How to Calculate Percentage Change Between Positive and Negative Number

What is Percentage Change?

Percentage change measures how much a quantity has increased or decreased relative to its original value. It's expressed as a percentage and is widely used in finance, economics, and everyday life to compare values over time.

The percentage change is particularly useful when comparing values that are not in the same units or when analyzing growth rates. For example, if a stock price increases from $50 to $60, the percentage change helps determine the relative growth regardless of the absolute difference.

Percentage Change Formula

Where:

• New Value - The value after the change
• Original Value - The initial value before the change

The result can be positive (increase) or negative (decrease). A positive percentage indicates growth, while a negative percentage indicates a decline.

Calculating Between Positive and Negative Numbers

When calculating percentage change between positive and negative numbers, the formula remains the same. The sign of the result depends on the relationship between the new and original values:

• If the new value is greater than the original value (both positive), the percentage change is positive.
• If the new value is less than the original value (both positive), the percentage change is negative.
• If the original value is negative and the new value is more negative, the percentage change is positive (the negative value has increased in magnitude).
• If the original value is negative and the new value is less negative (closer to zero), the percentage change is negative.

Worked Examples

Example 1: Positive to Positive

Original Value = $100
New Value = $120

Calculation: [(120 - 100) / 100] × 100% = 20%

Result: 20% increase

Example 2: Positive to Negative

Original Value = $100
New Value = $80

Calculation: [(80 - 100) / 100] × 100% = -20%

Result: 20% decrease

Example 3: Negative to More Negative

Original Value = -$50
New Value = -$60

Calculation: [(-60 - (-50)) / -50] × 100% = [( -10 ) / -50] × 100% = 20%

Result: 20% increase (the negative value has become more negative)

Example 4: Negative to Less Negative

Original Value = -$50
New Value = -$40

Calculation: [(-40 - (-50)) / -50] × 100% = [10 / -50] × 100% = -20%

Result: 20% decrease (the negative value has become less negative)

Common Mistakes

When calculating percentage change between positive and negative numbers, several common errors can occur:

1. Ignoring the sign of the original value: The formula requires division by the original value, which can change the sign of the result.
2. Incorrectly interpreting negative results: A negative percentage change doesn't always mean a decrease - it depends on the original value's sign.
3. Miscounting the order of subtraction: Always subtract the original value from the new value in the numerator.