Percentages: the essentials
Percentages show a value “per 100”. They’re used everywhere: discounts, interest rates, tax rates, and growth.
Basic formulas
- Percentage of a number:
value = base * (percent / 100) - Percent change:
changePercent = (new - old) / old * 100 - Before an increase:
original = final / (1 + percent / 100) - Before a decrease or discount:
original = final / (1 - percent / 100)
Percentage points vs percent
These two are easy to mix up:
- Going from 20% to 25% is +5 percentage points.
- Relative change is +25% (because 5 is 25% of 20).
Discounts and markups
A common surprise:
- Increase by 20% and then decrease by 20% does not return to the start.
Example:
- Start 100 → +20% = 120
- 120 → −20% = 96
Rounding
For money, rounding to whole currency units is often fine. For rates, one or two decimals can be more informative.
Use the calculator to explore scenarios quickly and avoid manual mistakes.