Regular Percentage Change Formula
- Old value
- 100
- You entered
- New value
- 120
- You entered
This calculator works out the regular percentage change between two numbers: you enter an old value and a new value, and it returns the percentage increase or decrease. It uses the standard formula (new − old) ÷ old × 100, which is the same one used in finance, retail, and statistics. The result tells you how much the new value has moved relative to the original, expressed as a percentage.
Formula
The regular percentage change formula is written as:
Percentage Change = (New Value − Old Value) ÷ Old Value × 100
- Old Value – the original amount (the baseline, or the starting point).
- New Value – the amount after the change.
- Percentage Change – the result, in percent (%).
A positive result means an increase; a negative result means a decrease. For example, if a price goes from $50 to $60, the change is (60 − 50) ÷ 50 × 100 = 20%.
Worked Example
Using the default values from the calculator above: old value = 100, new value = 120.
- Subtract the old value from the new value: 120 − 100 = 20.
- Divide that difference by the old value: 20 ÷ 100 = 0.2.
- Multiply by 100 to get a percentage: 0.2 × 100 = 20%.
The calculator shows 20.00%, so the new value is 20% higher than the old value.
When to Use This Formula
Use the regular percentage change formula whenever you need to compare a new amount to an old one and express the difference as a percentage of the original. Common situations include:
- Calculating a price increase or discount (e.g., a product went from $80 to $100).
- Measuring growth in sales, revenue, or population over time.
- Comparing test scores, temperatures, or any metric before and after a change.
- Working out inflation or interest rate changes when you have two values.
The formula works for both increases and decreases. If the new value is smaller than the old value, the result is negative, which indicates a percentage decrease.
How to Read the Result
The result tells you the size of the change relative to the starting point. A 20% increase means the new value is 120% of the old value (100% + 20%). A 20% decrease means the new value is 80% of the old value (100% − 20%).
Important: the percentage change is always based on the old value, not on the new value. This is why a 50% increase followed by a 50% decrease does not return you to the original number. For example, 100 increased by 50% gives 150, but 150 decreased by 50% gives 75, not 100. That asymmetry is a common source of confusion.
Common Mistakes and Pitfalls
- Using the new value as the denominator: Always divide by the old value, not the new one. Dividing by the new value gives a different (and usually wrong) number.
- Forgetting to multiply by 100: The raw fraction (new − old) ÷ old is a decimal like 0.2; you must multiply by 100 to express it as a percentage.
- Mixing up increase and decrease: If the new value is less than the old, the result is negative. Some people report the absolute value, but the sign matters for direction.
- Ignoring units: The old and new values must be in the same units (both dollars, both kilograms, etc.). If they are not, convert first.
- Rounding too early: Round only at the end, not during intermediate steps, to avoid errors.
Limitations and When Not to Use It
The regular percentage change formula works best when the old value is positive and not extremely close to zero. If the old value is zero, the formula is undefined because you cannot divide by zero. In that case, a percentage change cannot be calculated—you would need to describe the change in absolute terms instead.
Also, the formula treats the change as linear. For compound growth over multiple periods (e.g., annual growth over several years), you should use the compound annual growth rate (CAGR) formula, which accounts for the compounding effect. The regular percentage change only compares two points in time without considering what happened in between.
Finally, be cautious when comparing percentages of very different magnitudes. A change from 1 to 2 is a 100% increase, but in absolute terms it is only 1 unit. Always consider the context and the absolute change alongside the percentage.
Frequently Asked Questions
What is the difference between percentage change and percentage difference?
Percentage change uses the old value as the denominator, so it shows the change relative to the starting point. Percentage difference (also called relative difference) uses the average of the two values as the denominator, which gives a symmetric result that does not depend on which value is called “old.� Use percentage change when you have a clear baseline; use percentage difference when you want a directionless comparison.
How do I calculate a percentage decrease?
Use the same formula: (new − old) ÷ old × 100. If the new value is smaller, the result will be negative, e.g., a drop from 200 to 150 gives (150 − 200) ÷ 200 × 100 = −25%, meaning a 25% decrease.
Can the percentage change be more than 100%?
Yes. If the new value is more than double the old value, the percentage change exceeds 100%. For example, an increase from 50 to 150 is (150 − 50) ÷ 50 × 100 = 200%.
What if the old value is zero?
You cannot calculate a percentage change when the old value is zero because division by zero is undefined. In that case, report the absolute change or describe the situation without a percentage.
Why do I get a different answer when I reverse the order?
Because the denominator changes. Going from 100 to 120 is a 20% increase, but going from 120 to 100 is a 16.67% decrease. The formula always uses the starting value as the baseline, so the order matters.