Calculation of the covariance matrix, Q, is next. The covariance matrix consists of the coefficients of the unknowns from the observation equations, and is used to compute standard deviations and error ellipses. The following matrix formula, using the previously solved A and P matrices, is used:
The Q matrix appears as follows:
Next, the calculation of the degrees of freedom in an adjustment, r, is accomplished through the use of the following formula:
where
- m = the number of observation equations
- n = the number of unknowns (or 2n in the case of coordinates, since both x and y are unknown)
The next procedure is the calculation of the standard deviation of unit weight for a weighted adjustment, So, which is done through the following matrix formula:
where
- r = the degree of freedom in the adjustment
Calculation of the standard deviations of the individual adjusted quantities, 
, is next. These are determined by the following formula:
where
- So = the standard deviation of unit weight
- = the diagonal element in the ith row and ith column from the covariance matrix Q