Percentage and Variation Calculator
A percentage of an amount, a share, an increase or a decrease: these four operations cover most needs. The classic trap is the asymmetry of changes, which quick mental math hides.
The four formulas
Share of X/Y → X ÷ Y × 100
Change → (final − initial) ÷ initial × 100
Discounted price → price × (1 − discount ÷ 100)
A $30 discount on a $150 item is a 20% reduction. A 4% rent rise on $750 adds $30. Two different formulas, two different directions.
The asymmetry of changes
This is the most common confusion. A 20% drop followed by a 20% rise does not return to the start: 100 becomes 80, then 96. The second operation applies to a smaller base. To offset a 20% drop exactly, you need a 25% rise.
| Change suffered | Change needed to get back to the start |
|---|---|
| −10% | +11.1% |
| −20% | +25% |
| −30% | +42.9% |
| −50% | +100% |
Percentage points versus percentages
A move from 2% to 3% is one percentage point (3 − 2) but a 50% relative increase (1 ÷ 2). The distinction matters enormously for interest rates, tax rates and economic indicators: mixing them up misleads by an entire order of magnitude.
Compound annual growth rate
To smooth an evolution over several years, raise the final/initial ratio to the power 1/years, then subtract 1. Revenue going from 100 to 130 over three years grows 9.1% per year on average — not 10%.
FAQ
How do I compute 20% of an amount?
Multiply the amount by 0.20. For $250, that is $50. To add 20%, multiply by 1.20; to remove 20%, multiply by 0.80.
Does a 10% rise offset a 10% fall?
No. 100 increased by 10% is 110; 110 decreased by 10% is 99. Getting back to 100 requires a 9.09% fall, because the base changed.
How do I compute a discount percentage?
Divide the discount by the original price, then multiply by 100. A $30 discount on a $150 item is 20%.
Percentage or percentage point?
Going from 2% to 3% is a one-point gap but a 50% relative increase. Both readings are valid; they measure different things.