Percent Change Guide: Increase, Decrease, and Difference
Learn how to compare an old value and a new value as a percentage change.
Quick Answer
percent change = (new − old) / old × 100%When to Use This
Use percent change when two observations have a time order, such as last month and this month. The original value is the reference point. For an unordered comparison, a percentage-difference convention may be more appropriate and uses a different denominator.
Step-by-Step Method
- Label the earlier value old and the later value new.
- Subtract old from new to retain the direction.
- Divide by the nonzero original value.
- Multiply by 100 and report the sign or the words increase/decrease.
Calculator Tips and Limits
- The worked comparisons here use positive starting values.
- For a zero starting value, report the absolute change instead; ordinary percent change divides by zero.
Worked Examples
An increase and its reversal
From 80 to 100, the difference is 20. 20/80 × 100% = 25%. From 100 back to 80, the difference is -20 and -20/100 × 100% = -20%. Reversing the comparison changes the base, not just the sign.
A modest decrease
A count falls from 250 to 225. The change is -25, so -25/250 × 100% = -10%. Check: 250 × 0.90 = 225.
Common Mistakes
Dividing by the new value
For 80 to 100, dividing 20 by 100 yields 20%, but that is not the requested increase relative to 80.
Losing the direction with an absolute value
Absolute difference removes the sign. Keep new minus old when reporting growth or decline.
FAQ
What if the old value is zero?
The usual percentage change is undefined. Say, for example, that the count increased from 0 to 12, an increase of 12 units.
Is 20% to 25% a 5% increase?
It is 5 percentage points. Relative to the original 20% rate, it is a 25% increase.
References and corrections
OpenStax: Prealgebra 2e — further reading. The worked examples on this page are CalcSolver explanations. Read our calculation and correction method, or report an error with the input and expected result.