Maths⏱ 5 min read
How to Calculate Percentages: Every Type Explained
Percentages come up in almost every area of life — but there are several different types of percentage calculation, and people routinely mix them up. Here's every type with worked examples.
Percentages are everywhere — sales, tax, nutrition labels, statistics, grades — and most people can handle the basics but struggle with the trickier variations. Here's every type, clearly explained.
Type 1: What Is X% of Y?
Result = (X ÷ 100) × Y
What is 15% of £240?
= (15 ÷ 100) × 240
= 0.15 × 240
= £36
Type 2: What Percentage Is X of Y?
Percentage = (X ÷ Y) × 100
What percentage is 36 of 240?
= (36 ÷ 240) × 100
= 0.15 × 100 = 15%
Type 3: Percentage Increase
% Increase = ((New − Old) ÷ Old) × 100
Price rose from £80 to £94:
= ((94 − 80) ÷ 80) × 100
= (14 ÷ 80) × 100 = 17.5% increase
Type 4: Percentage Decrease
% Decrease = ((Old − New) ÷ Old) × 100
Salary cut from £45,000 to £39,600:
= ((45,000 − 39,600) ÷ 45,000) × 100
= (5,400 ÷ 45,000) × 100 = 12% decrease
Type 5: Finding the Original Value After a % Change
This is where most people go wrong. If a price is £117 after a 17% increase, what was the original price?
Original = New value ÷ (1 + % change)
WRONG: 117 − (117 × 0.17) = £97.11 ✗
CORRECT: 117 ÷ 1.17 = £100 ✓
After a 20% decrease, price is £64. Original?
= 64 ÷ (1 − 0.20) = 64 ÷ 0.80 = £80 ✓
Type 6: Applying Multiple Percentage Changes
Applying a 10% increase then a 10% decrease does NOT return to the original. Percentage changes multiply, they don't add.
£100 + 10% = £110
£110 − 10% = £99 (not £100!)
To apply multiple changes:
Final = Original × (1 + r₁) × (1 + r₂) × ...
+20%, then +15%, then −5%:
Final = Original × 1.20 × 1.15 × 0.95
= Original × 1.311 = net +31.1% overall
Type 7: Percentage Points vs Percentage Change
This distinction matters enormously in news and statistics. If interest rates rise from 2% to 5%, that's:
- 3 percentage points (the simple arithmetic difference)
- 150% increase (the percentage change: (5−2)/2 × 100)
Both are technically correct but describe different things. Politicians and journalists often deliberately confuse them. "Interest rates rose by 150%" and "interest rates rose by 3 percentage points" describe the same event but sound very different.
Mental Maths Shortcuts
10% = divide by 10
5% = half of 10%
1% = divide by 100
15% = 10% + 5%
17.5% = 10% + 5% + 2.5%
25% = divide by 4
75% = divide by 4, multiply by 3