Many percentage mistakes come from using the right arithmetic for the wrong question. Identify the base, the comparison, and whether the result is a percentage or percentage-point change.
Percentage of a number
To find P% of N, calculate P ÷ 100 × N. Fifteen percent of 240 is 0.15 × 240 = 36.
What percent is one value of another?
Divide the part by the whole and multiply by 100. If 36 is part of 240, 36 ÷ 240 × 100 = 15%. The denominator is the reference base.
Increase, decrease, and difference
Percentage increase uses (new − original) ÷ original × 100. Percentage decrease uses (original − new) ÷ original × 100. Percentage difference uses absolute difference ÷ average × 100 when neither value is the sole baseline.
Error and percentage points
Percentage error compares absolute error with an accepted value. A change from 20% to 30% is 10 percentage points but a 50% relative increase. State which interpretation you mean.
Sources
The figures and rules in this guide are checked against:
- Percent — Wolfram MathWorld
- Percent Change (CPI fact sheet) — U.S. Bureau of Labor Statistics
- The meaning of percent — Khan Academy
- Finding percentages — Khan Academy