, percentage change uses the absolute starting value as its base. State that convention when comparing losses, deficits or other signed quantities; percentage language can otherwise be misleading.
FAQ
Frequently asked questions
How do I calculate a percentage of a number? ▾
Divide the percentage by 100, then multiply by the number. For example, 20% of 150 is 20 ÷ 100 × 150 = 30. Select “What is X% of Y?” in the calculator.
How do I reverse a percentage to find the original amount? ▾
If a known amount is a percentage of the whole, divide it by the percentage as a decimal. If 30 is 20% of the whole, the whole is 30 ÷ 0.20 = 150. To undo a discount, divide the sale price by 1 minus the discount rate; 80 after a 20% discount came from 80 ÷ 0.80 = 100.
What is the percentage increase from 80 to 100? ▾
It is a 25% increase: (100 − 80) ÷ 80 × 100 = 25%. Going back from 100 to 80 is a 20% decrease because the starting value is now 100. Percentage change depends on which value is the starting point.
What is the difference between percentage change and percentage difference? ▾
Percentage change compares an ending value with a starting value. Percentage difference compares two non-negative values relative to their average, without choosing a starting point. For 80 and 100, the percentage difference is 20 ÷ 90 × 100, or approximately 22.22%.
What are percentage points and basis points? ▾
Percentage points are the subtraction of two percentage rates. Moving from 4% to 5% is an increase of 1 percentage point, or 100 basis points. Relative to the starting rate of 4%, it is a 25% increase. One percentage point equals 100 basis points.
Can a percentage be greater than 100%? ▾
Yes. A percentage above 100% means more than the reference whole. For example, 150 is 150% of 100. A relative increase of 100% doubles a positive starting amount.
Why is percentage change from zero undefined? ▾
The formula divides the change by the starting value, and division by zero is undefined. A move from zero to a positive value has an absolute increase but no finite percentage increase under this formula.
How does the calculator handle negative values? ▾
Percentage-of and part-to-whole calculations support signed numbers. Percentage change uses the absolute starting value as its denominator and displays that convention for a negative start. Percentage difference uses non-negative values. Reverse price adjustments require non-negative prices and valid adjustment rates.
Sources & Methodology
Arithmetic modes use a shared tested engine. The formulas and worked examples are visible, including denominator restrictions and the signed-change convention.
Standards and figures reviewed 9 September 2026.