About the percentage calculation
Percentage questions come in several shapes and people mix them up constantly. "What is 15% of 200?" and "15 is what percent of 200?" have completely different answers — 30 and 7.5 — from the same two numbers. This page answers every form at once so you can pick the one you actually meant.
Formula
X% of Y = (X ÷ 100) × Y
X is what % of Y = (X ÷ Y) × 100
Increase by X% = Y × (1 + X/100)
Decrease by X% = Y × (1 − X/100)
Remove X% = Y ÷ (1 + X/100)Worked example
15% of 200 = (15 ÷ 100) × 200 = 30. But 15 as a percentage of 200 = (15 ÷ 200) × 100 = 7.5%. Same inputs, different question.
Frequently asked questions
Why can I not just subtract to remove a percentage?
Because the percentage was applied to the smaller original number, not to the total. Removing 20% from 120 gives 100, not 96 — you divide by 1.20 rather than subtracting 20% of 120. This trips people up on tax-inclusive prices constantly.
Is a 50% increase cancelled by a 50% decrease?
No. 100 increased by 50% is 150, and 150 decreased by 50% is 75 — not 100. The second percentage applies to a larger base, so the two never cancel. This is why percentage gains and losses on investments are asymmetric.
What is the difference between percent and percentage points?
If a rate moves from 5% to 7%, that is a rise of 2 percentage points, but a 40% increase in relative terms. News reporting mixes these up regularly and the two can differ by an order of magnitude.
Sources
- Standard percentage arithmetic