On the previous page, you learned that the absolute error is the difference between the measured value and the true (or accepted) value. Often, scientists want to know what percent of the accepted value the absolute error represents. To do this, we can calculate the percent error. Percent error is absolute error divided by the accepted value and multiplied by 100.
Percent Error Equation
\(\text{Percent error} = \frac{\text{absolute error }}{\text{accepted value}} \times 100\)
Percent error is all about comparing a measured value to an accepted value. It can be used to determine the quality of a measuring device or to compare the results of an experiment to theoretical calculations.
For Example
A fence is measured as 12.50 meters long ± 0.05 m. We know that the fence could actually measure anywhere between 12.45 and 12.55 meters according to the absolute error provided. The absolute error is 0.05 and accounts for error up to 0.05 m less than the measured value through 0.05 m more than the measured value.
12.5 - 0.05 = 12.45 m
12.5 + 0.05 = 12.55 m
This reflects the range of acceptable values that can be measured by the instrument used. What is the percent error in the measurement of the fence?
To calculate the percent error in the measurement of the fence, apply the values to the percent error equation using the steps in this table.
| Step 1: Start with the equation for percent error. | \(\text{Percent error} = \frac{\text{absolute error}}{\text{accepted value}} \times 100\) |
| Step 2: Substitute the known values into the equation. | \(\text{Percent error} = \frac{0.05}{12.5} \times 100\) |
| Step 3: Solve for the unknown value. | \(\text{Percent error} = 0.4\% \) |
The smaller the percent error, the closer the measured value is to the accepted value. This can be used to evaluate the accuracy of experimental data.
If the absolute error is not provided to you. It can be found by subtracting the accepted value from the measured value.
Calculating Absolute Error
\(\text{Absolute error} = \text{measured value} - \text{accepted value}\)
If the measured value is greater than the accepted value, the error is positive. If the measured value is less than the accepted value, the error is negative. Because the absolute error tells us how far “off” a measurement is from the accepted value (value that is considered to be true), error is often reported as the absolute value of the difference. Keep in mind that when a value is absolute, it is not negative.
For Example
You measured an object to be 4.23 cm, but its actual measurement is 4.25 cm. What is the absolute error in your measurement?
To calculate the absolute error in the measurement, apply the values to the absolute error equation using the steps in this table.
| Step 1: Start with the equation for absolute error. | \(\text{Absolute error} = \text{measured value} - \text{accepted value} \) |
| Step 2: Substitute the known values into the equation | \(\text{Absolute error} = 4.23 - 4.25\ \) |
| Step 3: Solve for the unknown value. | \(\text{Absolute error} = 0.02\) |
Let's Practice
Complete this activity to practice using percent error to reflect the uncertainty of measurements. Calculating the percent error in the problem on each tab, then check your answer.
The temperature is recorded as 38°C ± 1°
Percent error = 2.6 %
If you need help arriving at this answer, click the Solution button.
| Step 1: Start with the equation for percent error. | \(\text{Percent error} = \frac{\text{absolute error}}{\text{accepted value}} \times 100\) |
| Step 2: Substitute the known values into the equation. | \(\text{Percent error} = \frac{1}{38} \times 100\) |
| Step 3: Solve for the unknown value. | \(\text{Percent error} = 2.6\% \) |
A plant is measured as 80.0 cm ± 0.5 cm
Percent error = 0.625%
If you need help arriving at this answer, click the Solution button.
| Step 1: Start with the equation for percent error. | \(\text{Percent error} = \frac{\text{absolute error }}{\text{accepted value}} \times 100\) |
| Step 2: Substitute the known values into the equation. | \(\text{Percent error} = \frac{0.5}{80.0} \times 100\) |
| Step 3: Solve for the unknown value. | \(\text{Percent error} = 0.625\% \) |
The measured mass is 4.5 g, but the actual mass is known to be 4.0 g.
Percent error = 12.5%
If you need help arriving at this answer, click the Solution button.
| Step 1: Start with the equation for percent error. | \(\text{Percent error} = \frac{\text{absolute error}}{\text{accepted value}} \times 100\) |
| Step 2: Substitute the known values into the equation. |
\(\text{Absolute error} = \text{measured value} - \text{accepted value}\) \(\text{Absolute error} = 4.0 - 4.5 = 0.5\) \(\text{Percent error} = \frac{0.5}{4.0} \times 100\) |
| Step 3: Solve for the unknown value. | \(\text{Percent error} = 12.5\% \) |
A water bottle contains 16.9 oz. but is measured to contain 16 oz.
Percent error = 5.3%
If you need help arriving at this answer, click the Solution button.
| Step 1: Start with the equation for percent error. | \(\text{Percent error} = \frac{\text{absolute error}}{\text{accepted value}} \times 100\) |
| Step 2: Substitute the known values into the equation. |
\(\text{Absolute error} = \text{measured value} - \text{accepted value}\) \(\text{Absolute error} = 16 - 16.9 = 0.9\) \(\text{Percent error} = \frac{0.9}{16.9} \times 100\) |
| Step 3: Solve for the unknown value. | \(\text{Percent error} = 5.3\% \) |
