A percentage is a fraction with a denominator of 100 — "per hundred". So 25% means 25 out of 100, which is the fraction 25/100 and the decimal 0.25. Moving between percent, fraction, and decimal is the foundation of every calculation here.
What Is a Percentage?
Core Percentage Formulas
- Percentage of a number: X% of Y = (X ÷ 100) × Y. Example: 25% of 200 = 50.
- What percentage is X of Y: (X ÷ Y) × 100. Example: 30 of 200 = 15%.
- Reverse percentage: if X is Y% of a number, the number is X ÷ (Y ÷ 100). Example: 50 is 25% of 200.
Percentage Increase and Decrease
Use (new − original) ÷ original × 100. A positive result is an increase; a negative result is a decrease. For example, 100 to 125 is a 25% increase, while 100 to 80 is a 20% decrease. The absolute difference (new − original) tells you the raw change in units.
Percentage Points vs Percentage Increase
A percentage point is the simple difference between two percentages: 5% to 7% is a move of 2 percentage points. The same change is also a 40% relative increase, because 2 is 40% of the starting 5%. Confusing the two is one of the most common percentage mistakes.
Common Mistakes to Avoid
- Using the new value instead of the original as the baseline for percentage change.
- Treating a percentage-point move as a percent move (or vice versa).
- Forgetting that 25% means 0.25 in a multiplication, not 25.