Percent Error Calculator

What Is Percent Error?

Percent error is a useful way to express how much a measured (observed) value differs from the actual, known, or accepted value. It’s often used in scientific experiments, data analysis, and quality control to determine how accurate your results are.

In most practical cases, the value you measure—like the weight of an object or the speed of a moving item—can vary from the exact or true value. These differences may be caused by estimation, limitations in instruments, or human mistakes. Percent error helps quantify this difference as a percentage, showing how close (or far) your result is from the expected value.

• A low percent error means the observed value is very close to the true value.

• A high percent error might suggest there was an issue with the experiment or measurement process.

For example, if your measurement is off by 90%, it’s a clear sign that something may be wrong with the procedure or the tools used.

How to Calculate Percent Error

To find percent error, you need two values: the observed (measured) value and the true (actual) value. The process involves three main steps:

1. Calculate the absolute error – the absolute difference between observed and true values.

2. Divide by the true value to get the relative error.

3. Multiply by 100 to express it as a percentage.

Formulas:

• Absolute Error = |Observed – True|

• Relative Error = |Observed – True| / True

• Percent Error = (|Observed – True| / True) × 100%

Example:

If the measured value is 56.891 and the actual value is 62.327:
Percent Error = (|56.891 − 62.327| / 62.327) × 100% = 8.722%

This tells us that the measured value is approximately 8.72% below the actual value.

  Note: These formulas assume that the true value is known. If it isn’t, tools like the standard deviation calculator are more appropriate for assessing error or variability.

Can Percent Error Be Negative?

Usually, percent error is shown as a positive value using absolute difference. This focuses on the size of the error, not its direction. But in some cases, showing whether the error is positive or negative can be useful.

Example of Negative Percent Error:

If:

• Observed value = 7

• True value = 9

Then:
Percent Error = (7 − 9) / 9 × 100% = −22.222%

A negative result simply means the observed value is lower than the expected value. A positive result means the observed value is higher. Regardless of direction, the closer your percent error is to 0%, the more accurate your measurement.