How percentages work: the complete guide
A percentage is a fraction of one hundred. Every percentage question, however specialised it sounds, reduces to one of four operations: finding a part of a whole, expressing one number as a share of another, measuring change between two numbers, or working backwards from a result to the original value.
The four operations
- Percentage of a number: value × percent ÷ 100. 15% of 240 is 36.
- One number as a percent of another: part ÷ whole × 100. 36 of 240 is 15%.
- Percentage change: (new − old) ÷ old × 100. From 240 to 300 is a 25% increase.
- Reverse percentage: final ÷ (1 ± rate/100). 80 after 20% off started at 100.
Percentages never simply add up
A 20% rise followed by a 20% fall does not return you to the start: 100 becomes 120 and then 96. Two stacked discounts of 20% and 10% total 28%, not 30%. Each percentage is taken from a new base, so changes multiply rather than add — which is also why a 50% loss needs a 100% gain to recover.
Percent versus percentage point
When a rate moves from 4% to 6% it has risen by two percentage points and by 50 percent. Finance avoids the ambiguity entirely by using basis points: 100 basis points is one percentage point. Whenever you are comparing two percentages, say percentage points.
Common questions
How do you calculate a percentage of a number?
Multiply the number by the percent and divide by 100. 15% of 240 = 240 × 15 ÷ 100 = 36.
How do you work out a percentage backwards?
Divide the final amount by the multiplier. An item costing 80 after 20% off was 80 ÷ 0.8 = 100 originally.
How do you minus a percentage on a calculator?
Multiply by (1 − rate/100). To take 15% off 240, press 240 × 0.85 = 204. On calculators with a % key, 240 − 15 % also works.
How do you calculate percentages in Google Sheets or Excel?
Use =part/total and format the cell as a percentage. For percentage change use =(new-old)/old, and wrap it in IFERROR to handle a zero base.
How do you calculate a percentage in SQL?
Cast to a decimal before dividing, for example ROUND(100.0 * COUNT(*) / SUM(COUNT(*)) OVER (), 2) — integer division otherwise returns zero.
What is the difference between percent and percentage point?
A move from 4% to 6% is two percentage points but a 50 percent increase. Use percentage points when comparing two percentages.
Key takeaways
- Every percentage problem is a part, a share, a change or a reversal.
- Reverse percentages divide by the multiplier — they never subtract.
- Percentage changes compound; they never cancel out.
- Say percentage points when comparing two rates, and percent for relative change.