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Percent Change

Percent change is a way to describe how much a value has increased or decreased, expressed as a percentage of the original amount. If a price goes from 50to50 to60, the percent change tells you that it increased by 20%.

Percent change measures the relative difference between an original value and a new value, expressed as a percentage. It is calculated by finding the difference between the new value and the original value, dividing by the original value, and multiplying by 100. A positive result indicates a percent increase, while a negative result indicates a percent decrease.

Key Formula

Percent Change=New Value−Original ValueOriginal Value×100\text{Percent Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100
Where:
  • NewValueNew Value = the value after the change
  • OriginalValueOriginal Value = the starting value before the change

Worked Example

Problem: A pair of shoes originally costs 80.Duringasale,thepricedropsto80. During a sale, the price drops to60. What is the percent change in price?
Step 1: Identify the original value and the new value.
Original Value=80,New Value=60\text{Original Value} = 80, \quad \text{New Value} = 60
Step 2: Subtract the original value from the new value to find the change.
60−80=−2060 - 80 = -20
Step 3: Divide the change by the original value.
−2080=−0.25\frac{-20}{80} = -0.25
Step 4: Multiply by 100 to convert to a percentage.
−0.25×100=−25%-0.25 \times 100 = -25\%
Answer: The percent change is −25%, meaning the price decreased by 25%.

Visualization

Why It Matters

Percent change shows up constantly in everyday life — tracking sale prices at a store, comparing population growth between years, or understanding how your grades shifted from one semester to the next. In finance, it's used to measure how stock prices, inflation rates, and savings accounts grow or shrink over time. Understanding percent change helps you make meaningful comparisons, especially when the original amounts are very different.

Common Mistakes

Mistake: Dividing by the new value instead of the original value.
Correction: Always divide by the original (starting) value. The formula measures change relative to where you started, not where you ended up.
Mistake: Confusing the direction of subtraction and losing the sign.
Correction: Always compute New Value minus Original Value. A negative result means a decrease, and a positive result means an increase. The sign carries important meaning.

Related Terms