Percentage Calculator
Percent of a number, what percent one number is of another, percentage change, and adding or removing a percentage.
Your numbers
Filled in with example values. Replace them with your own.
Results update as you type.
Result
20% of 150 is 30
Result
30
- Remaining80% of 150
- 120
How it’s calculated
Percentage as a decimal
20 ÷ 100 = 0.2
Multiply by the number
0.2 × 150 = 30
How the percentage calculator works
“Percent” means “per hundred”, so 20% is 20 ÷ 100 = 0.2. Every percentage question comes down to multiplying or dividing by that fraction. Choose the question you are asking and the calculator applies the matching formula, then shows each step.
The formulas
P% of X = P ÷ 100 × X
A as a percent of B = A ÷ B × 100
Change from A to B = (B − A) ÷ |A| × 100
X increased by P% = X × (1 + P ÷ 100)
X decreased by P% = X × (1 − P ÷ 100)
Worked examples
A discount
A jacket costs 80 and is reduced by 25%. The multiplier is 1 − 25 ÷ 100 = 0.75, so the sale price is 80 × 0.75 = 60, a saving of 20.
A score
You answered 42 questions correctly out of 48. As a percentage: 42 ÷ 48 = 0.875, and 0.875 × 100 = 87.5%.
A change in price
A monthly bill goes from 150 to 180. The difference is 30, and 30 ÷ 150 = 0.2, so it rose by 20%.
Rounding and limitations
- Results are calculated in full precision and rounded only for display, to at most six decimal places.
- Numbers can be negative, except where the question needs a positive percentage. Choose “Increase” or “Decrease” instead of typing a minus sign.
- Very large numbers (a thousand trillion or more) are not accepted, because computers cannot store every digit of them exactly.
Frequently asked questions
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages; percent measures relative change. If an interest rate rises from 4% to 5%, it has gone up by 1 percentage point, but by 25 percent (1 ÷ 4 × 100).
Why doesn’t a 20% fall undo a 20% rise?
Because each percentage is taken of a different starting value. 100 plus 20% is 120, but 120 minus 20% is 96. To get back from 120 to 100 you need a fall of 16.67%.
How do I find the original price before a percentage was added?
Divide by the multiplier instead of multiplying. If a price including 20% is 180, the original is 180 ÷ 1.2 = 150. Subtracting 20% of 180 would give 144, which is wrong.
Is 8% of 50 the same as 50% of 8?
Yes. Both are 8 × 50 ÷ 100 = 4. Swapping the numbers can make mental arithmetic easier.
How is a percentage change from a negative number calculated?
The difference is divided by the size of the original value, ignoring its sign. Going from −50 to −25 is a rise of 25, which is 50% of 50, so the calculator shows a 50% increase. A change from zero has no percentage, because it would mean dividing by zero.