## Calculator Use

The Percentage Change Calculator (% change calculator) quantifies the change from one number to another and expresses the change as an increase or decrease.

This is a % change calculator. Going from 10 apples to 20 apples is a 100% * increase* (change) in the number of apples.

This calculator is used when there is an “old” and “new” number or an “initial” and “final” value. A positive change is an increased amount of the percentage value while a negative change is a decreased amount of the percentage value.

Use the percent change calculation when the order of the numbers does matter; you have starting and ending values or an "old number" and a "new number."

When you are just comparing two numbers you may want to use the Percent Difference Calculator.

Related calculations can be done with Percentage Calculator and conversions can be solved with Decimal to Percent, Percent to Decimal, Fraction to Percent, or Percent to Fraction.

### Percentage Change Formula

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by 100.

\( \text{Percentage Change} = \dfrac{\Delta V}{|V_1|} \times 100 \)

\( = \dfrac{(V_2-V_1)}{|V_1|} \times 100 \)

## How to Calculate Percentage Change: Example 1

What is the percentage change, as an increase or decrease, to go from 3.50 to 2.625?

Let V_{1} = 3.50 and V_{2} = 2.625 and plug numbers into the percentage change formula

\( \dfrac{(V_2-V_1)}{|V_1|} \times 100 \)

\( = \dfrac{(2.625 - 3.50)}{|3.50|} \times 100 \)

\( = \dfrac{-0.875}{3.50} \times 100 \)

\( = -0.25 \times 100 = -25\% \; \text{change} \)

If you have a -25% change it's the same as saying you have a 25% decrease.

Note that if you let V_{1} = 2.625 and V_{2} = 3.50 you would get a 33.3333% increase. This is because these percentages refer to different amounts: 25% of 3.50 versus 33.3333% of 2.625.

## How to Calculate Percentage Change: Example 2

Let's look at a change that includes negative numbers, where taking the absolute value of V_{1} in the denominator makes a difference.

What is the percentage change, as an increase or decrease, to go from -25 to 25?

Let V_{1} = -25 and V_{2} = 25 and plug numbers into the percent change formula:

\( = \dfrac{(25 - -25)}{|-25|} \times 100 \)

\( = \dfrac{50}{25} \times 100 \)

\( = 2 \times 100 = 200\% \; \text{change} \)

If you have a 200% change it's the same as saying you have a 200% increase.

## How to Calculate Percentage Change: Example 3

Let's look at another change that includes negative numbers, where taking the absolute value of V_{1} in the denominator is important.

What is the percent change, as an increase or decrease, to go from -25 to -50?

Let V_{1} = -25 and V_{2} = -50 and plug numbers into the formula:

\( = \dfrac{(-50 - -25)}{|-25|} \times 100 \)

\( = \dfrac{-25}{25} \times 100 \)

\( = -1 \times 100 = -100\% \; \text{change} \)

If you have a -100% change it's the same as saying you have a 100% decrease.

## References

Wikipedia contributors. "Percent difference: percent change" Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, last visited 18 Feb. 2011.