Percentage Calculations Explained
Percentages express a number as a fraction of 100, making it easy to compare proportions regardless of scale. They show up everywhere from sale discounts and tax rates to test scores, statistics, and tip calculations — but the math behind "percentage change" trips up many people because it's not as simple as basic percentage-of calculations.
The most common confusion is percentage increase versus percentage points. If something goes from 20% to 30%, that's a 10 percentage point increase, but a 50% relative increase (since 10 is 50% of the original 20).
Key Formulas
X% of Y = (X ÷ 100) × Y
X is what % of Y = (X ÷ Y) × 100
% Change = [(New − Old) ÷ |Old|] × 100
Reverse %: Original = Result ÷ (% ÷ 100)
Worked Example
Example
If a product's price rose from $80 to $100, the percentage change is [(100−80)÷80]×100 = 25% increase. If you wanted to know what 20% of 150 is, the answer is (20÷100)×150 = 30. These are different calculations solving different questions, which is why this tool offers multiple modes.
Common Mistakes to Avoid
- Confusing percentage points with percentage change — a rate going from 5% to 10% is a 5 percentage point increase, but a 100% relative increase.
- Using the wrong base for % change — percentage change should always be calculated relative to the original (starting) value, not the new value.
- Forgetting that decreases aren't reversible by the same percentage — a 20% decrease followed by a 20% increase does not return you to the original number (it results in a net loss).
Frequently Asked Questions
What's the difference between percentage and percentage points? ▼
Percentage points measure the absolute difference between two percentages (e.g., 25% to 30% is a 5 percentage point increase), while percentage change measures the relative difference (that same move is a 20% increase, since 5 is 20% of the original 25).
If something decreases 20% then increases 20%, is it back to normal? ▼
No — this is a common trap. A $100 item that drops 20% becomes $80. Increasing that $80 by 20% only brings it to $96, not back to $100, because the second percentage is calculated on the new, smaller base.
How do I calculate reverse percentage? ▼
Reverse percentage finds the original number before a percentage was applied. If a result of $120 represents 80% of the original price, divide 120 by 0.8 to get the original price of $150. This is useful for figuring out pre-discount or pre-tax prices.
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