How to Calculate Relative Error

Step-by-Step Guide

1. 1

   Step 1: When given an expected value

   An expected value is usually found on tests and school labs.
   
   Basically, this is the most precise, common measurement to come up with, usually for common equations or reactions.
   
   You can compare your own results to get Absolute Error, which measures how far off you were from the expected results.
   
   To do so, simply subtract the measured value from the expected one.
   
   Even if the result is negative, make it positive.
   
   This is your absolute error!Example:
   You want to know how accurately you estimate distances by pacing them off.
   
   You pace from one tree to another and estimate that they're 18 feet apart.
   
   This is the experimental value.
   
   Then you come back with a long measuring tape to measure the exact distance, finding out that the trees are in fact 20 feet (6 meters) apart.
   
   That is the "real" value.
   
   Your absolute error is 20
   - 18 = 2 feet (60.96 centimeters).
2. 2

   Step 2: subtract the value you got from the expected value to get the Absolute Error.

   For example, if you're measuring something with a meter stick, the smallest unit marked on the meter stick is 1 millimeter (mm).
   
   So you know that your measurement is accurate to within + or
   - 1 mm; your absolute error is 1 mm.
   
   This works for any measurement system.
   
   Many scientific tools, like precision droppers and measurement equipment, often has absolute error labeled on the sides as "+/- ____ "
   
   Say your Absolute Error was "2 meters." This tells your viewers exactly how far off your error was.
   
   But if you write that your error was simply "2," this doesn't tell your audience anything.
   
   Use the same unites as the ones in your measurements., The best way to learn how to calculate error is to go ahead and calculate it.
   
   Take a stab at the following problems, then highlight the space after the colon (:) to see your answer.
   
   Jill is studying chemical reactions.
   
   After mixing and matching, her test tube contains 32 grams of substrate.
   
   The accepted value for her experiment was 34 grams.
   
   Her Absolute Error is: +/- 2 grams Clive is testing reactions in chemistry.
   
   It takes 10ml drops of water to cause a reaction, but his dropper claims it is "+/- .5ml." The Absolute Error in his measurements must be: +/- .5ml , No scientific study is ever perfectly error free
   -- even Nobel Prize winning papers and discoveries have a margin or error attached.
   
   Still, understanding where error comes from is essential to help try and prevent it:
   Human error is the most common.
   
   This is from bad measurements, faulty premises, or mistakes in the lab.
   
   Incidental energy/material loss, such as the little fluid left in the beaker after pouring, changes in temperature due to the environment, etc.
   
   Imperfect equipment used either for measurement or studies, such as very small, precise measurements or burners that provide uneven heat.
3. 3

   Step 3: Alternatively

4. 4

   Step 4: when measuring something

5. 5

   Step 5: assume the absolute error to be the smallest unit of measurement at your disposal.

6. 6

   Step 6: Always add the appropriate units.

7. 7

   Step 7: Practice with several examples.

8. 8

   Step 8: Understand what causes error

9. 9

   Step 9: and how you can work to eliminate it.

Detailed Guide

About the Author