Formula
Percentage change = ((New − Old) ÷ |Old|) × 100. A positive result is an increase; a negative result is a decrease. The original value is always the base.
How to use this calculator
Enter the original value and the new value. The result shows the percentage change with its sign (positive for an increase, negative for a decrease), the absolute difference, and a three-step breakdown. The calculator works for any two real numbers except when the original value is zero.
Percentage change formula
Percentage change measures how much a value has moved relative to its starting point, expressed as a percentage of that starting point:
$$\% \text{ Change} = \frac{\text{New} - \text{Old}}{|\text{Old}|} \times 100$$
The denominator uses the absolute value of Old so the sign of the result is determined entirely by the direction of change. For positive original values, |Old| = Old, so the formula reduces to the familiar (New − Old) ÷ Old × 100.
The result is signed: positive means the value grew, negative means it fell. There is no upper limit on positive results (a doubling is +100%, a tripling is +200%), and the lower limit for positive starting values is −100% (reaching zero).
Worked examples
Example 1: increase (salary)
A salary rises from 50,000 to 58,000.
$$\frac{58{,}000 - 50{,}000}{50{,}000} \times 100 = +16\%$$
The salary increased by +16%.
Example 2: decrease (product price)
A product price falls from 200 to 150.
$$\frac{150 - 200}{200} \times 100 = -25\%$$
The price decreased by −25% (or 25% less than the original).
Reverse: finding the new value from a known percentage change
To find the resulting value after a known percentage change, apply the multiplier to the original:
$$\text{New Value} = \text{Old} \times \left(1 + \frac{\%\text{ Change}}{100}\right)$$
Examples of the multiplier pattern:
- +10% change → multiply by 1.10
- −25% change → multiply by 0.75
- +100% change → multiply by 2.00 (doubles)
- −100% change → multiply by 0.00 (reaches zero)
Percentage change vs. percentage difference
These two terms are often confused but measure fundamentally different things:
| Percentage change | Percentage difference | |
|---|---|---|
| When to use | Before-and-after comparisons where one value is the clear starting point | Comparing two values with no defined starting point |
| Base | The original (old) value | The average of the two values |
| Sign | Signed (+ or −) | Always positive (unsigned) |
| Formula | (New − Old) ÷ Old × 100 | |V₁ − V₂| ÷ ((V₁ + V₂) ÷ 2) × 100 |
| Example use | Revenue this year vs. last year | Price of product A vs. product B |
Percentage difference formula for reference:
$$\% \text{ Difference} = \frac{|V_1 - V_2|}{\dfrac{V_1 + V_2}{2}} \times 100$$
Percentage change vs. percentage points
A percentage point is the arithmetic difference between two percentage values — it is an absolute measure. A percentage change is a relative measure.
Example: An approval rating rises from 40% to 50%.
- Change in percentage points: 50 − 40 = 10 percentage points
- Percentage change in the rating: (10 ÷ 40) × 100 = +25%
Both statements are correct but describe different quantities. News reporting frequently conflates them, which is why the distinction matters.
Common mistakes
Using the new value as the base
Always divide by the original value. For a move from 200 to 150: the correct base is 200, giving −25%. Using 150 gives −33.3%, which overstates the decrease.
Confusing percentage change with percentage points
If a conversion rate falls from 4% to 3%, it has dropped 1 percentage point but decreased by 25% relative to its original value. Always clarify which measure is being reported.
Treating sequential changes as additive
A +10% change followed by a −10% change does not return to the starting value. From 100: +10% gives 110, then −10% of 110 gives 99. Each percentage acts on a different base.
Frequently asked questions
What is the formula for percentage change?
Percentage change = ((New − Old) ÷ |Old|) × 100. Positive results are increases; negative results are decreases.
What is the difference between percentage change and percentage difference?
Percentage change requires a defined starting point and is signed. Percentage difference uses the average of two values as the base and is always positive. Use percentage change for before-and-after scenarios; use percentage difference when comparing two independent values with no reference direction.
What is the difference between percentage change and percentage points?
A percentage point is an absolute gap between two percentages (e.g. 20% → 25% is 5 pp). Percentage change is the relative movement (5 ÷ 20 × 100 = 25%). They measure different things.
Can percentage change be negative?
Yes. A negative result means the value decreased. A drop from 200 to 150 is −25%. The floor for positive original values is −100% (reaching zero).
Does a +20% change followed by a −20% change return to the original?
No. +20% on 100 gives 120; −20% on 120 gives 96. Because the base shifts with each step, symmetric percentages do not cancel out.
Why is the denominator |Old| and not just Old?
Using the absolute value prevents sign-flipping when the original value is negative. For positive originals, |Old| = Old and the formula is identical to the standard version.