Percentage Change
$$\text{Percentage Change} = \frac{\text{New} - \text{Old}}{|\text{Old}|} \times 100$$
What is Percentage Change?
Percentage change measures how much a quantity has changed relative to its original (starting) value, expressed as a percentage. It is signed: a positive result is an increase; a negative result is a decrease. The formula anchors the comparison to the starting point: $$\text{Percentage Change} = \frac{\text{New} - \text{Old}}{|\text{Old}|} \times 100$$
This directionality is what distinguishes percentage change from percentage difference. Percentage change has a clear temporal or causal order — there is a "before" and an "after." When that order does not exist (two independent measurements, two simultaneous observations), percentage difference using the average as the base is the appropriate metric.
Sequential percentage changes do not add linearly. A 30% increase followed by a 20% decrease yields a net change of 4% — not 10% — because the second change is applied to the already-modified value. Percentage changes must be multiplied as growth factors (1.30 × 0.80 = 1.04) rather than summed.
When to use Percentage Change
Use percentage change when there is a clear reference point — a prior period, a baseline measurement, or an original value — and you want to express how much it has grown or shrunk. Use percentage difference instead when comparing two values with no defined starting point. Use percentage points when comparing two percentage figures directly.
Worked examples
| Scenario | Old value | New value | Calculation | Result |
|---|---|---|---|---|
| Stock price | $80 | $100 | (100 − 80) / 80 × 100 | +25.00% |
| Monthly sales | $50,000 | $42,000 | (42,000 − 50,000) / 50,000 × 100 | −16.00% |
| Temperature | 20 °C | 25 °C | (25 − 20) / 20 × 100 | +25.00% |
| Website traffic | 1,200 | 900 | (900 − 1,200) / 1,200 × 100 | −25.00% |
Common pitfalls
When the original value is zero, percentage change is mathematically undefined — division by zero. When the original value is negative (e.g., a loss turning into a profit), the sign of the result can be counterintuitive. In both cases, report the absolute change alongside the percentage change, or note that the percentage is not meaningful.
Frequently asked questions
Why is a 50% increase followed by a 50% decrease not zero?
Because each percentage uses a different base. Starting at 100, a 50% increase gives 150. A 50% decrease on 150 gives 75 — a net loss of 25%. The net multiplier is 1.50 × 0.50 = 0.75, confirming a 25% net decline.
What is the difference between percentage change and percentage difference?
Percentage change uses the original value as the denominator and implies a before-and-after relationship. Percentage difference uses the average of both values and is symmetric — it does not matter which value is "first." Use percentage difference when there is no temporal order between the two values.
How do I calculate percentage change when the old value is negative?
The formula still applies mathematically, but the result can be misleading. If revenue was −$200k and improved to −$50k, the formula gives (−50 − (−200)) / 200 × 100 = +75%. This correctly shows improvement, but readers may interpret it as moving from a loss to a profit. Always state the absolute values alongside the percentage.