What is percentage change?
Percentage change measures how much a value has grown or shrunk relative to where it started. It is how we compare price rises, salary increases, sales growth, website traffic, test scores and stock prices on a common scale, whether the original number was 8 or 8 million.
A positive result is a percentage increase and a negative result is a percentage decrease. Because the change is always measured against the old value, the order matters: going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease.
How to use the calculator
- Choose Change between two values to compare an old and a new number, or Increase / decrease by % to apply a percentage to a number.
- Enter the values. Results update as you type.
- Read the percentage change, the absolute difference and the symmetric percentage difference, then copy the result if you need it.
Formulas
Percentage change = (New − Old) ÷ |Old| × 100
Percentage difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
Increase by p% = X × (1 + p ÷ 100) Decrease by p% = X × (1 − p ÷ 100)
Percentage change has a direction (old to new). Percentage difference has none and compares two values against their average, which is useful when neither number is the “starting point”, for example two quotes from different suppliers.
Examples
- A price rises from 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase.
- Traffic falls from 1,200 to 900 visits: (900 − 1,200) ÷ 1,200 × 100 = 25% decrease.
- A value of 250 increased by 12% is 250 × 1.12 = 280; decreased by 12% it is 220.
- A 50% fall followed by a 50% rise does not get you back to the start: 100 → 50 → 75.
More worked examples
House prices: a UK home that rose from £280,000 to £301,000 increased by 7.5%.
Share price: a stock that fell from $50 to $42 dropped by 16%. To get back to $50 it now needs to rise by about 19%.
Common mistakes to avoid
- Dividing by the new value. Percentage change is always measured against the original value.
- Confusing percent and percentage points. A rate moving from 4% to 5% is a 1-point rise but a 25% increase.
- Expecting equal ups and downs to cancel out. A 50% fall needs a 100% rise to recover. For “X% of Y” questions, use the percentage calculator.
Sources and methodology
The calculations on this page follow these published standards and references. The code is covered by automated tests against known values.
- Standard percentage arithmetic