To calculate percent change, subtract the original value from the new value, divide the result by the original value, and multiply by 100. A positive answer means an increase, while a negative answer means a decrease. The calculation is useful only when the original value is a meaningful, nonzero baseline.
For example, a value that moves from 80 to 100 has a percent change of ((100 − 80) ÷ 80) × 100 = 25%. It increased by 25%.
What Is Percent Change?
Percent change measures how much a quantity has risen or fallen relative to where it started. The original value is the baseline, so it belongs in the denominator. This makes the result a relative change rather than only an absolute difference.
Suppose two products both increase in price by 20 units. A rise from 40 to 60 is a 50% increase, while a rise from 1,000 to 1,020 is only a 2% increase. The absolute change is identical, but its importance depends on the original amount.
The U.S. Bureau of Labor Statistics describes the same sequence for index changes: subtract the earlier value from the later value, divide by the earlier value, and multiply by 100. This is the standard percent change calculation formula used throughout this guide.
How to Calculate Percent Change Step by Step
Identify the original value
Use the starting, earlier, previous, or baseline value. Confirm that it is not zero and that it represents the same unit and period as the new value.
Find the amount of change
Subtract the original value from the new value: change = new − original. Keep the sign because it tells you the direction.
Divide by the original
Divide the signed change by the original value. This compares the movement with the size of the starting point.
Convert the rate to percent
Multiply the decimal rate by 100 and add the percent sign. Label a positive result as an increase and a negative result as a decrease.
You can also divide the new value by the original value, subtract 1, and multiply by 100:
Both formulas give the same answer when the original value is nonzero.
Percent Change Examples
Example 1: Increase from 80 to 100
Change amount = 100 − 80 = 20
Change rate = 20 ÷ 80 = 0.25
Percent change = 0.25 × 100 = 25%
The value increased by 25%. The new value is 125% of the original.
Example 2: Decrease from 250 to 200
Change amount = 200 − 250 = −50
Change rate = −50 ÷ 250 = −0.20
Percent change = −0.20 × 100 = −20%
The signed percent change is −20%, which is normally reported as a 20% decrease.
Example 3: No change
If a value remains at 45, the change is 45 − 45 = 0. Dividing zero by the nonzero original gives zero, so the percent change is 0%.
| Original | New | Absolute change | Percent change | Interpretation |
|---|---|---|---|---|
| 40 | 60 | +20 | +50% | 50% increase |
| 80 | 100 | +20 | +25% | 25% increase |
| 500 | 425 | −75 | −15% | 15% decrease |
| 1,000 | 1,020 | +20 | +2% | 2% increase |
Why You Divide by the Original Value
Percent change answers a directional question: how large is the movement compared with the starting point? That is why calculating the percent change requires the original value as the denominator.
For a rise from 80 to 100, the change is 20. Dividing by 80 gives 25%. Dividing by 100 gives 20%, but that describes the increase as a share of the ending value. It is not the standard increase from the original baseline.
Direction also explains why reversing the values changes the result. An increase from 80 to 100 is 25%, but the decrease from 100 back to 80 is 20%. The change amount is 20 in both directions, yet each calculation uses a different starting value.
Percent Increase, Percent Decrease, and Signed Change
The general formula can produce a signed result:
- A positive result indicates growth. Report +15% as a 15% increase.
- A negative result indicates decline. Report −15% as a 15% decrease.
- A zero result indicates that the values are equal.
Dedicated increase and decrease calculators are useful when you want the direction enforced and the result labeled clearly. They reduce the chance of calling a negative increase a decrease or dividing by the wrong value.
Percent Change vs Percentage Difference
Percent change is directional and needs an original value. Percentage difference is generally used when comparing two peer values and neither one is the official baseline. It divides the absolute gap by a shared reference, often the average of the two values.
| Method | Reference value | Does order matter? | Best use |
|---|---|---|---|
| Percent change | Original value | Yes | Change over time or from a baseline |
| Percentage difference | Average of both values | No | Comparing two peer measurements |
| Percentage points | No denominator | Yes | Direct gap between two percentage rates |
For example, a rate moving from 20% to 25% rises by 5 percentage points. Its relative percent change is (25 − 20) ÷ 20 × 100 = 25%. Saying only “it rose by 5%” would be ambiguous.
