Percent calculations — quick, practical guide
Core idea
Three core questions cover 95% of use cases: X% of Y? What % is X of Y? X is Y% of what?
How it works
- X% of Y → (X ÷ 100) × Y
- What % is X of Y → (X ÷ Y) × 100%
- X is Y% of what → X ÷ (Y ÷ 100)
Sanity checks
- Whole (Y) must be > 0
- Units must match for X and Y
- Percent can be > 100% when X > Y
Shortcuts
- 10% = ÷10; 5% = ÷20; 1% = ÷100
- Increase by p% → ×(1 + p/100); decrease by p% → ×(1 − p/100)
Pitfalls
- Percent points vs percent change (12%→15% is +3 pp, +25%)
- Order matters in change: (New−Old)/Old
Micro‑examples
- 25% of 80 = 20
- 20 is 25% of 80
- 20 is 25% of what? 80
Mini‑FAQ
Negative values? The formulas still work; keep signs consistent and interpret in context.
Action tip
When reporting, state both the percent and the baseline number to avoid misreads.