Percent error measures how far an experimental result is from an accepted or actual value. It is useful in science, engineering, and everyday measurement because every measurement can have some error. A small percent error usually means the result is close to the true value, while a large percent error means the result may be inaccurate.
Thinking of the actual value as the bullseye and the experimental value as a point on a target helps show the size of the miss.
Key Facts
- Percent error = |experimental value - actual value| / |actual value| x 100%
- Absolute error = |experimental value - actual value|
- Percent error compares the size of the error to the actual value.
- A percent error of 0% means the experimental value equals the actual value.
- Example: experimental = 48 g, actual = 50 g, percent error = |48 - 50| / 50 x 100% = 4%
- Percent error is undefined when the actual value is 0 because division by zero is not allowed.
Vocabulary
- Experimental value
- The value found from a measurement, experiment, calculation, or observation.
- Actual value
- The accepted, true, or reference value used for comparison.
- Absolute error
- The positive difference between the experimental value and the actual value.
- Percent error
- The error written as a percentage of the actual value.
- Accuracy
- How close a measured or calculated value is to the actual value.
Common Mistakes to Avoid
- Forgetting the absolute value, which can give a negative percent error even though percent error is usually reported as a positive size of error.
- Dividing by the experimental value instead of the actual value, which changes the meaning of the comparison and gives the wrong percent error.
- Forgetting to multiply by 100, which leaves the answer as a decimal instead of a percent.
- Rounding too early, which can make the final percent error less accurate than it should be.
Practice Questions
- 1 A student measures the length of a table as 1.92 m. The actual length is 2.00 m. Find the absolute error and percent error.
- 2 A lab group finds the density of a metal to be 7.4 g/cm^3. The accepted density is 7.8 g/cm^3. Calculate the percent error to the nearest tenth of a percent.
- 3 Two students measure the same object. Student A has an absolute error of 2 cm on an actual length of 20 cm, and Student B has an absolute error of 2 cm on an actual length of 200 cm. Explain which measurement has the smaller percent error and why.