How to Calculate Percentage Change
Percentage change equals the new value minus the old value, divided by the old value, times 100: ((new − old) ÷ old) × 100.
Formula
Steps
- 1Identify the old and new values. The old value is the starting (earlier) number and the new value is the ending (later) number you are comparing to it.
- 2Subtract to find the change. Compute New value − Old value. A positive result is an increase; a negative result is a decrease.
- 3Divide by the OLD value. Divide the change by the old (original) value, never the new one. The starting value is always the denominator.
- 4Multiply by 100. Multiply by 100 to convert the decimal into a percent. A positive percent means growth; a negative percent means a decline.
Worked example
Suppose a good's price rises from $45 (old) to $54 (new). The change is 54 − 45 = 9. Divide by the old value: 9 ÷ 45 = 0.2. Multiply by 100: 0.2 × 100 = 20%. The price increased by 20%.
Frequently asked questions
What does the percentage change tell you?
It tells you how large a change is relative to where you started, not just the raw size of the change. A $9 jump is 20% off a $45 base but only 1% off a $900 base, so the percentage lets you compare changes of different sizes on a common scale. A positive value is an increase and a negative value is a decrease.
What is the difference between percentage change and percentage points?
Percentage change measures the relative change from the old value, while percentage points measure the simple arithmetic gap between two percentages. If unemployment goes from 5% to 8%, that is a 3 percentage-point increase but a 60% percentage change ((8 − 5) ÷ 5 × 100). Use percentage points when both figures are already percentages, like rates or shares.
Why do you divide by the old value and not the new one?
You divide by the old value because percentage change measures growth relative to the starting point, which is the baseline you are comparing against. Dividing by the new value instead would answer a different question and give a smaller number. This is the same base rule used in the inflation rate, real GDP growth, and elasticity formulas.
How can percentage change be negative?
The result is negative whenever the new value is smaller than the old value, because New − Old comes out negative. For example, a price falling from $50 to $40 gives (40 − 50) ÷ 50 × 100 = −20%, a 20% decrease. A negative percentage change simply signals a decline, such as deflation or a drop in output.
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