The one rule behind all of them
A percent is a number out of 100, so 15% is 15 ÷ 100 = 0.15. 15% of 80 is 0.15 × 80 = 12. The other questions rearrange that one sum: 12 is what % of 80 is 12 ÷ 80 × 100 = 15%, and 12 is 15% of what is 12 ÷ 0.15 = 80.
Percentage change
The change divided by where you started: from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% up. Going back down from 100 to 80 is only 20%, because the starting point is bigger. That is why a 25% rise followed by a 25% fall does not return you to where you began.
Increase or decrease by a percent
Adding 15% to 80 is 80 × 1.15 = 92; taking 15% off is 80 × 0.85 = 68. Use it for a price after a discount, a total with sales tax, or a pay rise. To undo a percentage that has already been added, divide instead: a price of 92 that already includes 15% was 92 ÷ 1.15 = 80 before it.
Questions
What is the difference between percent and percentage points?
Percentage points are the plain difference between two percentages. A rate going from 4% to 5% is up 1 percentage point, but up 25% (since 1 is 25% of 4).
How do I work out a tip?
That is the percent-of row: 18% of a $64 bill is $11.52. The Tip Calculator does it with the bill split between people.
Does it round?
Answers are shown to up to 4 decimal places, which is plenty for money and marks. The working shows the exact sum used.