Understanding Experimental Error
Mr. Gilliland - Honors Physical Science @ SHS

The Need for Experimental Error

Terms such as "a lot", "pretty good", "close" or "short" do not have a place in science since they lack a particular meaning. These examples are relative terms - words who's meaning can change depending on what they are compared to.

In science it is important that you express exactly what you mean so that others looking at your work know exactly what you meant. When you complete an experiment and want to know how well you did, you don't want to hear "you were close to getting it" or "you did pretty well". What you want to know is by what percent did you missed the answer? If you missed it by 3% you would receive a grade of 97%, miss it by 12 % and you get an 88%. Everyone understands what 88% means. Whether an 88% is a "good" or "bad" grade is relative to how well the person making that grade does in school.

In school you perform laboratory experiments to reinforce the learning of a procedure. The correct data has already been determined in a research lab - the correct data is called the "accepted value". The accepted value is the measurement that scientists throughout the world accept as true. Water freezes at 0 degrees Celsius is an accepted value. The density of water at 4 degrees Celsius is 1.0 g/mL is an accepted value. Accepted values are measurements that have been repeatedly tested and accepted throughout the world to be correct.

In the high school lab you are trying to duplicate an experiment so that you will come as close to the accepted value as you can and thus better understand the procedures and material. So, unlike real scientific research where the answer is not known, you are performing experiments that have known results. While you may not know them your teacher knows what those results should be.

Calculating Experimental Error

So how do you judge how close you came to duplicating the correct data in an experiment? By calculating the experimental error - that's how!

Experimental error (also known as Percent Error) is the percentage you missed the accepted value in the experiment. Experimental error is not relative - it has the same meaning to everyone. A 9% error is a 9% error - there is nothing relative about it.

Before we discuss how to calculate Experimental Error we must define a few terms. What you obtained in an experiment is called the experimental value. What is accepted throughout the world is called the accepted value. Now you are ready to move on.

So how do you calculate Experimental Error? It's easy - just follow these steps.

1. Calculate the difference between the experimental value (what you got in the experiment ) and the accepted value (the true value) by subtracting them. If it turns out negative then drop the negative sign. It is important you drop any negative sign since you cannot have a negative error. Zero error is as close as you can get - you cannot have a -2 % error.
2. Divide this difference (between the experimental value and the accepted value) by the accepted value.
3. Multiply times 100 to make the value a percent.
4. Use significant figures in all your calculations. When you subtract (Step #1) round your answer to the correct number of significant figures. When you divide (Step #2) round your answers to the correct number of sig figs. Do not use 100 in Step #3 to determine sig figs since in this case 100 is an exact number (percent is defined as out of 100).
5. Remember - if your value for experimental error is negative, drop the negative sign.
6. Use sig figs when you subtract your experimental value from the accepted value and again when you divide that difference by the accepted value. Do not use 100% for determining sig figs - it is an exact number.

Here is the formula for calculating experimental error:

That's it! Now you know exactly how close your calculated measurement comes to the actual accepted measurement. Now let's see an example.

Albert is involved in a lab in which he is calculating the density of aluminum. Here is his data:

Mass of Aluminum: 18.36 grams

Volume of Aluminum: 6.87 mL

Density: 18.36 grams / 6.87 mL = 2.672489 g/mL = 2.67 g/mL

Accepted Value for the Density of Aluminum: 2.70 g/mL

Here is his work for experimental error:

If you think your answer should only have one sig fig instead of two you are wrong. When multiplying or dividing in science you add an extra sig fig to your answer whenever it begins with a one. In this case it does so our answer has two sig figs instead of one.

Albert has an error of 1.1% in his experimental density for aluminum. Not too bad.

I realize that "not too bad" is relative, but still that's pretty good. Yeah - I know "pretty good" is another relative term. But Albert would get a 98.9% for accuracy - and that's not relative.

1. A student obtains the experimental value for the density of gold as 19.5 g/cc. The accepted value for the density of gold is 19.32 g/cc. What is her experimental error?

Solution:

2. A Washington D.C. scientist calculates the acceleration of a falling object in a vacuum at sea level to be 9.82 m/s/s while the accepted value is 9.801 m/s/s. What is his experimental error?

Solution:

That's it. Now you can calculate your experimental error whenever you know the accepted value. In the Density Lab, your teacher will give you the accepted values for the knowns and the unknowns. Be sure to show all your work, including units, when calculating error.

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2000 - Doug Gilliland, The Physical Science Series