Use std by row (axis=1):

df['stdDev'] = df[['A', 'B', 'C', 'D']].std(axis=1)

output:

  Key  A  B   C   D    stdDev
0   X  1  2   3   4  1.290994
1   y  4  5   6   7  1.290994
2   z  8  9  10  11  1.290994

It is expected, because if checking DataFrame.std:

Normalized by N-1 by default. This can be changed using the ddof argument

If you have one element, you're doing a division by 0. So if you have one column and want the sample standard deviation over columns, get all the missing values.

Sample:

inp_df = pd.DataFrame({'salary':[10,20,30],
                       'num_months':[1,2,3],
                       'no_of_hours':[2,5,6]})
print (inp_df)
   salary  num_months  no_of_hours
0      10           1            2
1      20           2            5
2      30           3            6

Select one column by one [] for Series:

print (inp_df['salary'])
0    10
1    20
2    30
Name: salary, dtype: int64

Get std of Series - get a scalar:

print (inp_df['salary'].std())
10.0

Select one column by double [] for one column DataFrame:

print (inp_df[['salary']])
   salary
0      10
1      20
2      30

Get std of DataFrame per index (default value) - get one element Series:

print (inp_df[['salary']].std())
#same like
#print (inp_df[['salary']].std(axis=0))
salary    10.0
dtype: float64

Get std of DataFrame per columns (axis=1) - get all NaNs:

print (inp_df[['salary']].std(axis = 1))
0   NaN
1   NaN
2   NaN
dtype: float64

If changed default ddof=1 to ddof=0:

print (inp_df[['salary']].std(axis = 1, ddof=0))
0    0.0
1    0.0
2    0.0
dtype: float64

If you want std by two or more columns:

#select 2 columns
print (inp_df[['salary', 'num_months']])
   salary  num_months
0      10           1
1      20           2
2      30           3

#std by index
print (inp_df[['salary','num_months']].std())
salary        10.0
num_months     1.0
dtype: float64

#std by columns
print (inp_df[['salary','no_of_hours']].std(axis = 1))
0     5.656854
1    10.606602
2    16.970563
dtype: float64