Percent error or percentage error expresses as a percentage the difference between an approximate or measured value and an exact or known value. It is used in chemistry and other sciences to report the difference between a measured or experimental value and a true or exact value. Here is how to calculate percent error, with an example calculation.

### Percent Error Formula

For many applications, percent error is expressed as a positive value.

The absolute value of the error is divided by an accepted value and given as a percent.

|accepted value - experimental value| \ accepted value x 100%

Note for chemistry and other sciences, it is customary to keep a negative value. Whether error is positive or negative is important. For example, you would not expect to have positive percent error comparing actual to theoretical yield in a chemical reaction.

[experimental value - theoretical value] / theoretical value x 100%

### Percent Error Calculation Steps

- Subtract one value from another. The order does not matter if you are dropping the sign, but you subtract the theoretical value from the experimental value if you are keeping negative signs. This value is your 'error'.
- Divide the error by the exact or ideal value (i.e., not your experimental or measured value). This will give you a decimal number.
- Convert the decimal number into a percentage by multiplying it by 100.

- Add a percent or % symbol to report your percent error value.

### Percent Error Example Calculation

In a lab, you are given a block of aluminum. You measure the dimensions of the block and its displacement in a container of a known volume of water. You calculate the density of the block of aluminum to be 2.68 g/cm^{3}.

You look up the density of a block aluminum at room temperature and find it to be 2.70 g/cm^{3}. Calculate the percent error of your measurement.

- Subtract one value from the other:

2.68 - 2.70 = -0.02 - Depending on what you need, you may discard any negative sign (take the absolute value): 0.02

This is the error. - Divide the error by the true value:
0.02/2.70 = 0.0074074

- Multiply this value by 100% to obtain the percent error: 0.0074074 x 100% = 0.74% (expressed using 2 significant figures)