Percent Change Calculator: Increase, Decrease and Difference

How to use the percent change calculator

1. Enter the old value (the starting number) in the first field.
2. Enter the new value (the ending number) in the second field.
3. The tool immediately shows the raw change, the percent change and whether it is an increase or decrease.
4. Read the percent difference row if you need the symmetric comparison instead of a directional one.

How percent change is calculated

The formula for percent change divides the difference between the new value and the old value by the absolute value of the old value, then multiplies by 100:

Percent change = ((New - Old) / |Old|) x 100

For example, if a product cost 80 last year and costs 100 this year, the calculation is ((100 - 80) / 80) x 100 = 25%. Because the result is positive, this is a percentage increase. If the price had dropped from 100 to 80, the math would be ((80 - 100) / 100) x 100 = -20%, which is a percentage decrease.

Using the absolute value of the old value in the denominator ensures that when both numbers are negative, the direction still makes sense. Going from -40 to -10 is an increase of 30, and dividing by |-40| gives 75%, correctly reflecting that the value moved upward toward zero.

Percent change versus percent difference

People often use these terms interchangeably, but they measure different things. Percent change is directional: it tells you how much a single quantity grew or shrank relative to its own starting point. The old value is always the reference.

Percent difference is symmetric. It compares two values without designating one as the starting point. The formula uses the average of the two values as the base:

Percent difference = (|A - B| / ((A + B) / 2)) x 100

If you compare 80 and 100, the percent difference is (20 / 90) x 100 = 22.22%. Notice this does not match either the 25% increase from 80 to 100 or the 20% decrease from 100 to 80. Use percent difference when neither value is naturally the baseline, such as comparing test scores between two students.

Common reference values

This table shows quick-reference results for frequently encountered scenarios. You can verify any of them using the percent change calculator above.

Practical uses for percentage changes

Tracking percentage increases and decreases is fundamental across many fields. In personal finance, you might use it to see how much your investment portfolio grew over a quarter. A jump from 10,000 to 11,200 is a 12% gain.

In retail, stores calculate markdowns as a percentage decrease. If a jacket originally priced at 120 is marked down to 90, the discount is 25%. Business analysts track revenue changes month over month to spot trends before they become problems.

Scientists and engineers use percent change to express measurement error or efficiency improvements. If a process used to take 45 minutes and now takes 36, that is a 20% reduction in time. Students working on lab reports or homework can also pair this tool with a decimal to fraction converter when their coursework requires fractional answers.

Mistakes to avoid

The most common error is swapping the old and new values. The denominator must always be the original value. Dividing by the new value produces a different number that does not represent the actual change relative to where you started.

Another mistake is dividing by zero. If the old value is zero, percent change is undefined because you cannot divide by zero. No finite percentage describes going from nothing to something. This percent change calculator will show an error in that case rather than returning infinity.

Finally, do not add percentages sequentially. If a price rises 10% and then falls 10%, it does not return to the original amount. Starting at 100, a 10% rise brings it to 110. A 10% fall from 110 subtracts 11, leaving 99. Always apply each percentage to the current value, not the original.

Worked examples

Each result below was produced by the same code the tool runs, so you can check your own numbers against them.