Six different percentage questions in one tool — with the formula shown, so you can check the working.
Pick what you are trying to work out; the labels change to match.
| Question | Formula | Example |
|---|---|---|
| What is A% of B? | A ÷ 100 × B | 25% of 200 = 50 |
| A is what % of B? | A ÷ B × 100 | 50 of 200 = 25% |
| % change A → B | (B − A) ÷ |A| × 100 | 200 → 250 = +25% |
| Increase A by B% | A × (1 + B ÷ 100) | 200 + 25% = 250 |
| Decrease A by B% | A × (1 − B ÷ 100) | 200 − 25% = 150 |
| A is B% of what? | A ÷ (B ÷ 100) | 50 is 25% of 200 |
Take 100, cut it by 20% to get 80, then add 20% back: 80 × 1.2 = 96, not 100. The second percentage is applied to a smaller base. To reverse a 20% decrease you need a 25% increase. This is the single most common percentage mistake, and it appears constantly in discount and salary-cut arithmetic.
If a rate moves from 5% to 7%, that is a rise of two percentage points but a 40% increase in the rate itself. Both statements are true and they describe the same change — mixing them up is a common source of misleading claims in reporting.
The formula divides by the absolute value of A, so a move from −50 to −25 registers as a 50% improvement rather than a −50% one. Percent change on quantities that cross zero is ambiguous by nature and is usually better reported as an absolute difference.
Subtract the old value from the new one, divide by the old value, then multiply by 100. From 200 to 250: (250 − 200) ÷ 200 × 100 = 25%.
Because the second percentage applies to a different base. A 20% fall needs a 25% rise to undo it, since the rise is calculated on the reduced figure.
A move from 5% to 7% is two percentage points, but a 40% increase in the rate. Percentage points measure the gap between two percentages; percent measures relative change.
Use the reverse mode. If an item costs 80 after a 20% discount, it was 80 ÷ 0.80 = 100 originally.
Yes for increases — doubling is +100%, tripling is +200%. Decreases cannot go below −100%, because that would mean the value fell past zero.