The Three Operations
What is X% of Y? — multiply Y by X/100. Used for discounts, tax amounts, and commission calculations. Example: 15% of $240 = $36.
X is what percent of Y? — divide X by Y and multiply by 100. Used in analytics: "our conversion rate is what percent?" or "what share of total revenue does this segment represent?" Example: 36 is what percent of 240? → 15%.
X is Y% more/less than Z? — percentage change = (X − Z) / Z × 100. Used in dashboards and performance metrics. Example: revenue went from $200 to $240 — that is a 20% increase.
Which Formula to Use
The confusion usually comes from conflating "percent of" with "percent change." If you are comparing a value to a baseline, use percentage change. If you are taking a fraction of a total, use "X% of Y." If you are figuring out what fraction one value is of another, use "X is what percent of Y."
Practical Examples
- E-commerce: apply a 10% discount to a cart total.
- Analytics: calculate week-over-week growth rate in signups.
- Pricing: add 20% VAT to a net price.
- Budgeting: determine what percentage of headcount budget remains after salaries.
A percentage calculator handles all three operations without mental arithmetic and reduces transposition errors on important numbers.