How to Calculate a Percent Difference

Percent Difference Formula:

\[ \text{Percent Difference} = \frac{|Value_1 - Value_2|}{\frac{Value_1 + Value_2}{2}} \times 100\% \]

Percent Difference:

1. What is Percent Difference?

The percent difference is a measure of how much two values differ relative to their average. It's commonly used to compare two experimental values or to compare an experimental value with a theoretical value.

2. How the Formula Works

The percent difference formula is:

\[ \text{Percent Difference} = \frac{|Value_1 - Value_2|}{\frac{Value_1 + Value_2}{2}} \times 100\% \]

Where:

\( Value_1 \) — First measurement or value
\( Value_2 \) — Second measurement or value
The numerator is the absolute difference between the values
The denominator is the average of the two values

Key Points: The absolute value ensures the difference is always positive, and dividing by the average makes the result relative rather than absolute.

3. When to Use Percent Difference

Applications: Percent difference is useful when:

Comparing two experimental measurements
Assessing the difference between theoretical and experimental values
Evaluating the variation between two methods of measurement
Comparing before-and-after values in an experiment

4. Calculation Example

Example: If you measure a length as 8.5 cm and then as 9.1 cm:

Difference = |8.5 - 9.1| = 0.6
Average = (8.5 + 9.1)/2 = 8.8
Percent Difference = (0.6/8.8) × 100 = 6.82%

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between percent difference and percent change?
A: Percent change compares a new value to an old value, while percent difference compares any two values without considering one as reference.

Q2: Can percent difference be negative?
A: No, because we use absolute value in the numerator. It always ranges from 0% to 200%.

Q3: What does a 0% difference mean?
A: It means the two values are identical (no difference between them).

Q4: What's a good percent difference?
A: This depends on your field. In some experiments <5% might be excellent, while in others <20% might be acceptable.

Q5: How is this different from percentage error?
A: Percentage error compares a measured value to a known or accepted value, while percent difference compares any two values.