Percentage calculator
Three percentage questions, answered as you type. No calculate button, no page reload — the answers update live.
Built and checked by Mubashir, who works in accounting and finance. Formula and sources shown below. Not financial advice.
Three calculations
What is X% of Y?
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X is what percentage of Y?
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Percentage change from X to Y
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The three formulas
X% of Y is Y × X ÷ 100. Fifteen percent of 200 is 30.
X as a percentage of Y is X ÷ Y × 100. Thirty out of 200 is 15%.
Percentage change from X to Y is (Y − X) ÷ X × 100. Going from 200 to 250 is a 25% increase. Note the denominator: the change is always measured against the starting value, not the ending one.
Percentage change is not symmetrical
This trips up more people than any other percentage question, and it appears constantly in financial reporting.
A value that falls from 100 to 50 has dropped 50%. To get back from 50 to 100 requires a 100% rise, not another 50%. The percentages differ because the base changed — the first calculation divides by 100, the second by 50.
The consequence for investing is unforgiving. A portfolio that loses 20% needs a 25% gain to break even. Lose 50% and you need 100%. Lose 80% and you need 400%. Losses are arithmetically more expensive than the equivalent gain, which is why capital preservation matters more than it intuitively seems to.
Percentage points against percent
These are different units and mixing them is a genuine source of confusion in reporting.
If an interest rate moves from 4% to 6%, it has risen by two percentage points. It has also risen by 50 percent. Both statements are true and they describe the same change. Headlines that say a rate "rose 50%" when it moved two points are technically accurate and thoroughly misleading.
The safe convention: use percentage points when comparing two percentages, and percent when describing relative change in any other quantity.
Successive percentages do not add
A 10% increase followed by a 10% decrease does not return you to the start. Starting at 100: up 10% gives 110, down 10% of 110 gives 99. You end a percent below where you began, and the gap widens with larger percentages.
The same applies to discounts. A 20% discount followed by a further 10% off is not 30% off — it is 28%, because the second reduction applies to the already-reduced price. Retailers know this; shoppers frequently do not.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For 15% of 200: 200 × 15 ÷ 100 = 30. Or move the decimal two places and multiply, which is faster mentally.
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages; percent measures relative change. A rate moving from 4% to 6% rose two percentage points and also rose 50 percent.
Why is percentage change not reversible?
Because it is always measured against the starting value, and that value changes. Falling from 100 to 50 is a 50% drop, but recovering from 50 to 100 is a 100% rise — the same absolute change against a smaller base.
Do successive discounts add up?
No. Twenty percent off followed by ten percent off is 28% off in total, not 30%, because the second discount applies to the already-reduced price.
How do I calculate percentage increase quickly?
Divide the new value by the old one and subtract one. If the result is 1.25, that is a 25% increase. A result below one indicates a decrease.
What if the starting value is zero?
Percentage change is undefined. Any increase from zero is infinite in relative terms, which is why reports usually describe such changes in absolute numbers instead.