Percentage Calculations: All Five Types
Percentages underpin finance, statistics, science, and everyday decision-making. There are five core calculation types — mastering all of them removes uncertainty in any situation involving percentages.
1. What is X% of Y?
Result = Y × (X ÷ 100)
Example: 15% of 240 = 240 × 0.15 = 362. X is what % of Y?
% = (X ÷ Y) × 100
Example: 36 is what % of 240? → (36 ÷ 240) × 100 = 15%3. X is Y% of what number?
Whole = X ÷ (Y ÷ 100)
Example: 36 is 15% of what? → 36 ÷ 0.15 = 2404. Percentage Increase/Decrease
% change = [(New − Old) ÷ Old] × 1005. Finding Original Value After % Change
Original = Current ÷ (1 + % change)
Example: Price after 20% rise is £120 → 120 ÷ 1.20 = £100Mental Maths Tricks
- 10% → move decimal left one place
- 5% → half of 10%
- 1% → move decimal left two places
- 25% → divide by 4
- 33.3% → divide by 3
Solve any percentage problem: Free Percentage Calculator
The Three Core Percentage Problems
- Type 1 — What is X% of Y? Formula: result = (X/100) × Y. Example: 15% of 80 = 0.15 × 80 = 12.
- Type 2 — X is what percent of Y? Formula: percent = (X/Y) × 100. Example: 12 out of 80 = (12/80) × 100 = 15%.
- Type 3 — X is Y% of what number? Formula: whole = X ÷ (Y/100). Example: 12 is 15% of what? → 12 ÷ 0.15 = 80.
Percentage Change vs Percentage Points
A percentage change measures relative change: if a price rises from £40 to £50, the percentage increase is (50-40)/40 × 100 = 25%. A percentage point measures absolute difference between two percentages: if interest rates rise from 4% to 5%, that is a 1 percentage point increase, but a 25% relative increase. Confusing these two is a common error in financial reporting and political statistics. When a news headline says "unemployment fell by 2%", it almost certainly means 2 percentage points, not a 2% relative decrease in the unemployment rate.
Frequently Asked Questions
What is the difference between markup and margin?
Both are percentages used in pricing but calculated differently. Markup = profit ÷ cost × 100. Margin = profit ÷ selling price × 100. A £20 item sold for £25 has a 25% markup (5/20) but a 20% margin (5/25). Mixing these up when setting prices is a costly business error.
How do I calculate a percentage decrease?
Percentage decrease = (original - new) ÷ original × 100. Example: a shirt marked down from £60 to £45 = (60-45)/60 × 100 = 25% decrease. Note that a 25% decrease followed by a 25% increase does not return to the original value: 60 × 0.75 × 1.25 = 56.25 ≠ 60.
How do discounts stack?
Two percentage discounts do not add — they compound. A 20% discount followed by an additional 10% discount gives a total discount of 1 - (0.8 × 0.9) = 1 - 0.72 = 28%, not 30%. This matters when comparing advertised cumulative discounts.