How can you define short column and long column?

A column is considered to be short when the ratio of its effective length to its least lateral dimension does not exceed12.
If the ratio of the the effective length to its least lateral dimension exceeds12 the column is considered to be a long column.

Long column is generally refer having slenderness ratio greater than12 else column is consider as long column in RCC.
In short column, column fails by compression whereas in Long column,if there is no any eccentric loading but  it fails by compression and bending thought column is axially loaded.
Buckling in long column may take place but in short column, there may not be.

According to BS8810 : A column is classified as short if Lex/h AND ley/b are :

-less than 15 for BRACED column .

-less than 10 for an UNBRACED column .

 

*About failures modes : Short columns usually fail by crushing ,but a slender column is liable to fail by buckling .

 

1_Short columns can't have a buckling but the long columns can have a buckling2-We can differentiate between Short columns and Long columns by the ratio of height to depth

SHORT COLUMNS ACCORDING TO THEORY IS DEFINED BY SLENDERNESS RATIO(L/R) IF SLENDERNESS RATIO IS LESS THAN12 IT IS SHORT AND IF IT IS GREATER THAN12 IT IS LONG COLUMN.LONG COLUMN IS ALSO SUBJECTED TO BUCKLIN THUS ADDITIONAL REINFORCEMENT CONSIDERING TRAVERSE SHEAR SHOULD ALSO BE CONSIDERED,DESPITE THIS WE HVE TO CONSIDER THE SUPPORT CONDITIONS WHILE DESIGNING 

Totally Agree with Usman Guni

Slenderness ratio for long column is >12.n for short < 12..long column fails by bucking n short one fails by crushing...eulers formula can be used for long column...n cant br used for short column