What Happens When the Original Value Is Zero?
A standard percent change from zero is undefined because the formula requires division by the original value. A move from 0 to 50 has an absolute increase of 50, but it does not have a finite standard percent increase.
In that situation, report the starting value, ending value, and absolute change. A different index, baseline, or subject-specific method may be appropriate, but it should be named explicitly rather than presented as the ordinary percent change formula.
How to Handle Negative Original Values
Negative baselines can make the ordinary formula hard to interpret. For example, moving from −100 to −50 is an improvement of 50 units, but dividing 50 by −100 produces −50%. Some fields use the absolute value of the original denominator, while others avoid a percent rate when values cross zero.
There is no single convention that works for profit and loss, temperature scales, account balances, and scientific measurements. State the original value, new value, and absolute change, then follow the method required by the subject.
Successive Percent Changes Do Not Simply Add
Each percentage change applies to its current baseline. A 20% increase followed by a 10% decrease is not a net 10% increase.
Start with 100.
After a 20% increase: 100 × 1.20 = 120.
After a 10% decrease: 120 × 0.90 = 108.
Overall percent change: (108 − 100) ÷ 100 × 100 = 8% increase.
For several periods, multiply the growth factors and compare the final result with the first value. Add the rates only when each percentage is independently measured against the same unchanged baseline.
How to Find a New or Original Value from a Known Change
When you know the original value and percent change, convert the percentage to a decimal and apply the growth factor:
Use a negative percent change for a decrease. If 800 increases by 15%, the new value is 800 × 1.15 = 920. If 800 decreases by 15%, it becomes 800 × 0.85 = 680.
To recover the original value from a final value and known rate:
If 920 is 15% above the original, divide 920 by 1.15 to get 800. Subtracting 15% of 920 would be wrong because the 15% was measured against the smaller original value.
Common Percent Change Mistakes
- Dividing by the new value instead of the original value.
- Subtracting in the wrong order and then mislabeling the direction.
- Reporting an absolute change amount as though it were a percentage.
- Comparing values with different units, date ranges, populations, or definitions.
- Calling a percentage-point change a relative percent change.
- Claiming a finite percent change when the original value is zero.
- Applying the standard formula to a negative baseline without stating a convention.
- Rounding intermediate values too early instead of rounding the final result.
- Adding successive percentage changes that apply to changing baselines.
Related Percentage Calculators
Frequently Asked Questions
What is the formula for percent change?
Subtract the original value from the new value, divide by the original value, and multiply by 100: ((new − original) ÷ original) × 100%.
How do I calculate percent change between two numbers?
Treat the earlier or starting number as the original. Subtract it from the later number, divide the change by the original, and multiply by 100.
Is percent change always positive?
No. A positive result indicates an increase, a negative result indicates a decrease, and zero indicates no change. You may report −12% as a 12% decrease.
Why is the original value the denominator?
Percent change measures the movement relative to where the quantity started. Dividing by the ending value would answer a different question.
What is the percent change from 80 to 100?
The increase is 20. Divide 20 by the original 80 and multiply by 100. The result is a 25% increase.
What is the percent change from 100 to 80?
The signed change is −20. Dividing −20 by 100 gives −0.20, so the result is −20%, normally stated as a 20% decrease.
Can I calculate percent change from zero?
No finite standard percent change exists because the formula would divide by zero. Report the absolute change or use a clearly stated alternative method.
Is percent change the same as percentage difference?
No. Percent change uses an original baseline and depends on direction. Percentage difference usually treats both values equally and uses their average as the reference.
What is the difference between percent change and percentage points?
Percentage points are the direct subtraction of two rates. Percent change divides that point change by the original rate and multiplies by 100.
Should I add consecutive percent changes?
Usually not. Consecutive changes compound because each rate applies to a new baseline. Multiply the growth factors, then compare the final value with the original.
The formula and baseline treatment were reviewed against the U.S. Bureau of Labor Statistics guide to calculating percent changes and the OpenStax financial statement analysis method. This article explains general arithmetic, not a subject-specific accounting, scientific, financial, or regulatory convention.
