Percentages Without Panic: The Five Formulas You Actually Need
Percent of, percent change, percent difference, percent off, and percent error — when to use each, with worked examples.
1. "What is X% of Y"
Convert to a decimal and multiply: 18% of 85 = 0.18 × 85 = 15.30. This is the restaurant-tip and sales-discount calculation — try it live in the percentage calculator.
2. Percent change (increase or decrease)
When a value grows or shrinks from an old number to a new one: change ÷ old value × 100. A price moving from 40 to 50 is a 25% increase; 50 back to 40 is a 20% decrease — the base changes, so up and down are not symmetric. The change tab handles the sign for you.
3. Percent difference
Comparing two values with no "correct" one (two labs, two stores): |V1 − V2| ÷ average × 100. Use this instead of percent change when neither value is clearly the reference. Our percent error calculator covers the case where one value is the true value.
4. Percent off
"30% off" means pay 70%: multiply by 0.70. Stacking two discounts (30% then 20%) multiplies the factors: 0.70 × 0.80 = 0.56 — a total 44% off, not 50%. The discount calculator shows stacked results instantly.
5. Percent error
Measured versus accepted value: |measured − accepted| ÷ accepted × 100. Chemistry and physics labs grade on this — see the percent error calculator for the worked formula.