How to Calculate Uncertainty

Step-by-Step Guide

1. 1

   Step 1: State uncertainty in its proper form.

   Let's say you're measuring a stick that falls near
   4.2 cm, give or take one millimeter.
   
   This means that you know the stick falls almost on
   4.2 cm, but that it could actually be just a bit smaller or larger than that measurement, with the error of one millimeter.
   
   State the uncertainty like this:
   4.2 cm ±
   0.1 cm.
   
   You can also rewrite this as
   4.2 cm ± 1 mm, since
   0.1 cm = 1 mm.
2. 2

   Step 2: Always round the experimental measurement to the same decimal place as the uncertainty.

   Measurements that involve a calculation of uncertainty are typically rounded to one or two significant digits.
   
   The most important point is that you should round your experimental measurement to the same decimal place as the uncertainty to keep your measurements consistent.
   
   If your experimental measurement is 60 cm, then your uncertainty calculation should be rounded to a whole number as well.
   
   For example, the uncertainty for this measurement can be 60 cm ± 2 cm, but not 60 cm ±
   2.2 cm.
   
   If your experimental measurement is
   3.4 cm, then your uncertainty calculation should be rounded to .1 cm.
   
   For example, the uncertainty for this measurement can be
   3.4 cm ± .1 cm, but not
   3.4 cm ± 1 cm. , Let's say you're measuring the diameter of a round ball with a ruler.
   
   This is tricky because it'll be difficult to say exactly where the outer edges of the ball line up with the ruler since they are curved, not straight.
   
   Let's say the ruler can find the measurement to the nearest .1 cm
   -- this does not mean that you can measure the diameter to this level of precision.Study the edges of the ball and the ruler to get a sense of how reliably you can measure its diameter.
   
   In a standard ruler, the markings at .5 cm show up clearly
   -- but let's say you can get a little bit closer than that.
   
   If it looks like you can get about within .3 cm of an accurate measurement, then your uncertainty is .3 cm.
   
   Now, measure the diameter of the ball.
   
   Let's say you get about
   7.6 cm.
   
   Just state the estimated measurement along with the uncertainty.
   
   The diameter of the ball is
   7.6 cm ± .3 cm. , Let's say you're measuring a stack of 10 CD cases that are all the same length.
   
   Let's say you want to find the measurement of the thickness of just one CD case.
   
   This measurement will be so small that your percentage of uncertainty will be a bit high.
   
   But when you measure 10 CD cases stacked together, you can just divide the result and its uncertainty by the number of CD cases to find the thickness of one CD case.Let's say that you can't get much closer than to .2 cm of measurements by using a ruler.
   
   So, your uncertainty is ± .2 cm.
   
   Let's say you measured that all of the CD cases stacked together are of a thickness of 22 cm.
   
   Now, just divide the measurement and uncertainty by 10, the number of CD cases. 22 cm/10 =
   2.2 cm and .2 cm/10 = .02 cm.
   
   This means that the thickness of one CD case is
   2.20 cm ± .02 cm. , To increase the certainty of your measurements, whether you're measuring the length of on object or the amount of time it takes for an object to cross a certain distance, you'll be increasing your chances of getting an accurate measurement if you take several measurements.
   
   Finding the average of your multiple measurements will help you get a more accurate picture of the measurement while calculating the uncertainty.
3. 3

   Step 3: Calculate uncertainty from a single measurement.

4. 4

   Step 4: Calculate uncertainty of a single measurement of multiple objects.

5. 5

   Step 5: Take your measurements multiple times.

Detailed Guide

About the Author