How to Calculate Percentages: A Simple Guide
The four percentage calculations you will use most, with formulas and worked examples for discounts, increases and comparisons.
A percentage is a number expressed out of 100. Most everyday percentage questions fall into four types.
1. Finding X% of a number
Formula: (X ÷ 100) × number. Example: 20% of 150 is 0.20 × 150 = 30.
2. Finding what percentage one number is of another
Formula: (part ÷ whole) × 100. Example: 45 out of 60 is 45 ÷ 60 × 100 = 75%.
3. Percentage increase and decrease
Formula: (new − old) ÷ old × 100. A positive result is an increase and a negative result is a decrease. Going from 80 to 100 is a 25% increase. Going from 100 to 80 is a 20% decrease. The two differ because each uses a different starting value.
4. Percentage difference
When neither number is the original, divide the gap by the average of the two: |a − b| ÷ ((a + b) ÷ 2) × 100. For 50 and 70 that is 20 ÷ 60 × 100 ≈ 33.33%.
Watch out for
- Dividing by zero: a percentage change from 0 is undefined.
- Mixing up percentage points and percent. Moving from 10% to 12% is 2 percentage points, but a 20% relative increase.
Try your own numbers with the Percentage Calculator.