The method of solving a column calculation involves several steps.

First you need to know the total load per column, or P.
Next the dimensions of the column itself.
With these we can determine the axial force in the column.
Enter total load on the column, (P)lbs
Enter the weak axis depth of the column, (D)inches
Enter the width of the column, (B)inches
Enter the effective length of the column, (Le)inches
Each species and grade of wood has different allowable compressive strength and stiffness. Select Species and Grade

fc(axial stress)psi = Plbs / Asquare inches

These are some other numbers related to the column;
We now know how many pounds per square inch are bearing on and travelling through the column,
The allowable compressive stress for the species and grade (Fc) is psi, in a dry environment.
For a short column with a length to least depth ratio under 1:12 crushing is the main concern, there is little risk of buckling due to slenderness.
In a short column, as long as the axial load (fc) is less than the allowable fiberstress in compression (Fc) the column checks out.
So for brutally basic engineering keep the L/D ratio at under 1:12, or for a freestanding 8' column an 8"x8" post only needs a compressive check

As a column gets longer, up to the maximum allowable ratio of 1:50, the risk of buckling due to slenderness becomes a concern.
The allowable compressive strength must be modified by the "column stability factor"
Calculating (CP) and using it to modify Fc is the next problem;

CP=1+(FcE/Fc)/2C - Sqrt ([(1+(FcE/Fc))/2C]2 - (FcE/Fc)/C)

Fc= adjusted compression design value. The base design value comes from the NDS.
The value here is unadjusted for duration of load(10 year) and moisture(dry service)psi

FcE= Critical buckling design value, (.822*Emin)/(le/d)2psi
This is the allowable axial load for buckling based on the stiffness of the wood, the span, and the weak axis depth entered above
C= .8 for sawn lumber

Putting all those variables to work in the formula above gives the Column stability Factor; Cp=
"Slenderness" causes this column to lose % of its strength.

Finally this is the formula to give the adjusted allowable compression load, compare it to the actual axial stress.
If the adjusted allowable compressive load (Fc') in psi is greater than the actual axial load (fc) in psi, then the column checks.
Fc'= Fc * CD * CM * CP = psi
This is the allowable stress in the column,psi
It must be greater than the actual stress,psi