{"id":2674,"date":"2022-05-17T15:13:59","date_gmt":"2022-05-17T19:13:59","guid":{"rendered":"https:\/\/www.alpharithms.com\/?p=2674"},"modified":"2022-05-17T15:13:59","modified_gmt":"2022-05-17T19:13:59","slug":"percent-error-calculator","status":"publish","type":"post","link":"https:\/\/www.alpharithms.com\/percent-error-calculator-591315\/","title":{"rendered":"Percent Error Calculator"},"content":{"rendered":"

Percent error is a measure used to quantify the difference in an observed value compared to an expected value. Alternatively, it can be thought of as the measure of the difference between an experimental value and a theoretical value. It is used in science to describe the outcome of experiments observing natural phenomena or related simulations.<\/p>\n

Percent error is sometimes referred to as\u00a0approximation error<\/strong> which is descriptive of this formula’s intent. The main difference is that the Percent error provides results in a range of 0-100 (as a percent<\/em>). An approximation error can also be reported as a relative error<\/strong> or absolute error<\/strong>. We’ll take a look at each of those later \u2014 for now let’s consider how to calculate percent error.<\/p>\n

Percent Error Formula & Calculation<\/h2>\n

Percent error can be calculated in three easy steps in which two variable values are used. The steps are as follows1<\/sup>:<\/p>\n

    \n
  1. Calculate the difference between the Experimental Value (VE<\/sub>) and the Theoretical Value (VT<\/sub>).<\/li>\n
  2. Divide the value from #1 by the Theoretical Value (VT<\/sub>).<\/li>\n
  3. Multiply the absolute value of the result of #2 by 100.<\/li>\n<\/ol>\n

    These three steps can be expressed via the following formula where the large vertical bars represent the absolute value (i.e. drop the sign) of steps #1 & #2 assigned to the variable delta (lowercase) as is common convention.<\/p>\n

    \"percent
    Figure 1: Percent Error formula<\/figcaption><\/figure>\n

    Absolute & Relative Error vs. Percent Error<\/h2>\n

    Absolute and relative error calculations are similar to percent error calculations but omit the multiplication of 100. As such, both of these calculations return decimal values. The absolute error omits the second step while the relative error goes through steps 1 and 2 as shown in the following figure:<\/p>\n

    \"relative
    Figure 1: Comparison between the relative error formula and absolute error formula<\/figcaption><\/figure>\n

    Applications of Percent Error<\/h2>\n

    Percent error is used to gauge the proximity of an unknown value to a known value. The vocabulary varies based on the field of study \u2014 sometimes “expected” is observed <\/em>or inferred<\/em> and “theoretical” is sometimes\u00a0expected,\u00a0<\/em>known,\u00a0<\/em>or\u00a0measured<\/em>. These measures help researchers and scientists around the world describe the outcomes of observations in a contextual manner. The following are some possible examples of how percent error can be applied:<\/p>\n