Percentage change · growth · price rise
Percentage change calculator – work out growth and decline
Enter the old and new value to get the change both as a percentage and as an amount. The calculator draws a clear line between a per cent and a percentage point – two things that get muddled in the news and in reports all the time.
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Per cent or percentage point? This difference costs money
Suppose a mortgage rate rises from two per cent to three. The rise is one percentage point. But your interest cost goes up 50 per cent, because three is one and a half times two. Both numbers are correct, and they describe the same change – but only one tells you how much money leaves your account.
| Situation | Change | Percentage points | Per cent |
|---|---|---|---|
| Loan interest rate | 2% → 3% | +1 | +50% |
| Tax rate | 20% → 22% | +2 | +10.00% |
| Party poll rating | 18% → 21% | +3 | +16.67% |
| Unemployment rate | 8% → 7% | −1 | −12.50% |
Rule of thumb: when both numbers are already percentages, their difference is in percentage points. When you compare numbers that are not percentages – pounds, items, miles – the difference relative to the original is in per cent.
Why 20% up and 20% down doesn't get you back to the start
This is the best-known trap in percentage maths. Take £100:
- A 20% rise →
100 × 1.2 = £120 - A 20% fall →
120 × 0.8 = £96
The result is £96, not £100. The reason: the first 20% was taken from a hundred, the second from a hundred and
twenty. The reference number changed mid-calculation. To get back to a hundred you'd need a rise of
(100 − 96) / 96 × 100 = 4.17%.
The same asymmetry shows up in a comparison: 120 is 20% bigger than 100, but 100 is only 16.67% smaller than 120. The calculator's Compare two numbers tab shows both directions at once, so you don't accidentally report the wrong figure.
Where percentage change is used
Price rises and inflation
An electricity bill of £78 → £96 is a rise of 23.08%. To see the yearly impact, multiply the difference in pounds by twelve: £18 × 12 = £216 a year. You can get the pound impact of a fuel price rise more precisely with the fuel price calculator, which takes consumption and mileage into account.
Revenue and sales trends
In business, growth is talked about over two horizons: month on month (MoM) and against the same period last year (YoY). Both use the same formula, only the comparison period changes. Because of seasonality, the year-on-year comparison is usually more reliable. The average annual growth over several years (CAGR) is worked out by the margin and growth calculator.
Pay and income
A pay rise of £2,850 → £2,990 is 4.91%. A gross rise doesn't reach your account unchanged, though, because some goes to tax and National Insurance. You can get an estimate of the net effect from the salary percentage calculator.
Research and reporting
When you report results, always state the reference point. "The share rose 3 percentage points (from 18% to 21%)" is unambiguous. A bare "rose 3 per cent" misleads the reader. There's a dedicated page for percentages in a dissertation: percentages in a dissertation.
The formulas at a glance
change % = (new − old) / old × 100
percentage points = new % − old %
A compared with B = (A − B) / B × 100
The third formula is the same as the first, but the wording changes: "how much bigger" means that B is the reference number, i.e. 100%. If you swap the numbers, you get a different answer – and that's correct, because the question is different too.
The basics of percentage change
A change is always calculated from the starting value. That's why a rise and a fall don't cancel out and why comparing two numbers gives a different result in each direction.
Formulas and examples
Percentage change
(new − old) / old × 100Example
240 → 312: 72 / 240 × 100 = 30% growth.
Note
A negative result means a decrease.
Difference in percentage points
new % − old %Example
An interest rate 2% → 3% is 1 percentage point but a 50% higher rate.
Note
Use this whenever both numbers being compared are already percentages.
Difference between two numbers
(A − B) / B × 100Example
120 vs. 100: +20%. The other way, 100 vs. 120: −16.67%.
Note
The base B decides. That's why the directions aren't symmetric.
Return to the original
(old − new) / new × 100Example
£100 → £120 → getting back needs −16.67%, not −20%.
Note
This row appears in the calculator's result automatically.
Concepts and classification
| Growth | A positive change relative to the starting value. |
|---|---|
| Decline | A negative change relative to the starting value. |
| Percentage point | The difference between two percentages. |
| MoM / YoY | Comparison with the previous month or the same period a year earlier. |
| Multiplier | The new value divided by the old; 1.3 means 30% growth. |
Limitations of the calculator
- A change starting from zero cannot be expressed as a percentage.
- Growth over several periods isn't added together – use the average annual growth rate.
- Seasonality distorts a month-on-month comparison; a year-on-year comparison is more reliable.
- The calculator does not judge whether a change is statistically significant.
How up to date the information is
When it was checked
Content and the percentages used were checked on 12 August 2026.
Disclaimer
The calculator gives a mathematical result from the numbers you enter. It is not an official decision, an offer or professional advice. See the terms of use.
Topics
This calculator belongs to the following topic areas. On the topic page you'll find all the calculators and guides on the same theme in one place.
Calculators that involve percentage change
Frequently asked questions about percentage change
How do I work out the percentage change between two numbers?
Subtract the old value from the new one, divide by the old value and multiply by 100: (new − old) / old × 100. For example 240 → 312 is (312 − 240) / 240 × 100 = 30% growth.
What is a percentage point?
A percentage point is the difference between two percentages. When an interest rate rises from 2% to 3%, the rise is one percentage point. In relative terms, though, the rate rose 50%. Use percentage points whenever both numbers being compared are already percentages.
Why doesn't a 20% fall cancel a 20% rise?
Because the percentage is calculated from a different number. £100 + 20% = £120, and £120 − 20% = £96. To get back to £100 you'd need a 4.17% rise. The calculator shows a "Return to the original needs" row so you don't have to work it out separately.
How much bigger is A than B?
The formula is (A − B) / B × 100, where B is the reference number. 120 is 20% bigger than 100. Note that the other way round the number is different: 100 is 16.67% smaller than 120. The calculator shows both directions.
How do I work out growth over several years?
You don't add or average the individual yearly growth percentages. Use the compound annual growth rate (CAGR), which you get from the margin and growth calculator by entering the start and end values and the number of periods.
Can I work out a percentage change when the original value is zero?
No. Growing from zero to any number would be a mathematically infinite percentage change, because the denominator of the division would be zero. In that case, report the change as a count instead, e.g. "0 → 15 items".