Use the Percentage Increase vs Percentage Difference
Use percentage increase or decrease when one number is clearly the old starting value and the other is the new value. Use percentage difference when you are comparing two numbers and neither number is the obvious starting point.
If the question says “from” one value “to” another value, use percentage change. If the question asks how different two values are, use percentage difference.
Want the correct formula automatically?
The percentage calculator includes modes for percentage increase, percentage decrease and percentage difference.
The main difference
Percentage increase or decrease is directional. It tells you how much a number has changed compared with its original starting value.
Percentage difference is neutral. It compares two values against their average, so the result is the same whichever number you put first.
| Calculation | Best for | Uses a starting value? | Example question |
|---|---|---|---|
| Percentage increase | Growth, rises, price increases | Yes | How much did £100 rise to £125? |
| Percentage decrease | Falls, reductions, drops | Yes | How much did £125 fall to £100? |
| Percentage difference | Comparing two values fairly | No | How different are 100 and 125? |
What is percentage increase?
Percentage increase measures how much a value has gone up compared with where it started. The old value is the base.
Percentage increase = (new value − old value) ÷ old value × 100
Example:
Old value = £100
New value = £125
Increase = £25
£25 ÷ £100 × 100 = 25% increaseThis is the right formula for pay rises, bill increases, price rises, investment growth, rent increases and any situation where you have a clear “before” and “after”.
For salary examples, the pay rise calculator is usually more useful because it converts the rise into yearly, monthly and weekly figures.
What is percentage decrease?
Percentage decrease works the same way, but the new value is lower than the old value. The old value is still the base.
Percentage decrease = (old value − new value) ÷ old value × 100
Example:
Old value = £125
New value = £100
Decrease = £25
£25 ÷ £125 × 100 = 20% decreaseThis is why a 25% increase followed by a 20% decrease can bring you back to the original number. The base changed between the two calculations.
What is percentage difference?
Percentage difference compares two values against their average. It is useful when neither value is the original or “correct” value.
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Example:
A = 100
B = 125
Difference = 25
Average = 112.5
25 ÷ 112.5 × 100 = 22.22%Use percentage difference for neutral comparisons, such as comparing two quotes, two measurements, two prices from different shops, or two estimates where neither is the original value.
Side-by-side example: 100 and 125
The same two numbers can produce different percentage answers depending on the question being asked.
| Question | Formula | Answer |
|---|---|---|
| What is the increase from 100 to 125? | (125 − 100) ÷ 100 × 100 | 25% increase |
| What is the decrease from 125 to 100? | (125 − 100) ÷ 125 × 100 | 20% decrease |
| What is the percentage difference between 100 and 125? | 25 ÷ 112.5 × 100 | 22.22% difference |
None of these answers is “wrong”. They answer different questions.
Percentage points are different again
A percentage point is the direct difference between two percentages.
Example:
A rate moves from 20% to 25%.
Percentage point change = 25% − 20% = 5 percentage points
Percentage increase = 5 ÷ 20 × 100 = 25%This matters with interest rates, tax rates, conversion rates, pass rates and survey results. “Up 5 percentage points” is not the same as “up 5%”.
Everyday examples
If the comparison is about shopping value, the unit price comparison calculator may give a clearer answer than percentage difference.
Common mistakes
Which formula should you use?
| Your situation | Use this calculation | Related tool |
|---|---|---|
| A price rose from old to new | Percentage increase | Percentage Calculator |
| A price fell from old to new | Percentage decrease | Discount Calculator |
| You are comparing two quotes | Percentage difference | Percentage Calculator |
| You are adding or removing VAT | VAT formula | VAT Calculator |
| You are comparing pack sizes | Unit price | Unit Price Calculator |
FAQs
Is percentage difference the same as percentage increase?
No. Percentage increase compares a new value with an old starting value. Percentage difference compares two values against their average.
Why is the percentage increase from 100 to 125 not the same as the decrease from 125 to 100?
Because the base value changes. The increase uses 100 as the base, while the decrease uses 125 as the base.
When should I use percentage difference?
Use percentage difference when you are comparing two values and neither is clearly the original or starting value.
What is the difference between percent and percentage points?
Percentage points measure the direct gap between two percentages. Percent change measures the size of the change relative to the starting percentage.
Can I use percentage difference for discounts?
Usually no. A discount has an original price and a sale price, so percentage decrease or discount percentage is normally the right calculation.