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
Positive result = increase | Negative result = decrease
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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
£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
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
How Percentage Change Calculations Work: The Methodology
Percentage change is a fundamental mathematical concept that expresses the degree of change over time as a proportion of the original value. The calculation relies on a straightforward ratio that compares the difference between two values against the original (or reference) value, then multiplies the result by 100 to convert it into a percentage.
The core formula, ((New Value - Old Value) / Old Value) x 100, works in three distinct steps. First, you find the absolute difference between the two values by subtracting the old value from the new value. Second, you divide this difference by the old value to express it as a decimal proportion. Third, you multiply by 100 to convert the decimal into a percentage. A positive result indicates an increase, while a negative result indicates a decrease.
It is important to note that percentage change is always calculated relative to the original value, not the new value. This distinction matters because a 50% increase followed by a 50% decrease does not return you to the original amount. For example, if £100 increases by 50% to £150, then decreases by 50%, you get £75 -- not the original £100. This asymmetry is a common source of confusion and errors in financial calculations.
When dealing with successive percentage changes, you should multiply the individual multipliers together rather than simply adding or subtracting the percentages. For instance, a 10% increase followed by a 20% increase is calculated as 1.10 x 1.20 = 1.32, which represents a 32% total increase, not 30%.
UK-Specific Context: Percentage Changes in Everyday Life
Percentage changes are deeply embedded in UK financial and economic reporting. The Consumer Prices Index (CPI), published monthly by the Office for National Statistics (ONS), measures inflation as a percentage change in the cost of a basket of goods and services. As of early 2025, UK inflation has been tracking around 3-4%, meaning the average cost of goods has risen by that percentage over the previous year.
The Bank of England base rate, which directly influences mortgage rates and savings account yields, is often discussed in terms of percentage point changes. It is crucial to understand the difference between a percentage change and a percentage point change. If the base rate moves from 4.5% to 5.0%, that is a 0.5 percentage point increase but represents an 11.1% percentage change in the rate itself.
Council tax increases in England are typically capped at around 5% per year (including the adult social care precept) without a local referendum. Understanding how to calculate these percentage increases helps residents verify their council tax bills and budget accordingly. Similarly, utility price changes under Ofgem's energy price cap are regularly reported as percentage changes, helping consumers understand how their bills will be affected each quarter.
In the UK property market, percentage changes are used to track house price growth. The Land Registry House Price Index and reports from Halifax and Nationwide all express property value changes as percentages. The average UK house price has seen significant percentage swings over recent decades, from double-digit annual growth in the mid-2000s to negative percentage changes during the 2008 financial crisis.
Worked Examples: Real-World UK Scenarios
Example 1: Energy Bill Increase
Your quarterly energy bill was £450 last quarter and is now £520 this quarter.
Step 1: Difference = £520 - £450 = £70
Step 2: Divide by original = £70 / £450 = 0.1556
Step 3: Multiply by 100 = 15.56% increase
Example 2: House Price Change
You bought a flat for £225,000 in 2020. It is now valued at £258,000.
Change = ((£258,000 - £225,000) / £225,000) x 100 = 14.67% increase
This represents a gain of £33,000 in equity before mortgage interest and costs.
Example 3: Supermarket Price Comparison
A pack of butter cost £1.85 last year and now costs £2.15.
Change = ((£2.15 - £1.85) / £1.85) x 100 = 16.22% increase
This is sometimes called "shrinkflation" when product sizes also decrease alongside price rises.
Common Mistakes and Tips
Frequently Asked Questions
What is the difference between percentage change and percentage difference?
Percentage change measures how a value has moved from one point to another over time and uses the original value as the base. Percentage difference compares two values at the same point in time and uses their average as the base. For instance, comparing this year's price to last year's price is a percentage change, while comparing the price of the same product at two different shops is a percentage difference.
How do I calculate reverse percentage to find the original price before a discount?
To find the original price before a percentage was added or removed, divide by the multiplier. If an item costs £90 after a 10% discount, the original price is £90 / 0.90 = £100. If a price is £120 after a 20% increase, the original was £120 / 1.20 = £100. This technique is useful for working out pre-VAT prices (divide by 1.20 for the standard 20% VAT rate).
Can percentage change be more than 100%?
Yes. A percentage change exceeding 100% means the value has more than doubled. For example, if a share price goes from £5 to £15, that is a 200% increase. In the UK property market, many homes purchased before 2000 have seen percentage increases well above 100% in total value growth.
How do I calculate the overall percentage change from multiple consecutive changes?
Convert each percentage change to a multiplier (e.g., +10% = 1.10, -5% = 0.95), multiply all the multipliers together, then subtract 1 and multiply by 100. For example, +10% then -5% then +20% = 1.10 x 0.95 x 1.20 = 1.254, so the total change is +25.4%. Simply adding 10 - 5 + 20 = 25% would be incorrect.
Percentage Change in UK Economic and Financial Contexts
Understanding percentage change is essential for interpreting key UK economic indicators that directly affect household finances. The Consumer Prices Index (CPI), published monthly by the Office for National Statistics (ONS), measures the percentage change in the price of a basket of goods and services over 12 months. This figure, commonly referred to as the UK inflation rate, influences Bank of England interest rate decisions, wage negotiations, pension uprating, and government benefit adjustments. When CPI rose above 11% in October 2022, it represented the highest percentage increase in living costs in over 40 years, triggering a cost-of-living crisis that affected millions of UK households.
UK house prices are another area where percentage change calculations are critical. The ONS House Price Index, the Land Registry index, and private indices from Halifax and Nationwide all report monthly and annual percentage changes in average house prices across different UK regions. A 5% annual increase on the UK average house price of approximately 290,000 pounds represents a gain of 14,500 pounds, illustrating how even modest percentage changes translate to significant sums in the property market. First-time buyers, investors, and homeowners all rely on these percentage change figures to make informed property decisions.
In the workplace, UK employees frequently encounter percentage changes when negotiating pay rises, understanding bonus calculations, and interpreting pension fund performance. The Annual Survey of Hours and Earnings (ASHE), published by the ONS, reports median wage growth as a percentage change, providing a benchmark for salary negotiations. Understanding whether a 3% pay rise keeps pace with inflation (comparing it to the CPI percentage change) is a fundamental financial literacy skill that directly affects purchasing power and long-term wealth accumulation for workers across the United Kingdom.
Frequently Asked Questions About Percentage Change
How is UK inflation (CPI) calculated using percentage change?
What is the difference between percentage change and percentage point change?
How do I calculate the real percentage change in my UK salary after inflation?
James Mitchell, ACCA
Chartered Accountant & Former HMRC Advisor
James is a Chartered Certified Accountant (ACCA) specialising in UK personal taxation and financial planning. With over 12 years in practice and a background as a former HMRC compliance officer, he brings authoritative insight to complex tax topics.