Percent Error Calculator

Sometimes, we try to estimate the value of a particular quantity by making repeated measurements. For example, we can try to find out what gravitational acceleration is by measuring the time of free fall from a specific height.

The measured acceleration will probably deviate a bit from the actual acceleration of 9.80665 m/s². To check what is the relative — or percent — error, you need to know two values: the real value and the observed (measured) one.

Our percent error calculator is based on the following equation:

percent error = (TV - OV) / TV × 100%

where:

• TV — True value; and
• OV — Observed value.

To help you understand percent error, we'll analyze a simple example. Let's assume that we want to find out the relative error between the measured and true values of the speed of sound.

1. Check the real value of the speed of sound. In the air at 20 °C, it is 343 m/s.

2. Take your measurement. You found it was equal to 329 m/s.

3. Subtract the observed value from the true value:

   343 - 329 = 14 m/s

4. 14 m/s is the absolute error. To calculate the percent error, you need to divide it by the true value:

   percent error = 14 / 343 × 100% = 4.082%

5. The percent error, otherwise known as the relative error, is equal to 4.082%.

And that's how you calculate percent error.

There are many terms similar to percent error. To ensure you don't get confused and mix them up, we provide a short explanation of each of them here.

Percent error, or relative error, is precisely what we described above – the relative difference between the observed and true value. You can apply the aforementioned percent error formula to calculate it. You might also be interested in our error propagation calculator.

Standard error is a value that can be calculated for a set of data. It is a statistical term that describes the accuracy with which a sample represents the whole population. Visit the standard error calculator to find out more.

Margin of error, on the other hand, is closely related to the confidence interval. It can be calculated by multiplying the standard error with the z-score corresponding to a certain confidence level. See the confidence interval calculator to find out more.