# Percent difference

Percent difference, also referred to as percentage difference, is another measure used to compare two values. It is similar to percent change and percent error (refer below for more detail). The equation for percent difference is:

Where V_{1} and V_{2} are two values being compared.

When measuring percent difference, the order of the two values (V_{1} or V_{2}) in the formula doesn't matter. This is because percent difference is used for values that should not be distinguishable in such a way that one value would stand out to be used as a reference over the other (as is the case when using the percent error/change formulas). Percent difference may be used to compare two heights, ages, hours worked, or other numbers.

Examples

1. If John is 5 feet 8 inches tall (172.72 cm) and James is 6 feet 2 inches tall (187.96 cm), what is the percent difference between their heights?

Plugging 172.72 in for V_{1} and 187.96 in for V_{2},

2. If Katie ran 1900 meters and Blake ran 1500 meters, what is the percent difference between the distances they ran?

Since we use the absolute value for the difference, the order of the values does not matter. In either of the examples above, we could've switched which value was used for V_{1} and V_{2}, and the result would have been the same.

### Percent difference, percent change, and percent error

These three measures, though similar, are not interchangeable. They are used in different contexts.

Percent difference

- Reference value: neither value has any obvious precedence over the other, so the reference value is the average between the two.
- Example: if we have two sticks, one with length 100 cm, and another with length 50 cm, we can calculate the percent difference between their lengths.

Percent change

Percent change assumes that there is an "old" and a "new" value and compares values relative to the old value. So, the reference value is the old value, and percent change is used to determine whether the new value is the same, an increase, or a decrease, relative to the old value.

- Reference value: old value.
- Example: if we have a plant that grew to being 60 cm tall from 55 cm tall in some time period, we can calculate the percent change in the plant's height over that time period with 55 cm being the old value, and 60 cm being the new value.

Percent error

Percent error is mostly used in more scientific settings. In the context of experiments, percent error is used when there is some known/theoretical value being compared to an experimental value.

- Reference value: expected value
- Example: Say we have a factory manufacturing a part that is supposed to have a length of exactly 10 cm. If a part was manufactured that had a length of 9.5 cm, we would use percent error to measure how large a difference there is between the expected length and the length we actually got.

So, in all three measures, we are comparing the difference between two values to some reference value. The difference between the three is what the reference value is, which affects which of these measures we choose to use.