Percentage Formula Sheet
All key formulas with worked examples. Print-ready revision aid.
Percentage Formula Sheet
Finding a Percentage of an Amount
Amount × (Percentage ÷ 100)
or: Amount × decimal multiplier
Example: Find 30% of 250
250 × (30 ÷ 100) = 250 × 0.30 = 75
30% of 250 = 75
Expressing as a Percentage
(Part ÷ Whole) × 100
Example: Express 18 as a percentage of 60
(18 ÷ 60) × 100 = 0.30 × 100 = 30%
18 is 30% of 60
Percentage Increase
New value = Original × (1 + r ÷ 100)
e.g. +12%: multiply by 1.12
Example: Increase £350 by 12%
£350 × 1.12 = £392
New value = £392
Percentage Decrease
New value = Original × (1 − r ÷ 100)
e.g. −25%: multiply by 0.75
Example: Decrease 480 by 25%
480 × 0.75 = 360
New value = 360
Percentage Change
((New − Original) ÷ Original) × 100
Positive = increase. Negative = decrease.
Example: A value rises from 80 to 92
((92 − 80) ÷ 80) × 100 = (12 ÷ 80) × 100 = 15%
15% increase
Reverse Percentage (after an increase)
Original = New value ÷ (1 + r ÷ 100)
e.g. after +20%: divide by 1.20
Example: After a 20% increase, price is £360
£360 ÷ 1.20 = £300
Original price = £300
Reverse Percentage (after a decrease)
Original = New value ÷ (1 − r ÷ 100)
e.g. after −15%: divide by 0.85
Example: After a 15% decrease, price is £340
£340 ÷ 0.85 = £400
Original price = £400
Compound Interest / Growth
A = P × (1 + r ÷ 100)ⁿ
P = principal, r = rate %, n = years, A = final amount
Example: £1,000 at 5% compound interest for 3 years
£1,000 × 1.05³ = £1,000 × 1.157625 = £1,157.63
Final amount = £1,157.63
Compound Depreciation / Decay
A = P × (1 − r ÷ 100)ⁿ
e.g. 20% depreciation p.a.: multiply by 0.80 each year
Example: Car worth £12,000 depreciates 20% p.a. for 2 years
£12,000 × 0.80² = £12,000 × 0.64 = £7,680
Value after 2 years = £7,680
Useful Multipliers
Key Tips
- Multiplier method: Always convert the percentage change to a decimal multiplier before calculating. It is faster and reduces errors.
- Reverse percentages: Divide by the multiplier, never subtract the percentage from the result.
- Two successive changes: Multiply the multipliers together. A 20% increase then a 20% decrease gives × 1.20 × 0.80 = × 0.96, which is a 4% overall decrease.
- Compound interest: Use the formula A = P(1 + r/100)ⁿ. Do not calculate each year separately unless asked to show working.
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