Any quantity calculated from uncertain values will itself have an uncertainty. How do we calculate this propagation of the uncertainties. We will see several methods, from very simple to more sophisticated using calculus. In all of the descriptions below we assume the quantity q is calculated from 4 measured quantities:
How do we find the uncertainty 
?
These overestimate the uncertainties. They will be accepted here in this class, however you must be aware that they no longer will be regarded as correct in any experimental course at the university level.
1 Sums and Differences
Add the absolute uncertainties:
if 
, then 
.
2 Products and Quotients
Add the fractional uncertainties:
if 
, then 
.
3 Multiplication by an exact number
if 
, then 
.
Another way to view this is that the fractional uncertainty of q is the same as the fractional uncertainty on x. Multiplying by an exact number does not change the fractional uncertainty.
4 Uncertainty in a power
if 
, then 
.
5 Upper-Lower bound method for complex functions
if an angle is measured to be 
, what is the uncertainty on 
? In that case q must be found in the range 
and 
.
The uncertainty on q is therefore: 
.
Click here for an example of the propagation of uncertainties.
Are you ready for more? page 2.