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percent change (percent difference)

Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value. The figures are arrived at by comparing the initial (or before) and final (or after) quantities according to a specific formula. It is assumed that both the initial and the final quantities are positive (larger than 0).

Suppose a quantity has an initial value of x1, and then increases or decreases to a final value of x2. The percent change, D%, is calculated by finding the difference x2 - x1 (subtracting the initial value from the final value), then dividing the result of this subtraction by x1 (the initial value), and finally multiplying by 100. Expressed as a formula:

D% = 100 (x2 - x1) / x1

If x2 > x1 (the final value is larger than the initial value, representing an increase in the variable quantity), then D% is a positive number. If x2 < x1 (the final value is smaller than the initial value, representing a decrease), then D% is a negative number.

As an example, suppose you buy stock in two companies A and B, both at a price of USD $1.25 per share in January of a given year. Suppose that by July, stock A has risen in value to USD $3.35 per share. Then for stock A:

DA% = 100 ($3.35 - $1.25) / $1.25 = +168%
Percent change is +168%, also expressed as a percent increase of 168%.

Imagine that stock B has fallen to USD $1.00 per share in the same time period. Then for stock B:

DB% = 100 ($1.00 - $1.25) / $1.25 = -20%
Percent change is -20%, also expressed as a percent decrease of 20%.

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This was last updated in March 2011

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