Percentage change: formula, calculator and worked example

What the symbols mean

$p$: the percentage change; positive is an increase, negative a decrease (%)
$V_{1}$: the original (old) value
$V_{2}$: the new value

When to use it

Use it for price rises and discounts, population or sales changes, and test-score improvements. Solving for $V_{1}$ is the "reverse percentage" problem: a price after a 15% rise is 92, what was it before?

Worked example

A price rises from 80 to 92. What is the percentage change? (V₁ = 80, V₂ = 92)

Start from the formula.
$p = \frac{V_{2} - V_{1}}{V_{1}} \cdot 100$
Substitute $V_{1}$ = $80$ , $V_{2}$ = $92$ and work it out.
$p = \frac{92 - 80}{80} \cdot 100$
$= \frac{12}{80} \cdot 100$
$= 0.15 \cdot 100$
$= 15 %$
Positive: an increase of 15%.

Answer p = 15%

Common mistakes

Dividing by the new value. Percentage change is always relative to the *old* value.
Undoing a percentage by applying the opposite percentage: a 20% rise then a 20% fall gives 96%, not 100%.
Confusing percentage change with percentage points: 5% to 7% is a rise of 2 points, or 40%.

Calculator

What the symbols mean

When to use it

Worked example

Common mistakes