Take the number of variances you have, one for each observed variable, then add the number of covariances between all of them. The formula for this is (p*(p+1))/2, where p is the number of observed variables. So for a 5 observed variable model you have 5*6/2 = 15 variances and covariances. That's the data you have.

Now add up the number of parameters you wish to estimate. Subtract those from the number of variances and covariances, and that's your degrees of freedom.

For example, with five observed variables, I have 15 elements in the variance/covariance matrix. Let's say I specify a one-factor CFA, with all five factors loading on the single factor. This means I will estimate four loadings (not five, since one is fixed to 1), and five variances-one for each observed variable, plus one variance for the latent variable, meaning I'm estimating 4+5+1 = 10 parameters. With 15 variances/covariances - 10 estimated parameters, I should have 5 degrees of freedom for this model.

Most SEM output will show you the parameters that were estimated and those that were fixed, so you can do parameter counts if you like.

Take the number of variances you have, one for each observed variable, then add the number of covariances between all of them. The formula for this is (p*(p+1))/2, where p is the number of observed variables. So for a 5 observed variable model you have 5*6/2 = 15 variances and covariances. That's the data you have.

Now add up the number of parameters you wish to estimate. Subtract those from the number of variances and covariances, and that's your degrees of freedom.

For example, with five observed variables, I have 15 elements in the variance/covariance matrix. Let's say I specify a one-factor CFA, with all five factors loading on the single factor. This means I will estimate four loadings (not five, since one is fixed to 1), and five variances-one for each observed variable, plus one variance for the latent variable, meaning I'm estimating 4+5+1 = 10 parameters. With 15 variances/covariances - 10 estimated parameters, I should have 5 degrees of freedom for this model.

Most SEM output will show you the parameters that were estimated and those that were fixed, so you can do parameter counts if you like.

Scot has there right formula, but your output should include the DoF so that you don't need to do any guesswork.

I agree with you Davis.  However I am using the SEM builder in STATA 14 and the output does  not seem to indicate df.  I must be missing something it would be odd if df was not reported. 

I don't know anything about STATA, so take the following with a grain of salt, but checking a couple examples of STATA output on the web, I find things like a comparison between models:

chi2_ms(5)

and

chi2_ms(10)

I'm pretty sure the numbers in parentheses are your D of F.

http://www.ats.ucla.edu/stat/stata/faq/sem_baseline.htm

It is very very simple. you just know number of question and arrows between latent variables. [(Q(Q-3))/2]-R

Method Calculating Degrees of Freedom in Structural Equation Modeling

One of the easiest books I have read to understand what and how degrees of freedom increases/decreases is "A Step-by-Step approach to using sas for factor analysis and structural equation modeling".

This blog provides also provide useful explanation:

https://clavelresearch.wordpress.com/2014/05/03/disentangling-degrees-of-freedom-for-sem/