The MathBlog percentage difference calculator is a tool designed to help you quickly and easily calculate the percentage difference between two numbers. Whether you’re comparing prices, weights, or any other measurements, our calculator makes it simple to find the relative difference expressed as a percentage.

## Percentage difference calculator

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Percent difference formula

$$\frac {|V1 - V2|}{ \frac {V1 + V2}{2}} \times 100$$

## What is Percentage Difference?

Percentage difference is a measure that compares the absolute difference between two values relative to their average. Unlike percentage change, which measures the relative change from one value to another, percentage difference provides a symmetric comparison of two values, without considering direction.

### How to Calculate Percentage Difference

To calculate the percentage difference between two numbers, follow these steps:

1. Find the Absolute Difference: Subtract the smaller number from the larger number to ensure a positive result.
$$\text{Difference} = |V1 – V2|$$
2. Calculate the Average of the Two Numbers: Add the two numbers and divide by 2.
$$\text{Average} = \frac{V1 + V2}{2}$$
3. Divide the Difference by the Average: This normalizes the difference relative to the average value.
$$\text{Relative Difference} = \frac{\text{Difference}} {\text{Average}}$$
4. Multiply by 100 to Convert to a Percentage: This step converts the relative difference into a percentage.
$$\text{Percentage Difference} = \left( \frac{|V1 – V2|}{\frac{V1 + V2}{2}} \right) \times 100$$

### Example Calculation

Let’s walk through an example to see how this works. Suppose you want to compare the heights of two buildings: one is 150 meters tall and the other is 180 meters tall. Here’s how you can calculate the percentage difference:

1. Identify the Values: V1=150 meters, V2=180 meters.
2. Calculate the Absolute Difference:
$$\text{Difference} = |150 – 180| = 30 \text{ meters}$$
3. Calculate the Average:
$$\text{Average} = \frac{150 + 180}{2} = 165 \text{ meters}$$
4. Calculate the Relative Difference:
$$\text{Relative Difference} = \frac{30}{165} \approx 0.1818$$
5. Convert to a Percentage:
$$\text{Percentage Difference} = 0.1818 \times 100 \approx 18.18\%$$

Thus, the percentage difference between the heights of the two buildings is approximately 18.18%.

### Practical Applications

• Finance: Compare financial figures such as profits, expenses, or stock prices.
• Science: Measure differences in experimental results, data points, or sample measurements.
• Everyday Use: Compare prices, sizes, or quantities in day-to-day scenarios.

## Frequently Asked Questions

1. What is the difference between percentage difference and percentage change?

• Percentage Difference compares the absolute difference between two values relative to their average, without considering direction.
• Percentage Change measures the relative change from one value to another, considering the direction of change.

2. Can I use this calculator for any two numbers?

• Yes, the calculator works for any two positive numbers, allowing you to compare them easily.

3. Why is the average used in the calculation?

• Using the average as a reference point provides a balanced comparison between the two values, making the percentage difference symmetric and more meaningful.