Percentage Change Calculator Formula
Understand the math behind the percentage change calculator. Each variable explained with a worked example.
Formulas Used
Percentage Change (%)
pct_change = ((new_val - old_val) / abs(old_val)) * 100Absolute Change
absolute_change = new_val - old_valNew / Old Ratio
ratio = new_val / old_valVariables
| Variable | Description | Default |
|---|---|---|
old_val | Old Value | 80 |
new_val | New Value | 100 |
How It Works
How to Calculate Percentage Change
Formula
% Change = [(New - Old) / Old
Percentage change measures the relative difference between two values. A positive result indicates an increase; negative indicates a decrease. Using the absolute value of the old value in the denominator handles cases where the old value is negative.
Worked Example
A price changes from $80 to $100.
- 01Change = 100 - 80 = 20
- 02% Change = (20 / 80) * 100 = 25%
- 03Ratio = 100 / 80 = 1.25
- 04The price increased by 25%
Frequently Asked Questions
Is percentage change symmetric?
No. Going from 80 to 100 is a 25% increase, but 100 to 80 is a 20% decrease. The asymmetry arises because the base (denominator) changes. For symmetric comparison, use the percentage difference formula with the average as the base.
What if the old value is zero?
Percentage change is undefined when the old value is zero because you cannot divide by zero. In such cases, report the absolute change instead or use a small baseline value.
How is percentage change different from percentage difference?
Percentage change measures change from a specific reference (old to new). Percentage difference compares two values symmetrically using their average as the base: 2*|A-B|/(|A|+|B|)*100.
Ready to run the numbers?
Open Percentage Change Calculator