Relative Error Calculator
Enter the measured value and accepted value to calculate absolute error, relative error, and percent error.
Step by Step Solution
Enter values and click calculate to see the solution.
Use this relative error calculator to find how large an error is compared with the accepted value. Enter the measured value and accepted value, and the calculator will show relative error, absolute error, percent error, and the full solution steps.
Relative error is useful when you want to compare the size of an error with the size of the actual value. A small absolute error can still be important if the accepted value is small. A larger absolute error may not be serious if the accepted value is very large.
This is why relative error is commonly used in science, physics, chemistry, engineering, lab measurements, and numerical calculations.
What Is Relative Error?
Relative error measures the size of an error compared with the accepted value. It tells you whether the error is small or large in relation to the true value.
For example, an error of 1 is small when the accepted value is 1000. The same error of 1 is large when the accepted value is 2.
Absolute error only tells you the difference. Relative error gives that difference proper context.
Relative Error Formula
The relative error formula is:
Relative Error = |Measured Value − Accepted Value| ÷ |Accepted Value|
Where:
Measured value is the value found from an experiment, measurement, or calculation.
Accepted value is the correct, true, exact, or reference value.
Absolute error is the positive difference between the measured value and accepted value.
Relative error has no unit because the units cancel during division.
How to Calculate Relative Error?
To calculate relative error, first subtract the accepted value from the measured value. Then take the absolute value of the difference. After that, divide the absolute error by the accepted value.
Example:
Measured value = 9.8
Accepted value = 10
Absolute error = |9.8 − 10|
Absolute error = 0.2
Relative error = 0.2 ÷ 10
Relative error = 0.02
So the relative error is 0.02.
If you want the answer as a percentage, multiply by 100.
Percent error = 0.02 × 100
Percent error = 2%
Relative Error Example
Suppose a student measures a value as 48, but the accepted value is 50.
First, find the absolute error.
|48 − 50| = 2
Now divide the absolute error by the accepted value.
2 ÷ 50 = 0.04
The relative error is 0.04.
To write it as percent error:
0.04 × 100 = 4%
So the percent error is 4%.
Relative Error vs Absolute Error
Absolute error shows the actual difference between the measured value and accepted value. Relative error shows how large that difference is compared with the accepted value.
If the measured value is 98 and the accepted value is 100, the absolute error is 2 and the relative error is 0.02.
If the measured value is 8 and the accepted value is 10, the absolute error is also 2, but the relative error is 0.2.
Both examples have the same absolute error, but the second one has a much larger relative error because the accepted value is smaller.
Use absolute error when you need the actual difference. Use relative error when you need to compare the error with the size of the true value.
Relative Error vs Percent Error
Relative error and percent error are closely connected. Percent error is just relative error written as a percentage.
The formula is:
Percent Error = Relative Error × 100
If relative error is 0.05, percent error is 5%.
If relative error is 0.12, percent error is 12%.
Relative error is usually written as a decimal. Percent error is easier to read when you want to explain the error in percentage form.
When Should You Use Relative Error?
Use relative error when the size of the value matters. It helps you understand whether the error is important or minor.
Relative error is useful for:
Lab measurements
Physics calculations
Chemistry experiments
Engineering measurements
Scientific data
Numerical approximations
Comparing errors from different values
It is especially helpful when two measurements have different sizes. Absolute error alone may not give a fair comparison.
Why Relative Error Matters?
Relative error gives meaning to the error. Without it, you only know how far the measured value is from the accepted value.
For example, an error of 5 may look small or large depending on the accepted value.
If the accepted value is 10, an error of 5 is very large.
If the accepted value is 10,000, an error of 5 is very small.
Relative error makes this comparison clear.
Common Mistakes
One common mistake is using the measured value in the denominator instead of the accepted value. In most basic relative error problems, the accepted value is used in the denominator.
Another mistake is forgetting to take the absolute value. Relative error is usually written as a positive number.
Some people also confuse relative error with percent error. Relative error is the decimal form. Percent error is the percentage form.
Relative error should not have a unit. Since the same unit appears in the numerator and denominator, the unit cancels out.
Accepted value should not be zero. If the accepted value is zero, relative error is not defined because division by zero is not possible.
When to Use Absolute Error?
Use absolute error when you need the exact size of the difference between a measured result and the correct value.
It is useful for:
Experiments
Measurements
Instrument accuracy checks
Quality control
Engineering calculations
Scientific reports
FAQs
Related Calculators
Use the Absolute Error Calculator if you only need the difference between measured value and accepted value.
Use the Percent Error Calculator if you want the error as a percentage.
Use the Significant Figures Calculator to round your answer to the correct number of significant figures.
Use the Rounding Calculator if you need to round decimal results after calculating error.