Basic Math
Percentage Change
$$
\text{Percentage Change} = \frac{P_1 - P_0}{|P_0|} \times 100\%
$$
Variables:
$P_0$ -- original value (non-zero)
$P_1$ -- new value
Example:
Original Value = 50, New Value = 75 → Percentage Change = 50%
\[\text{Percentage Change} = \frac{75 - 50}{|50|} \times 100\% = \frac{25}{50} \times 100\% = 50\%\]
Example:
Original Value = 80, New Value = 60 → Percentage Change = -25%
\[\text{Percentage Change} = \frac{60 - 80}{|80|} \times 100\% = \frac{-20}{80} \times 100\% = -25\%\]
Percentage Difference
$$
\text{Percentage Difference} = \frac{|P_1 - P_0|}{\frac{|P_0| + |P_1|}{2}} \times 100\%
$$
Variables:
$P_0$ -- first value (non-zero)
$P_1$ -- second value (non-zero)
Percentage difference quantifies the relative difference between two values, regardless of their order. It is useful for comparing the magnitude of change between two quantities, providing a normalized measure of how different they are relative to their average.
Example:
Value 1 = 50, Value 2 = 75 → Percentage Difference = 40%
\[\text{Percentage Difference} = \frac{|75 - 50|}{\frac{|50| + |75|}{2}} \times 100\% = \frac{25}{62.5} \times 100\% = 40\%\]
Example:
Value 1 = 80, Value 2 = 60 → Percentage Difference = 28.57%
\[\text{Percentage Difference} = \frac{|60 - 80|}{\frac{|80| + |60|}{2}} \times 100\% = \frac{20}{70} \times 100\% \approx 28.57\%\]
Percentage change measures how much a quantity has increased or decreased relative to its original value, expressed as a percentage. It quantifies the proportional difference between an initial value and a new value, providing a normalized way to compare changes across different scales.