Calculate Negative Percentage Change

Negative percentage change indicates a decrease in value. This calculator helps you determine how much a value has decreased relative to its original amount, expressed as a percentage.

What is Negative Percentage Change?

Negative percentage change measures the decrease in value from an original amount to a new amount, expressed as a percentage. It's commonly used in finance, economics, and science to track declines in performance, costs, or other metrics.

For example, if a stock price drops from $100 to $80, the negative percentage change is -20%. This means the value decreased by 20% relative to its original value.

How to Calculate Negative Percentage Change

To calculate negative percentage change, follow these steps:

Identify the original value (V_original).
Identify the new value (V_new).
Calculate the difference between the original and new values: Difference = V_original - V_new.
Divide the difference by the original value: Relative Change = Difference / V_original.
Multiply by 100 to convert to a percentage: Percentage Change = Relative Change × 100.

The result will be negative if the new value is less than the original value.

Formula

Percentage Change = [(V_original - V_new) / V_original] × 100

Where:

V_original = Original value
V_new = New value

If the result is negative, it indicates a decrease in value.

Worked Example

Suppose a company's revenue decreases from $50,000 to $40,000. Calculate the negative percentage change.

Original value (V_original) = $50,000
New value (V_new) = $40,000
Difference = $50,000 - $40,000 = $10,000
Relative Change = $10,000 / $50,000 = 0.2
Percentage Change = 0.2 × 100 = -20%

The revenue decreased by 20% relative to its original value.

Interpretation

A negative percentage change indicates a decrease in value. For example:

-10% means the value decreased by 10%.
-50% means the value decreased by 50%.

Negative percentage changes are often seen in:

Financial markets (stock prices, bond yields)
Economic indicators (GDP, inflation)
Performance metrics (sales, productivity)

Common Mistakes

When calculating negative percentage change, avoid these common errors:

Using the wrong order of values: Always subtract the new value from the original value (V_original - V_new).
Ignoring the negative sign: A negative result indicates a decrease, so don't drop the negative sign.
Using absolute values: Percentage change should be calculated using the actual values, not their absolute differences.

FAQ

What does a negative percentage change mean?: A negative percentage change indicates a decrease in value. For example, a -20% change means the value decreased by 20%.
How is negative percentage change different from positive percentage change?: Positive percentage change indicates an increase in value, while negative percentage change indicates a decrease. The calculation method is the same, but the sign of the result differs.
Can percentage change be more than 100%?: Yes, percentage change can be more than 100% if the new value is significantly larger than the original value. For example, if a value increases from 10 to 15, the percentage change is +50%.
When would I use negative percentage change?: Negative percentage change is used in finance to track declines in stock prices, bond yields, and economic indicators. It's also used in science to measure decreases in experimental results.
How do I calculate percentage change if the original value is zero?: Percentage change cannot be calculated if the original value is zero because division by zero is undefined. In such cases, you may need to reconsider your approach or use a different metric.