Master Percentages: Discounts, Tips & Tax Made Easy
Percentages express a part per hundred. The key is identifying the base value before choosing the operation.
Start with the idea
To find p percent of x, calculate p ÷ 100 × x. To find what percentage a is of b, calculate a ÷ b × 100. Percentage change is (new − old) ÷ old × 100.
A percentage-point change is different from a percentage change. Moving from 10% to 12% is an increase of 2 percentage points, but a 20% relative increase.
Worked example
20% of 150 is 0.20 × 150 = 30. If a price rises from 80 to 100, the increase is 20 and the percentage increase is 20 ÷ 80 × 100 = 25%.
Reversing a percentage is not symmetric. A 20% fall from 100 gives 80, but a 20% rise from 80 gives 96, not 100.
Quick reference
| Item | Meaning |
|---|---|
| Find p% of x | p/100 × x |
| a is what % of b? | a/b × 100 |
| Percentage change | (new−old)/old × 100 |
| Percentage points | New rate − old rate |
Common mistakes
- Using the new value as the base for an increase
- Confusing percentages with percentage points
- Assuming equal increases and decreases cancel
- Dividing by zero
Practical steps
- Identify the base or original value.
- Convert the percentage to a decimal.
- Apply the correct formula.
- Check whether the result is reasonable.
- State clearly whether the change is relative or in percentage points.
Run your own numbers
Use the related Fynzo tool to test different inputs and compare results.
Open the Percentage Calculator →Sources and review note
This article was reviewed for language, calculation examples and source links by Yasser Chahir, Fynzo editor. Last reviewed: July 31, 2026. It is general educational information, not medical, financial, tax or legal advice.