Percent Error Calculator & Formula

Percent error calculator is used to find the relative error between an observed value and a true value in a measurement. With this online tool, you can make a quick assessment of whether or not you made an accurate measurement. The article covers details on how to calculate percent error.

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How to use the percent error calculator?

Even without a percent error formula, you can find the value for the percent error using this percent error calculator. This is a simple tool which works the same way as a relative error calculator or an absolute error calculator. Here are the steps to follow when using this online tool:

  • First, enter the True Value in the appropriate field.
  • Then enter the Observed Value in the appropriate field.
  • After entering both of these values, the calculator automatically generates the value for the percent error for you.

How do you calculate the percent error?

Often, when you try to come up with an estimated value of a specific quantity, you do this by making several measurements repeatedly. For instance, you can try to solve for the gravitational acceleration by measuring how much time a free-falling object would take from top to bottom from a certain height.

In this case, you may try performing the experiment several times in order to get a good estimate of the actual acceleration time. However, your observed measurement may deviate slightly from the actual gravitational acceleration. If you want to check the percent error, you can use the relative error calculator or the absolute error calculator.

You may also find this value by performing a manual calculation using the percent error equation which is:

percent error = (TV – OV) / TV * 100%

TV refers to the true value
OV refers to the observed value

For you to understand the concept of percent error better, let’s look at an example. For instance, let’s say that you want to solve for the relative error between your observed value and the true value of the speed of sound. To solve for the percent error using this example, here are some steps:

  • Go online and find out the real value of the speed of sound. For this example, let’s use the speed of sound in the air at a temperature of 20°C which is 343 m/s.
  • Then take your own measurement based on your observation. Here, let’s assume that the value you acquired was 329 m/s.
  • With both values, you can start solving for the percent error using the percent error formula:
    percent error = 343 – 329 = 14 m/s
  • The value you acquired is the absolute error. Then you can continue with the formula in order to get the percent error. To do this, divide 14 m/s by the true value. Therefore:
    percent error = 14 / 343 *100% = 4.082%
  • So for our example, the percent error or the relative error is 4.082%. After performing the calculation, you can check the accuracy of your answer using the percent error calculator.

What percentage error is acceptable?

How acceptable the percentage error depends on the application. Sometimes, the measurement might be too difficult to take that you may consider an error of 10% or more acceptable. But in other cases, an error as small as 1% is already too high. In most schools, instructors may accept a percentage error of 5%.

Some say that the percentage error can never be too high as long as you perform the calculation correctly. The utilization of any value with a high percent error in measurement depends on your own judgment. To make sense of this measurement, you have to take other factors into consideration too.

Along with the percent error, the other factors are precision and accuracy. Statisticians and scientists both say that there’s no upper limit when it comes to percent error. There’s only the individual’s judgment on whether or not he can make use of the data he acquired. But this doesn’t apply to both precision and accuracy.

In measurement designs, both precision and accuracy are inherent. They are what they are and you can only improve them when you improve the device or equipment. Several measurements may help improve the statistic accuracy of a measurement. However, these measurements cannot change the measurement error which is inherent.

You can calculate the percent error as the range of deviation of a certain measurement from the best and most recent fixed metric point. On the other hand, precision refers to the consistency of the device in delivering the same value for a specific measurement over and over again.

This is typically a function of the device’s construction and how it’s used, unlike accuracy which is often related to the device’s calibration. Percent error then refers to determining how possible values may differ from the “true value” because of any device limitations.

Can your percent error be over 100?

The short answer to this is – yes, it can be. A value of a given quantity “x” you acquired from your experiment is the approximation of an average “x” of a specific number of “n” measurements. The relativity of this value is what you take as the standard error.

The percent error can become over 100 if the fraction on the right is more than 1 and this is a possibility. Generally, this occurs when you take the measurement of a quantity that’s small on average but has a distribution that’s wide and has a small number of measurements.

In other words, a percent error of more than 100 is entirely possible. Another way you can acquire this value when your observed value is twice as large as the true value. When you perform experiments, there’s always the possibility of getting a value which is either lesser or greater than the true value because of experimental or human errors.

Can percent error be negative?

Percent error is always a positive value. If you get a negative value, this only means that you forgot to use the sign of the absolute value. Simply make the number you calculate positive by changing the sign to make it the correct value for percent error.