Assumptions
- Results are rounded to 4 decimal places.
- Percent change divides by the absolute old value and is undefined at 0. Reverse calculation is also undefined at B=-100%.
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). To find the rate that reverses the rise, enter 150 as the old value and 100 as the new value. To recover the original amount instead, enter A=150 and B=50 in the add/reverse section; its reverse result is 100.
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%; using the absolute value is the convention chosen here. It gives a different sign from division by the signed old value, so check which convention your report requires.
How many decimals are shown?
Calculated results are rounded to six decimal places, then displayed with up to four. Very small values may appear as zero; this is not arbitrary-precision arithmetic. Recalculate from the original inputs if you need more digits.
Is anything saved?
No. Calculations run only in your browser and nothing is transmitted.