**Percent Error Definition**

Percent error, sometimes referred to as percentage error, is an expression of the difference between a measured value and the known or accepted value. It is often used in science to report the difference between experimental values and expected values.

The formula for calculating percent error is:

Note: occasionally, it is useful to know if the error is positive or negative. If you need to know the positive or negative error, this is done by dropping the absolute value brackets in the formula. In most cases, absolute error is fine. For example, in experiments involving yields in chemical reactions, it is unlikely you will obtain more product than theoretically possible.

**Steps to Calculate the Percent Error**

- Subtract the accepted value from the experimental value.
- Take the absolute value of step 1
- Divide that answer by the accepted value.
- Multiply that answer by 100 and add the % symbol to express the answer as a percentage.

Now let’s try an example problem.

You are given a cube of pure copper. You measure the sides of the cube to find the volume and weigh it to find its mass. When you calculate the density using your measurements, you get 8.78 grams/cm^{3}. Copper’s accepted density is 8.96 g/cm^{3}. What is your percent error?

**Solution:**

experimental value = 8.78 g/cm^{3}

accepted value = 8.96 g/cm^{3}

Step 1: Subtract the accepted value from the experimental value.

8.96 g/cm^{3} – 8.78 g/cm^{3} = -0.18 g/cm^{3}

Step 2: Take the absolute value of step 1

|-0.18 g/cm^{3}| = 0.18 g/cm^{3}

Step 3: Divide that answer by the accepted value.

Step 4: Multiply that answer by 100 and add the % symbol to express the answer as a percentage.

0.02 x 100 = 2

2%

The percent error of your density calculation was 2%.