Everyday percentages, without the confusion
Work out discounts, percentage change, tips and bill splits with the right base — and avoid the classic percentage-point mistake.
Percentages are simple arithmetic wrapped in confusing language. “30% off,” “up 2 percentage points” and “a 20% increase” all sound similar, but they use different bases.
Here is the mental model, followed by the tools that do the arithmetic.
The one rule: find the base
A percentage is always a percentage of something. The base is the number you multiply by.
- 30% off a $120 jacket means the discount is 30% of $120, or $36.
- A salary going from $52,000 to $58,000 rises by $6,000, which is about 11.5% of the original $52,000.
- 20% of 50 is 10, but 50% of 20 is also 10. Same answer, different base.
If the base is unclear, the percentage is unclear.
Discounts and markups
A discount subtracts a percentage. A markup adds one. The percentage calculator has an Add or subtract a % mode for both.
Remember that a 20% discount followed by a 20% increase does not return to the original price. From $100, a 20% fall leaves $80; a 20% rise from $80 gives $96. Each step uses a new base.
Percent change vs percentage points
This is the most common trap in news and finance writing.
- Going from 10% to 12% is 2 percentage points.
- It is also a 20% relative increase, because 2 is 20% of 10.
Both statements can be true. They answer different questions. The calculator’s Percentage change mode measures relative change; percentage points are a direct subtraction.
Tips and bill splitting
A tip is a percentage of the bill, and a split divides the total. The tip calculator handles both, including rounding and any group size.
Two practical checks:
- Read the bill for an automatic service charge before adding a tip.
- Decide whether you are tipping on the pre-tax subtotal or the final total.
Quick reference
| Question | Operation |
|---|---|
| What is 15% of 200? | 200 × 0.15 = 30 |
| 30 is what percent of 150? | 30 ÷ 150 × 100 = 20% |
| Change from 150 to 120? | (120 − 150) ÷ 150 × 100 = −20% |
| 80 increased by 25%? | 80 × 1.25 = 100 |
| 80 decreased by 25%? | 80 × 0.75 = 60 |
For the definitions behind these terms, see the glossary — and use the percentage calculator when you want the answer rather than the explanation.