Percentage change is used everywhere - from price increases to discount calculations. This guide shows you how to calculate percentage changes quickly and accurately.
Percentage Change Formula
Percentage Change = ((New - Old) ÷ Old) × 100
Positive result = increase | Negative result = decrease
Percentage Increase Examples
Price Increase
Old price: £50 | New price: £60
Change = ((60 - 50) ÷ 50) × 100 = 20% increase
Salary Rise
Old salary: £30,000 | New salary: £32,500
Change = ((32,500 - 30,000) ÷ 30,000) × 100 = 8.3% increase
Percentage Decrease Examples
Sale Discount
Original: £80 | Sale price: £60
Change = ((60 - 80) ÷ 80) × 100 = -25% (25% off)
Calculate New Value from Percentage
For Increase: New = Old × (1 + Percentage/100)
£100 with 20% increase = £100 × 1.20 = £120
For Decrease: New = Old × (1 - Percentage/100)
£100 with 25% off = £100 × 0.75 = £75
Quick Reference Table
| Change | Multiply by | Example (£100) |
|---|---|---|
| +10% | 1.10 | £110 |
| +20% | 1.20 | £120 |
| +50% | 1.50 | £150 |
| +100% | 2.00 | £200 |
| -10% | 0.90 | £90 |
| -25% | 0.75 | £75 |
| -50% | 0.50 | £50 |
| -75% | 0.25 | £25 |
Finding Original Value
If you know the increased price
Price after 20% increase: £120
Original = £120 ÷ 1.20 = £100
If you know the discounted price
Price after 25% off: £75
Original = £75 ÷ 0.75 = £100
Warning: A 20% increase followed by a 20% decrease does NOT return you to the original. £100 +20% = £120, then £120 -20% = £96. You lose 4%!
Practical Applications
- Price comparisons: Has my shopping basket cost increased?
- Investment returns: How much has my portfolio grown?
- Salary negotiations: What percentage raise should I ask for?
- Sales and discounts: Is this really a good deal?
- Year-on-year changes: Compare business metrics