What Is the Formula for Percent Change? How to Calculate It
The formula for percent change is: Percent Change = ((New Value − Old Value) ÷ Old Value) × 100. In plain terms, you subtract the original (old) value from the new value, divide that difference by the original value, and multiply by 100 to express the result as a percentage. Percent change measures how much a quantity has grown or shrunk relative to where it started, which is why the original value is the divisor. That single relationship answers “what is the formula for percent change” and applies whether the result is a rise (positive) or a fall (negative).
The Percent Change Formula
Percent change expresses the relative difference between two values over time or across two states. It tells you the size of a change as a fraction of the starting point, not just the raw gap between the numbers.
The core formula is:
Percent Change = ((New Value − Old Value) ÷ Old Value) × 100
Each variable has a specific role:
- Old Value (original value): the starting amount, sometimes called the base or initial value. This is the reference point you measure against.
- New Value (final value): the amount after the change has occurred.
- New Value − Old Value: the absolute difference between the two, which can be positive or negative.
- Old Value (in the denominator): converts that raw difference into a proportion of the starting amount.
- × 100: turns the decimal proportion into a percentage.
If the new value is larger than the old value, the result is a positive percent increase. If the new value is smaller, the result is a negative percent decrease. This mirrors the general approach to comparing quantities taught in basic arithmetic, where a change is always measured relative to its starting point (Khan Academy).
Some people phrase the formula as “difference over original, times one hundred.” The two most important things are the order of subtraction (new first) and the choice of denominator (always the original value).
A Worked Example
Suppose a monthly subscription fee rises from $40 to $46.
- New Value − Old Value = 46 − 40 = 6
- Divide by Old Value: 6 ÷ 40 = 0.15
- Multiply by 100: 0.15 × 100 = 15%
The fee increased by 15%. If instead the fee had dropped from $46 to $40, the difference would be −6, and −6 ÷ 46 × 100 gives roughly −13%. You can report a decrease using the absolute value (“a 13% decrease”) or keep the negative sign to signal direction. Just remember that a rise and a fall between the same two numbers are not mirror images, because each is measured against a different starting point.
| Scenario | Old Value | New Value | Difference | ÷ Old | × 100 | Result |
|---|---|---|---|---|---|---|
| Subscription fee | $40 | $46 | +6 | 0.15 | 15 | +15% increase |
| Subscription fee | $46 | $40 | −6 | ≈ −0.13 | ≈ −13 | ≈ −13% decrease |
Common Mistakes to Avoid
A few recurring errors account for most incorrect answers. Watching for them keeps your results reliable.
- Dividing by the new value instead of the original. The denominator must always be the starting (old) value, since percent change is measured relative to where you began. Dividing by the new value gives a different, misleading figure.
- Swapping the subtraction order. Always subtract the old value from the new value. Reversing it flips the sign and misstates whether the change was an increase or a decrease.
- Forgetting the × 100 step. Without multiplying, you have a decimal (like 0.15), not a percentage (15%). The two are not interchangeable.
- Mixing up percent change with percentage points. When comparing two percentages, the difference in percentage points is not the same as the percent change between them. Going from 10% to 15% is a 5-percentage-point rise but a 50% relative increase. Resources such as Math is Fun illustrate how relative and absolute comparisons differ.
- Ignoring a zero original value. Dividing by zero is undefined, so percent change cannot be calculated when the starting value is zero.
Percent Change vs. Related Measures
Percent change is often confused with two neighboring concepts, and distinguishing them sharpens the calculation.
Percentage points measure the arithmetic difference between two percentages, while percent change measures the relative difference. If a rate moves from 4% to 5%, that is a rise of 1 percentage point but a 25% percent change (because 1 ÷ 4 = 0.25).
Percent difference compares two values without a natural direction, so it typically divides by the average of the two numbers instead of the original. Use percent change when one value logically precedes the other; use percent difference when the two values are simply being compared side by side.
One consequence of measuring against the base is that gains and losses do not cancel out. Start at 100, drop 50% to reach 50, then rise 50% from 50 and you land at 75 — not 100. Each percentage is calculated from a different base, which is why a 50% decrease followed by a 50% increase does not return you to where you started. Understanding this asymmetry prevents a common misreading of financial and statistical data.
Key Takeaways
- The formula is ((New Value − Old Value) ÷ Old Value) × 100.
- Always divide the difference by the original value, never the new one.
- A positive result is an increase; a negative result is a decrease.
- The final × 100 step converts the decimal into a percentage.
- Don’t confuse percent change with percentage-point differences.
- Percent change cannot be computed when the original value is zero.
