sd() function calculates the standard deviation.

sd(x, na.rm=FALSE)

x: numeric vector
na.rm: missing values should be removed or not

> x <- c(1,2.3,2,3,4,8,12,43,-4,-1)
> r <- sd(x)
> r

[1] 13.39602

The standard error equals sd/√n:

> x <- c(1,2.3,2,3,4,8,12,43,-4,-1)
> se <- sd(x)/sqrt(length(x))
> se

[1] 4.236195

Calculate the SD of data frame (matrix):

>BOD #R Biochemical Oxygen Demand database

Time demand
1 1 8.3
2 2 10.3
3 3 19.0
4 4 16.0
5 5 15.6
6 7 19.8

> apply(BOD,2,sd)

Time demand
2.160247 4.630623