To calculate percentage change, subtract the original value from the new value, divide the difference by the original value, and multiply by 100. A positive result represents an increase, while a negative result represents a decrease.
Enter an original value and a new value to calculate the percentage change, numerical difference, direction, and multiplier.
The original value provides the reference for measuring how large the change was.
Percentage Change Formula
Percentage change measures the difference between an earlier value and a later value relative to the earlier value.
The original value is used as the denominator because it is the starting point of the comparison.
Enter both values into the Percentage Change Calculator to calculate the change automatically.
Step-by-Step Method
The same four-step method works for both increases and decreases.
- Identify the original value and the new value.
- Subtract the original value from the new value.
- Divide the difference by the original value.
- Multiply by 100 and interpret the sign.
Worked Example: Change from 100 to 120
The original value is 100 and the new value is 120.
Subtracting 100 from 120 gives an absolute change of 20.
Dividing 20 by 100 gives 0.2. Multiplying by 100 produces a percentage change of 20 percent.
How to Identify an Increase
When the new value is greater than the original value, the calculation produces a positive result.
For example, a change from 50 to 65 produces a difference of 15.
Dividing 15 by 50 and multiplying by 100 gives a 30 percent increase.
How to Identify a Decrease
When the new value is lower than the original value, the result is negative.
A change from 200 to 150 produces minus 25 percent.
The negative sign is normally expressed in words as a 25 percent decrease.
Absolute Change vs Percentage Change
Absolute change reports the numerical difference between the two values.
Percentage change reports the size of that difference relative to the original amount.
An increase of 20 is large relative to an original value of 40 but small relative to an original value of 2,000.
| Measurement | Formula | Example: 100 to 120 |
|---|---|---|
| Absolute change | New value − Original value | 20 |
| Percentage change | Difference ÷ Original × 100 | 20% |
| Multiplier | New value ÷ Original value | 1.2× |
What Happens When the Values Are Equal?
When the original and new values are identical, the difference is zero.
Dividing zero by a non-zero original value gives zero.
The result is zero percent, meaning there was no change.
What Happens When the Original Value Is Zero?
Standard percentage change is undefined when the original value is zero.
The formula would require division by zero, which is not mathematically defined.
Report the actual change in units instead, such as saying the value rose from zero to 50.
Do not describe a change from zero as a finite percentage increase under the standard formula.
Percentage Change with Decimal Values
The formula works with decimals in the same way as whole numbers.
For a change from 2.5 to 3, the difference is 0.5.
Dividing 0.5 by 2.5 and multiplying by 100 gives a 20 percent increase.
Percentage Change with Negative Numbers
Negative starting values require careful interpretation.
The standard formula can produce a mathematical result that does not match ordinary language about improvement or decline.
When negative values are involved, report the original value, new value, absolute change, and context alongside the percentage.
Common Uses
Percentage change is commonly used to compare prices, salaries, revenue, website traffic, population, test results, quantities, and measurements over time.
It is especially useful when changes from different starting values need to be compared.
A numerical increase of 100 may represent a large percentage change in one situation and a small percentage change in another.
Common Mistakes
Do not divide by the new value; use the original value as the denominator.
Do not forget to multiply the decimal result by 100.
Do not confuse percentage change with percentage difference, which uses a different reference value.
Conclusion
Subtract the original value from the new value, divide by the original value, and multiply by 100.
A positive result represents an increase, while a negative result represents a decrease.
Use the Percentage Change Calculator to calculate the result, absolute difference, and multiplier.
FAQs
What is the percentage change formula?
Subtract the original value from the new value, divide by the original value, and multiply by 100.
Which value goes in the denominator?
Use the original or starting value.
What does a negative percentage change mean?
It normally means the value decreased.
Can percentage change be greater than 100 percent?
Yes. A value can increase by more than its complete original amount.
What is the percentage change from zero?
It is undefined under the standard formula because division by zero is not possible.