Percentage calculator
Three percentage questions, answered without guessing which formula applies.
Result
36
36
- Value + X%
- 276
- Value − X%
- 204
- 1% of value
- 2.4
The three questions behind every percentage
Almost every percentage question is one of these, and they use different formulas:
- What is X% of Y? — multiply.
- X is what percent of Y? — divide, then multiply by 100.
- What is the percentage change from X to Y? — subtract, divide by the original, then multiply by 100.
Picking the wrong one is the usual reason an answer looks plausible but is wrong, so this calculator makes you choose the question rather than the formula.
Percent of a number
result = value × percent ÷ 10015% of 240 is 240 × 0.15 = 36. The same line gives the increased and decreased values next to the result: 276 and 204, which is what most people actually wanted when they typed “15% of 240” into a search box.
What percent is one number of another
percent = part ÷ whole × 10036 out of 240 is 36 ÷ 240 = 0.15, or 15%. The whole must not be zero; there is no percentage of nothing.
Percentage change
change = (new − old) ÷ |old| × 100From 240 to 300 the change is +60 on a base of 240, which is +25%. From 300 back to 240 the change is −60 on a base of 300, which is −20%. Same 60, two different percentages, because the base changed.
That asymmetry is the single most useful thing to understand about percentages. A 50% loss needs a 100% gain to recover. A 20% loss needs 25%. This is why investment losses hurt more than the equivalent gains help.
Percentages do not add
Two successive 10% increases are not a 20% increase. They multiply:
1.10 × 1.10 = 1.21 → +21%The same applies to discounts. “20% off, then a further 10% off” is 0.80 × 0.90 = 0.72, which is 28% off, not 30%. Stacked percentages always compound, and the second one applies to the already-reduced price.
Percentage points vs percent
If a rate moves from 4% to 6%, that is 2 percentage points but a 50% increase. Both statements are true and they describe different things. When a figure matters — interest, unemployment, a tax rate — check which one is being quoted before acting on it.
Percentage difference
When neither value is “before” and neither is the reference, use the average as the base:
difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100100 and 120 differ by 18.18% by this measure, and swapping them gives the same answer — unlike percentage change, which would give +20% one way and −16.67% the other.
Frequently asked questions
What is the difference between percentage change and percentage difference?
Percentage change compares a new value against an old one, so direction matters and the base is the old value. Percentage difference compares two values with no direction, using their average as the base, so swapping the numbers gives the same answer. Use change for "before and after", and difference for "how far apart are these two".
Why is a 20% drop not cancelled by a 20% rise?
Because the two percentages use different bases. Dropping from 100 to 80 is a 20% fall of 100. Rising from 80 back to 100 is a 25% rise of 80. To undo a 20% fall you need a 25% increase, and to undo a 25% fall you need a 33.3% increase.
How do I add a percentage to a number in one step?
Multiply by 1 + the rate as a decimal. A 20% increase on 80 is 80 × 1.20 = 96. To subtract, multiply by 1 − 0.20 = 0.80. Adding the percentage of the original separately gives the same answer, but the single multiplication avoids rounding twice.
What does "percentage points" mean?
It is the arithmetic difference between two percentages. A rate moving from 4% to 6% has risen by 2 percentage points, but by 50% in relative terms. News reports mix the two constantly, which is why the distinction matters.
Why does the calculator refuse to divide by zero?
A percentage of zero has no meaning — "X is what percent of 0" has no answer, and a change from 0 is infinite. Rather than print Infinity or a misleading zero, the result shows a dash and explains why.
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