Assumptions
- Results are rounded to 4 decimal places.
- Percent change uses the old value as the base and is undefined when the old value is 0.
How it is calculated
| Question | Formula | Example |
|---|---|---|
| B% of A | A × B ÷ 100 | 200 × 15 ÷ 100 = 30 |
| A is what % of B | A ÷ B × 100 | 30 ÷ 200 × 100 = 15% |
| Change from A to B | (B − A) ÷ |A| × 100 | (125 − 100) ÷ 100 × 100 = +25% |
| Add B% to A | A × (1 + B ÷ 100) | 100 × 1.10 = 110 |
| Reverse | result ÷ (1 + B ÷ 100) | 110 ÷ 1.10 = 100 |
| Percentage points | B% − A% | 4.25 − 3.5 = 0.75 pp |
Examples
- Sales growth: $42,000 last month → $48,300 this month = +15%.
- Pre-tax price: a $107 total with 7% sales tax was $107 ÷ 1.07 = $100 before tax.
- Test score: 41 correct out of 50 = 82%.
- Tip: 18% of $64.50 = $11.61.
- Rates: 3.50% → 4.25% is +0.75 pp, or +21.43% relative.
Common mistakes
- "20% off" and "25% more" can describe the same two prices — $100 → $80 is a 20% discount; $80 → $100 is a 25% increase. The base matters.
- Averaging percentages across groups of different sizes gives the wrong overall percentage; weight by size.
- Stacked discounts and compound interest multiply, they don\'t add — see the discount calculator.
FAQ
What is the difference between percent and percentage points?
If a rate goes from 3.5% to 4.25%, it rose 0.75 percentage points. You could also say it rose 21.4% (0.75 ÷ 3.5), which means something different. Differences between two rates are points; relative change of a quantity is percent. Fed rate and poll coverage use points.
If something goes up 50% and then down 50%, is it back where it started?
No. 100 → 150 → 75. Each percent change is measured from the value at that moment, so undoing a 50% rise takes only a 33.3% fall (150 × 2/3 = 100). The "reverse" field gives that original value.
Can percent change be computed from zero or a negative base?
From zero it is undefined and shows "–". From a negative base (a loss of −100 improving to −50) the tool divides by the absolute value and shows +50%; in financial reporting such changes are usually described in words rather than as a percentage.
How many decimals are shown?
Up to four, rounded. Floating-point artifacts like 0.1 + 0.2 are cleaned up during calculation. For more precision use Excel's ROUND().
Is anything saved?
No. Calculations run only in your browser and nothing is transmitted.