The Percent Change Formula

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Formula

\text{Percent Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%

Used to calculate: The percentage increase or decrease from an original value to a new value.

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What Is the Percent Change Formula?

The percent change formula measures how much a value has increased or decreased relative to its original value. It expresses the difference between the new and original values as a percentage of the original value.

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Formula and Variables

\text{Percent Change} = \frac{N - O}{O} \times 100\%

Symbol MeaningUnit
NNew or final valueDepends on the problem
OOriginal or initial valueDepends on the problem
Percent ChangeRelative change from the original valuePercent (%)

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How to Use the Formula

Identify the original value and the new value. Subtract the original value from the new value, divide the difference by the original value, and multiply the result by 100 to express the change as a percentage. A positive result represents an increase, while a negative result represents a decrease.

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When Is This Formula Used?

The percent change formula is used to compare how a quantity changes over time or between an original and updated value.

Common uses:

– Measuring changes in prices or costs
– Comparing changes in measurements or quantities
– Measuring increases or decreases in financial and statistical data

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Important Notes

– A positive percent change indicates an increase, while a negative percent change indicates a decrease.
– The original value cannot be zero because division by zero is undefined.
– The original and new values should use the same units before the formula is applied.
– A common point of confusion is dividing by the new value instead of the original value.

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Alternate Forms

Alternate form:

\text{Percent Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%

Alternate form:

\text{Percent Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100\%

Alternate form:

\text{Relative Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}}

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