ToolCalcu

Percentage Change Calculator

Compare an old and a new value to see the percentage increase or decrease, or start from a number and apply a percentage change to it.

Your numbers

Result

Please correct the highlighted fields.
Percentage change
+25%
Difference
+20
Direction
Increase

How percentage change is calculated

Percentage change compares the difference between two values with the starting value. A positive result is an increase and a negative result is a decrease.

If the starting value is negative, its absolute value is used as the base so that the sign still shows the direction of the change. When the starting value is 0 the percentage is undefined, because any change from zero is infinite in relative terms.

Formulas used

Change % = (Ending − Starting) ÷ |Starting| × 100
Increase: Result = Starting × (1 + Percentage ÷ 100)
Decrease: Result = Starting × (1 − Percentage ÷ 100)

Worked example

A value rises from 80 to 100:

  1. Difference: 100 − 80 = 20
  2. Change: 20 ÷ 80 × 100 = 25%

80 → 100 is a +25% change.

Assumptions and limits

  • The starting value is the reference; swapping the two values gives a different percentage.
  • Percentage points (for example a rate going from 4% to 5%) are a different measure from percentage change.
  • Values are limited to plus or minus one trillion.

Common questions

Why is a 50% decrease not undone by a 50% increase?

Each percentage applies to a different starting value. Losing 50% of 100 leaves 50, and gaining 50% of 50 adds only 25, giving 75. To get back to 100 you need an increase of 100%.

Should I use percentage change or percentage difference?

Percentage change has a clear starting point, such as last year’s price compared with this year’s. When neither value is a natural reference, other formulas that divide by the average of both values are sometimes used. This calculator always uses the starting value as the reference.

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