Percentage Calculator
Rather than making you pick which kind of percentage question you have, this answers all of them from two numbers. Enter A and B, then read the line that matches what you meant.
Your inputs
Your result
Formula
The three questions people actually mean
Nearly every percentage problem is one of three: what is a share of a total, what share is one number of another, or how much did something change. They use the same symbol and different arithmetic, which is why percentage questions are so easy to get backwards.
Percentage points are not percentages
If a rate rises from 4 percent to 5 percent, that is one percentage point, but a 25 percent increase. Both statements are true and they describe the same event very differently. Reporting frequently blurs the two, usually in whichever direction makes the number sound larger.
Increases and decreases do not cancel
Add 20 percent then subtract 20 percent and you are not back where you started — you are 4 percent down, because the second calculation applies to a larger base. This is the same asymmetry that makes investment losses harder to recover than they first appear: a 50 percent fall needs a 100 percent gain to undo.
Frequently asked questions
How do I find what percentage one number is of another?
Divide the first by the second and multiply by 100. The "A as a percentage of B" line does this.
How do I calculate percentage increase?
Subtract the old value from the new, divide by the old value, multiply by 100. The "change from A to B" line does this.
Why is a 50% loss not fixed by a 50% gain?
Because the gain applies to the smaller remaining amount. Falling from 100 to 50 then gaining 50 percent returns you to 75, not 100.