Percentage Change
Use the Percentage Change Calculator → Try the Percentage Change Quiz →Percentage change measures how much a quantity has increased or decreased relative to its original value. A positive result is a gain; a negative result is a loss.
- Percentage change = (New - Old) / |Old| × 100; the original value anchors the denominator and gives the result its direction: positive = increase, negative = decrease.
- Sequential percentage changes multiply as growth factors, not add: a 30% increase followed by a 20% decrease yields +4%, not +10% (1.30 × 0.80 = 1.04).
- Percentage change is undefined when the original value is zero (division by zero); report the absolute change only in that case.
- Percentage change is asymmetric: the change from 80 to 100 is +25%, but from 100 back to 80 is -20% - each percentage uses a different base.
- Use percentage change when there is a clear reference point (a prior period, a baseline, an original value); use percentage difference when neither value is privileged.
$$\text{Percentage Change} = \frac{\text{New} - \text{Old}}{|\text{Old}|} \times 100$$
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.
Percentage Change explained to a beginner
Percentage change tells you how much something grew or shrank relative to where it started. The starting value is always the yardstick. If your salary goes from $2,000 to $2,500, the increase is $500. Divide that by the original $2,000: 500 ÷ 2,000 = 25%.
If you mistakenly divided by the new salary ($2,500) you would get 20% - a different answer. The starting point is the only fair reference because that is what you were actually comparing against. This same principle explains why a 50% increase followed by a 50% decrease does not net to zero: the second 50% is taken from the larger, new number.
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 for Percentage Change
This table quickly gives you the overview you need to understand Percentage Change and its most important comparisons.
| 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 about Percentage Change
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.
Quiz: how well do you know percentage change?
1. From the examples table, what is the percentage change for a stock price rising from $80 to $100?
2. A 30% increase followed by a 20% decrease - what is the net percentage change?
3. When is percentage change mathematically undefined?
4. Why is a 50% increase followed by a 50% decrease not zero net change?