Calculating Percent Error

To err is human, to forgive is divine. - Alexander Pope

We humans are bound to make errors. We learn through rectification of our errors. Although divine perfection is unattainable, to improve precision, one must have a quantified idea of how much you have erred. If you are a newbie to scientific experimentation and have just begun your first lab course in school, you will have to calculate percent error in various physics, chemistry and biology experiments. This article will explain how to calculate percentage error.

What is an Error?

Error calculation is so important that a whole subject called 'Error Analysis' is devoted to it. Error is the amount of deviation from accurate values. Error calculation is not possible, unless you make a quantitative measurement of the various quantities involved in your experiment. Measurement can help us in calculating errors and knowing how right we are in our theoretical models.

Steps of the scientific method consist observation, theory and experiment. We observe a phenomenon in nature and come up with a theory to explain the phenomenon. Mathematics is the language of nature. The only way in which one can test the validity of this theory is through experiment. What confirms the theory is the precise matching between observed experimental and predicted theoretical results. The degree of error, which is the difference between observed and predicated experimental values can be the undoing of that theoretical model. Even small changes or errors, mean that there is something we do not understand and need to account for it. We keep improving the theory and calculate the error in experimental results, until precision is achieved.

Small errors get magnified over time to create bigger problems later. This is especially true about a giant machinery. Be it any form of engineering, uncorrected error that has exceeded error tolerance limits can destroy the greatest of plans.

How to Calculate Percentage Error?

To calculate error percentage, you do not need advanced mathematical machinery. Just an ability to subtract, divide and multiply numbers is enough. Let us go about calculating percent error, step by step.

Step 1: Get the Observed Value & Accurate Value
First step in calculating error is getting the observed value and the value which you are aiming at, which is the precise value. Say you are making a measurement with a scale. The accurate value should be 30 cm. However, you are getting an observed value of 29.7 cm.

Step 2: Subtract Observed Value from Accurate Value & Take Modulus
Next step is to subtract the observed value from the accurate value. That is perform the following operation: (29.7 cm - 30 cm ) = -0.3. The error is negative. Next we take the modulus of this difference. That is if the difference is negative, we will make it positive, and if the difference is positive, it stays the way it is. This is what taking a modulus means. It ensures that we always get a positive difference. So after taking modulus, the difference or 'Raw Error' becomes 0.3.

Step 3: Divide Raw Error By The Accurate Value
Next one must divide the raw error by the accurate value. (0.3/30) = 0.01. This value that you get after division is the 'Relative Error' which is 0.01 here.

Step 4: Multiple Relative Error By 100
Multiply the relative error by 100 to get the percent error. In this case, (0.01 x 100) = 1%. Thus our measurement had 1 percent error.

You will get used to calculating percent error as you advance through your lab courses in school. Knowing how much and where you err is important if you intend to improve!