Yes, the standard error of the mean is the standard deviation divided by the square root of the sample size. As sample size increases SD becomes constant but SEM goes down.
SEM, therefore, provides an estimate of how close the sample mean is to the true population mean. It is not a descriptive statistic and generally is of little value to the reader of your paper/report etc.
Most researchers don’t report the SEM in their manuscripts… So why might you want to calculate it?
LaNts and Laminins 