Understanding change
Use percentage change when one value is the original baseline and another is the later or updated value.
Formula & methodology
Formula: ((New value − original value) ÷ |original value|) × 100
Example: From 80 to 100: ((100 − 80) ÷ 80) × 100 = 25% increase; the absolute change is 20.
Three related calculations.
Choose the formula that matches the relationship between your values. Percentage change needs a clear starting point; percentage difference treats both values equally; reverse percentage recovers the starting value.
((New value − original value) ÷ |original value|) × 100(|First value − second value| ÷ ((first value + second value) ÷ 2)) × 100Final ÷ (1 + rate ÷ 100) for an increase; final ÷ (1 − rate ÷ 100) for a decreaseFollow the numbers.
Original 80; new 100
Working: ((100 − 80) ÷ 80) × 100
Result: 25% increase; absolute change 20
First 40; second 60
Working: |40 − 60| ÷ 50 × 100
Result: 40% difference
Final 80; decrease 20%
Working: 80 ÷ (1 − 0.20)
Result: Original value 100
Choose the right baseline before interpreting a percentage.
Percentage change assumes the original value is the meaningful baseline and cannot be calculated from an original value of zero. Percentage difference is symmetric instead: it treats two non-negative values equally and divides their absolute difference by their average, so it answers a different question from before-and-after change.
Reverse percentage assumes one stated increase or decrease was applied once to produce the final value. A reverse decrease of 100% or more has no finite original value under this formula. Repeated changes compound from new baselines, so equal percentage increases and decreases do not cancel each other.
Results are mathematical comparisons only. They do not account for inflation, taxes, fees, rounding rules, uncertainty, measurement error, weighting, time periods, or whether the selected baseline is appropriate for a financial, scientific, medical, statistical, or business decision. Keep the original units alongside the absolute change and use domain-specific methods when those factors matter.
Step-by-step guidance.
- Enter the original value.
- Enter the new value.
- Read the direction, percentage magnitude, and absolute change.
Questions people ask.
How do I calculate percentage change?
Subtract the original value from the new value, divide by the absolute original value, and multiply by 100. The change sign identifies an increase or decrease.
What is the difference between percentage change and percentage difference?
Percentage change uses an original baseline and answers how far the later value moved relative to that starting point. Percentage difference treats two non-negative values equally and compares their absolute difference with their average. Use change for before-and-after data; use difference when neither measurement is the baseline.
Why is percentage change undefined when the original value is zero?
The formula divides by the original value. A zero baseline requires division by zero, so no finite percentage change exists.
Can percentage difference be more than 100%?
Yes. For non-negative values it can reach 200%, such as when one value is zero and the other is positive.
How do I reverse a percentage increase?
Divide the final value by one plus the rate as a decimal. To reverse a 25% increase, divide by 1.25.
How do I reverse a percentage decrease?
Divide the final value by one minus the rate as a decimal. The decrease rate must be below 100%.
Does a 20% decrease undo a 20% increase?
No. They use different baselines. Increasing 100 by 20% gives 120, but decreasing 120 by 20% gives 96 because the decrease is calculated from 120. To return from 120 to 100 requires a 16.67% decrease. This baseline effect is important when reading price changes, investment losses, test scores, and repeated growth rates.
What is absolute change?
Absolute change is the distance between the original and new values without regard to direction. Signed change separately shows whether the value rose or fell. Report the absolute change with its original unit—for example, euros, kilograms, points, or people—while the percentage describes that movement relative to a selected denominator.