Calculation
Mathematical Formula For Calculating Percentage Difference
$$\text{Percentage Difference} = \frac{\left| \text{Value 1} – \text{Value 2} \right|}{\frac{\text{Value 1} + \text{Value 2}}{2}} \times 100$$
Example Broken Down With Steps
$$
\text{Given: Value 1 = 80, Value 2 = 100}
$$
$$
\text{Step 1: Subtract smaller value from larger value: } 100 – 80 = 20
$$
$$
\text{Step 2: Find the average of 80 and 100: } \frac{80 + 100}{2} = 90
$$
$$
\text{Step 3: Divide the difference by the average: } \frac{20}{90} = 0.2222
$$
$$
\text{Step 4: Multiply by 100: } 0.2222 \times 100 = 22.22
$$
$$
\text{Result: Percentage Difference is 22.22%.}
$$
Further Explained
Example: Compare 80 and 100.
Steps:
- Find the absolute difference between the values:
$$ 100 – 80 = 20 $$ - Find the average of the two values:
$$ \frac{80 + 100}{2} = 90 $$ - Divide the difference by the average:
$$ \frac{20}{90} = 0.2222 $$ - Convert to a percentage: Multiply by 100:
$$ 0.2222 \times 100 = 22.22\% $$ - Conclusion: The percentage difference is 22.22%.
Percentage Points vs. Percentage Difference
When comparing two values that are already expressed as percentages, it is important to distinguish between percentage point difference and relative percentage difference.
The Difference
Percentage points measure the arithmetic gap between two percentages
Percentage difference (or relative change) measures how large that gap is compared to one of the values
Example Broken Down With Steps
A test score improves from 60% to 75%.
Percentage point difference:
75% − 60% = 15 percentage points
Relative percentage difference:
(75 − 60) / 60 × 100 = 25%
The score increased by 15 percentage points, which represents a 25% relative improvement.
Why This Distinction Matters
Consider this statement: “Inflation fell by 2%.” This could mean either of two very different things:
Inflation dropped by 2 percentage points (for example, from 6% to 4%)
Inflation dropped by a 2% relative decrease (for example, from 6% to 5.88%)
The practical difference is significant. Our Percentage Difference Calculator above computes the difference between any two values. For absolute point differences between percentages, simply subtract one from the other.