How to calculate percentages without re-learning them every time
Three formulas cover 99% of percentage questions. Here is how each one works and which to use when.
Percentages come up in everyday life more than any other math operation, and most people relearn the formulas every time. The Percentage Calculator is the cheat sheet, but the underlying math is short enough to actually internalize.
The three formulas
1. What is X% of Y?
result = (X / 100) × Y
Example: 20% of 80 = 0.2 × 80 = 16. This is the most common percentage question (tips, discounts, taxes).
2. X is what percent of Y?
result = (X / Y) × 100
Example: 16 is what percent of 80? 16 / 80 × 100 = 20%. Used for proportions ("you got 16 out of 20 — what's that as a percentage").
3. Percent change from old to new:
result = ((new - old) / |old|) × 100
Example: from 80 to 100? (100 − 80) / 80 × 100 = +25%. From 100 to 80? (80 − 100) / 100 × 100 = −20%. Used for tracking growth or shrinkage.
Notice the asymmetry
A common puzzle: if a stock goes up 25% and then down 25%, does it end up where it started?
No. It ends up 6.25% lower.
Why: 100 × 1.25 = 125. Then 125 × 0.75 = 93.75. The "down 25%" is 25% of 125, not 25% of 100. Percent changes don't symmetrically cancel.
To recover from a 25% drop, you need a 33.3% gain. To recover from a 50% drop, you need a 100% gain. This is why losses hurt more than gains in any percentage-based system — and why long-term steady growth crushes volatile growth.
Tips, taxes, and discounts in one move
These are all the same operation in disguise.
- Tip on $42 at 18%:
0.18 × 42 = $7.56. Total:42 + 7.56 = $49.56. - Sales tax of 8.25% on $120:
0.0825 × 120 = $9.90. Total:$129.90. - 30% off a $250 jacket: discount is
0.30 × 250 = $75. Final:$175.
The Percentage Calculator's tip / discount mode shows you both the "added" and "subtracted" amounts so you don't have to think about which case you're in.
A common stumble: percentage points
If unemployment goes from 5% to 7%, that's:
- 2 percentage points increase (absolute change).
- 40% relative increase (because 2/5 × 100 = 40%).
Both numbers are correct; they answer different questions. News articles use them interchangeably, often misleadingly. When you see "X went up by Y%" — ask "Y% relative or Y percentage points?" The answer changes the meaning by an order of magnitude.
For everyday math, the calculator gives you the absolute and relative figures side by side.