How to Calculate Percentage Change and What It Tells You
What Is Percentage Change?
Percentage change measures how much a value has grown or shrunk relative to its starting point, expressed as a percentage of that starting value. It is the standard way to describe movement between two numbers — a stock price moving from $50 to $60, a monthly electric bill falling from $200 to $170, a city's population rising from 1.2 million to 1.35 million. By comparing the change to the original value rather than to the new value, percentage change normalizes differences of scale: a $10 increase means something very different on a $20 item than on a $2,000 item.
Percentage change is one of the most widely used metrics in finance, economics, science, and everyday decision-making. It is the language of quarterly earnings reports ("revenue up 14% year over year"), inflation ("the CPI rose 3.2%"), personal budgeting ("my grocery spend is down 8% this month"), and performance reviews ("sales grew 22% versus last quarter"). Understanding how it is calculated — and where it can mislead — is foundational to reading numbers critically.
The Formula
The percentage change between an original (old) value and a new value is calculated with the standard percentage change formula:
Percentage Change = ((New − Old) / Old) × 100
Where:
- New = the ending or current value
- Old = the starting or baseline value
- The numerator (New − Old) is the absolute change
- Dividing by Old expresses that change as a fraction of the starting point
- Multiplying by 100 converts the fraction into a percentage
What Each Variable Means
| Variable | Meaning | Typical Values |
|---|---|---|
| New | Ending or current value | $60, $170, 1.35M |
| Old | Starting or baseline value | $50, $200, 1.2M |
| New − Old | Absolute change | +$10, −$30, +150K |
| (New − Old) / Old | Relative change (decimal) | 0.20, −0.15, 0.125 |
| × 100 | Percentage change | +20%, −15%, +12.5% |
Worked Example
Suppose a share of stock rises from $50 to $60 over the course of a year.
- Old = 50
- New = 60
Plugging into the formula:
- New − Old = 60 − 50 = 10
- (New − Old) / Old = 10 / 50 = 0.20
- 0.20 × 100 = 20%
So the stock gained 20% over the year. Notice that the same $10 increase on a $100 starting price would be only 10 / 100 × 100 = 10% — the absolute change is identical, but the percentage change is half as large because the baseline was twice as big.
Now consider a decrease: a household's monthly electricity bill falls from $200 to $170.
- Old = 200
- New = 170
- New − Old = 170 − 200 = −30
- (New − Old) / Old = −30 / 200 = −0.15
- −0.15 × 100 = −15%
The bill fell by 15%. The negative sign indicates a decrease; a positive result indicates an increase. Reporting the sign (or the words "increase" / "decrease") matters — saying "the bill changed by 15%" without direction is ambiguous.
Percentage Increase vs. Percentage Decrease
The formula is identical for increases and decreases; only the sign of the result differs. A positive percentage change is an increase (the new value is larger than the old), and a negative percentage change is a decrease (the new value is smaller than the old). Some contexts drop the sign and report the magnitude alongside a direction word — "a 15% decrease" rather than "a −15% change" — but the underlying calculation is the same.
A common point of confusion is that percentage increases and decreases are not symmetric. If a $100 item increases by 50%, it becomes $150. If that $150 item then decreases by 50%, it falls to $75 — not back to $100. The two changes use different baselines ($100 versus $150), so equal percentage moves in opposite directions do not return you to the starting value. This asymmetry matters whenever you compare gains and losses over time.
Common Use Cases
Percentage change appears in nearly every domain that tracks values over time:
- Prices and inflation: The Consumer Price Index reports monthly and annual percentage changes in the cost of a basket of goods, which is the headline inflation figure.
- Investment returns: A stock's annual return is a percentage change between its price at the start and end of the year (plus any dividends).
- Growth rates: Revenue growth, user growth, and GDP growth are all percentage changes measured between two reporting periods.
- Comparisons across scales: A small company growing from $1M to $2M in revenue (100% growth) and a large company growing from $1B to $1.1B (10% growth) can be compared meaningfully only after converting to percentages.
- Budgeting and personal finance: Comparing this month's spending to last month's, or this year's tax bill to last year's, in percentage terms makes the change interpretable regardless of the dollar amounts involved.
Input Definitions
- Old Value (baseline): The reference or starting value against which the change is measured. This is the denominator of the formula, so its value determines the scale of the resulting percentage. Choosing the correct baseline is the single most important decision in any percentage change calculation.
- New Value: The ending or current value being compared to the baseline. This is the numerator's "after" figure; the difference between it and the Old Value is the absolute change.
- Direction (sign): Whether the change is an increase (New > Old, positive result) or a decrease (New < Old, negative result). Always report the direction alongside the magnitude to avoid ambiguity.
- Time period (implicit): Percentage change is meaningful only when both values refer to the same kind of measurement over a defined interval — for example, "month over month," "year over year," or "from January to June." State the period explicitly when reporting results.
Important Caveats
The Baseline Cannot Be Zero
The formula divides by the Old Value, so a baseline of zero makes percentage change undefined. Going from $0 to $100 is not an "infinite percent increase" in any useful sense — it is simply a new value with no prior reference point. When the baseline is zero, report the absolute change instead and note that no percentage comparison is possible.
Negative Baselines Produce Misleading Results
If the Old Value is negative, the formula can produce results that contradict intuition. A company whose profit moves from −$10M to +$10M has clearly improved, but the formula gives (10 − (−10)) / (−10) × 100 = −200%, a negative number for an improvement. Percentage change is designed for positive baselines; for values that can be negative (profits, temperature in some scales, net cash flow), use a different metric such as absolute change or a ratio.
Small Baselines Exaggerate Percentages
A change from $1 to $2 is a 100% increase, as is a change from $1M to $2M — but the practical significance is wildly different. Small baselines amplify percentage changes, which is why a startup's "300% revenue growth" from a tiny starting base is not comparable to an established company's 15% growth on a billion-dollar base. Always pair a percentage with the underlying absolute values when the baseline may be small.
Percentage Change Is Not the Same as Percentage Points
A change from 10% to 13% is a 3 percentage point increase, but it is a 30% relative change in the rate itself (3 / 10 × 100). Confusing the two is a common error in reporting interest rates, tax rates, and any other figure that is already a percentage. Specify which you mean.
Direction and Baseline Choice Can Frame the Story
The same data can tell different stories depending on which value is the baseline. A stock that falls from $100 to $80 and then recovers to $90 has fallen 10% from its peak but risen 12.5% from its trough. Neither is wrong — both are accurate percentage changes — but the choice of baseline shapes the impression the number leaves. Always disclose the comparison points.
Finance Information Disclaimer
This guide is provided for general informational and educational purposes only. It is not financial, investment, legal, or tax advice. Interest rates, account terms, tax treatment, and fees vary by institution, jurisdiction, and individual circumstances. Past performance does not guarantee future results. Always consult a licensed financial advisor, tax professional, or your financial institution before making decisions about saving, investing, borrowing, or retirement planning.
Calculate Your Own Percentage Change
Want to apply the formula to your own numbers? Use our live percentage change calculator to enter your old and new values and instantly see the percentage increase or decrease, along with the absolute change.