How can I calculate the cable size for given load current? With out using any tables or charts.

For aluminium cables; consider 1 ampere per square mm. of cross section. For copper cable consider 1.4 ampere per sq.mm. of cross section. But, moreover to this; depending on grouping of cables, ambient temperature, laying over the ground or under ground, no. of tiers in cables trays... derating factor to be considered.

How can I calculate the cable size

It is not advisable to calculate cable size for a given load under given environmental conditions. You should refer to manufacturer's tables taking into consideration all the derating factors. Earth wire size could be calculated using the formula I^2.t=K^2.S^2

How can I know, what is cable size in mm square from cable dia(O.D)?
What is the formula to calculate cable size

Please calculate for me if I know cable dia is 8mm and 6.5mm by using calipar

MY DEAR FRIENDS FROM ANY WHERE SEE UNDER THE PERFECT AND SUITABLE CABLE SIZING FORMULAS:

FOR COPPER CONDUCTOR: AREA(mm2) = 0.005 *I * L (SINGLE PHASE) WHERE: 0.005 FOR MULTIPLY FACTOR
I = LOAD CURRENT, L = LENGTH OF CABLE IN METERS.
AREA(mm2) = 0.002488*I*L (THREE PHASE)
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FOR ALUMINUM CONDUCTORS.:- AREA(mm2) = 0.00805*I*L ( FOR SINGLE PHASE)
AREA(mm2) = 0.004 * I * L (FOR THREE PHASE) WHERE: I = LOAD CURRENT, L = LENGTH OF THE CONDUCTOR IN MTRS.
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DESIGNED FORMULAS BY
ENGR.MUHAMMAD YOUNAS KHAN
M.Sc.Engg.MIEE(UK)
DATE: 16/01/2014

Properties of insulation and other factors too should be taken into account in addition to cross sectional area.