Percentage Calculator
30
The percentage calculator handles the five questions people actually ask: what is X% of Y, X is what percent of Y, increase or decrease X by Y%, and the percentage change from X to Y. Each mode shows the formula it used, so the arithmetic is checkable rather than a black box.
How it works
- X% of Y: (X / 100) × Y. The everyday case. 15% of 200 is 30.
- X is what percent of Y: (X / Y) × 100. Used for scores and shares.
- Increase X by Y%: X × (1 + Y/100). Not X + Y, which is the most common mistake.
- Decrease X by Y%: X × (1 − Y/100).
- Change from X to Y: ((Y − X) / |X|) × 100. The absolute value handles negative starting points sensibly.
Percentage change is not symmetric. Going from 100 to 150 is a 50 percent increase, but going back from 150 to 100 is a 33.3 percent decrease. The base changes, so the two do not cancel.
Examples
A percentage of a value
Mode
What is X% of Y?
X
15
Y
200
Result
30
(15 / 100) × 200. The formula shown above the result is the one used, not a generic description.
An increase and its reverse
Mode
Percentage change from X to Y
X
100
Y
150
Result
50%
Reversing the inputs gives −33.33%, not −50%. The denominator changes from 100 to 150, which is why an increase and the decrease that undoes it never match.
Increasing by a percentage
Mode
Increase X by Y%
X
80
Y
25
Result
100
80 × 1.25. Adding 25 to 80 would give 105, which is the error this mode exists to prevent.
Frequently asked questions
Why does a 50% increase not cancel out a 50% decrease?
Because each percentage applies to a different base. 100 increased by 50% is 150; 150 decreased by 50% is 75, not 100. To undo a 50% increase you need a 33.3% decrease. This asymmetry is behind a great deal of misleading statistics.
What is the difference between a percentage and a percentage point?
If a rate rises from 4% to 6%, that is a 2 percentage point rise but a 50 percent increase. Both are correct and they mean very different things, reporting the larger one without saying which is the standard way to exaggerate a change.
How do I reverse a percentage increase to find the original price?
Divide rather than subtract. A price of 120 after a 20% increase was 120 / 1.2 = 100, not 120 − 20% = 96. Use the "X is what percent of Y" mode with the known values to check your working.
What happens with a negative starting value?
The percentage change mode divides by the absolute value of the start, so going from −50 to −25 reports a 50% change rather than −50%. Percentage change from a negative base is genuinely ambiguous, and taking the absolute value is the least surprising convention.