How to Calculate Percent Error

The concept of percentage error can be used in any kind of performance measurement. Right from how effective is your driving for greater to fuel economy to complex nuclear physics estimates. The existence of error is universal and mathematicians have found out a simple method that helps us rationally observer the severity of the existence of error. In the following two paragraphs, the formula to calculate percent error, its logic and the reason that is a successful parameter of measurement have been given. Moving on to the answer to the query 'how to calculate percent error'...

About Percentage Error

Before we begin with the equation to calculate percent error, let us define what an error is. Broadly speaking, an error is a mistake and mathematically specking it can be defined as an incidence where the expected accurate result is not derived, instead the result has off shot or fallen short of the expected result. Calculating percent error is a great way to derive a rational figure that defines the error.

Why 'percentage' error?, is a question that one might ask. Well answer is quite simple. A percentage provides an excellent parameter of comparison. Normal numbers such as an actual target of 11 units per day and achievement of just 8.5 units does not completely define the error properly. Conversion of the same into percentage works just fine as you have a figure that is neutral and is based upon the parameter of 100. The simpler comparison and a more rational view is the reason why percentage error is more logical and realistic connotation to compute the error.

How to find Percent Error?

The percent error formula can be written in several different ways, though the final result is always the same. The basic motive of the percentage error is to derive, by how much has the error occurred on a platform of percentage. Thus division of multiplication by 100% or simply 100 is necessary. Apart from the percentage value, accepted value (also referred to as the theoretical value, measurement, expected value, target value, etc) and the actual value (also known as practical, experimental, etc). These two values basically point out the difference between what should have been (expected target or value) or what is (achievement), which is the error. This difference is to be converted into percentage. Here are some formulas of percentage error:

% error = {(amount of error) / accepted value} × 100

In such a case, amount of error is the difference between what was expected and what is the actual result. The accepted value is basically the expected result. For example: a machine was supposed to churn out 75 bases in 1 hour, however, it ended up churning only 72. The % error thus becomes

% error = {(75-72) / 75} × 100
= {(3) / 75} × 100
= {300 / 75}
= 4%

Thus the % error in the machines output was 4%. In such cases, an off shoot of the expected target is good but in structural design and chemistry related calculations or in formulas related to physics, the off shoot is also a bad error or is viewed in a negative light. When one asks the question, "How to calculate percent error?", there are some other formulas which can be used. These formulas are of similar nature and derive the same output, :

% error = (estimated value - actual value / actual value) × 100

% error = estimated value - actual value / actual value × 100%

% error = {(measures value - actual value) / actual value} × 100%

The aforementioned 4 values of percentage error basically, mean the same and are just written in a different manner. I hope that the answer to the query, "How to calculate percent error?" is resourceful.