Percentage Calculator
The three percentage questions everyone actually asks — each solved instantly as you type.
1. What is X% of Y?
2. X is what percent of Y?
3. Percentage change from X to Y
The three formulas
| Question | Formula | Example |
|---|---|---|
| What is 15% of 200? | 200 × 15 ÷ 100 | 30 |
| 45 is what % of 180? | 45 ÷ 180 × 100 | 25% |
| Change from 80 to 100? | (100 − 80) ÷ 80 × 100 | +25% |
The classic mistake: percentage change direction
A 25% increase followed by a 25% decrease does not return you to the start: 80 → 100 → 75. Percentage change is always relative to the starting value, so the same absolute change is a bigger percentage of a smaller number. This is why a stock that drops 50% needs a 100% gain to recover.
Percentage points vs. percent
If a tax rate rises from 10% to 12%, it rose 2 percentage points but 20 percent (2 ÷ 10). News headlines mix these up constantly; now you won't.
Mental shortcuts worth learning
Most everyday percentage questions can be answered without a calculator once you know a few tricks:
- 1% is two decimal places left. 1% of $847 is $8.47. Everything else builds from this.
- 10% is one place left. 10% of $847 is $84.70. Need 30%? Triple it.
- 5% is half of 10%. 15% = 10% + 5% — the fastest way to tip in your head.
- Percentages are reversible. 16% of 25 is awkward; 25% of 16 is 4. Same answer, and x% of y always equals y% of x.
- Halving and doubling. 50% = half, 25% = half again, 75% = the price minus a quarter.
Where percentages mislead
Small bases exaggerate
"Sales up 200%!" sounds impressive until you learn it means three sales instead of one. Percentages on small numbers are volatile and easy to spin — always ask what the base was. Conversely, a 2% improvement on a large base can be enormous.
Percentages of percentages
If a survey reports 40% of people did something, and next year it's 44%, that's a rise of 4 percentage points but 10 percent (4 ÷ 40). Both descriptions are accurate; one sounds far more dramatic. News coverage routinely picks whichever suits the story, so it's worth checking which is meant.
Averaging percentages
You generally can't average percentages directly. If you score 50% on a 10-mark quiz and 90% on a 90-mark exam, your overall result isn't 70% — it's (5 + 81) ÷ 100 = 86%. Percentages must be weighted by the size of what they describe. This is exactly why GPA uses credit weighting.
Percentage change in both directions
The asymmetry catches almost everyone. An amount that falls by a given percentage needs a larger percentage to recover:
| Fall of | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 25% | 33.3% |
| 50% | 100% |
| 75% | 300% |
| 90% | 900% |
The reason is that the recovery is calculated against the smaller base. $100 losing 50% becomes $50; getting back to $100 requires doubling. This single fact explains a great deal about why avoiding large losses matters more than chasing large gains.