Capacitors with same voltage, same capacitance, same temp, different diameter?
The answer lies in the datasheet and the designer requirements for cost, space, reliability, cost and temperature rating.  There are many choices. (Did I say cost;)

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The Part Number defines;   e.g. KF102M025I200A   


KF Family construction of foil film and dielectric, there are many others
xxe value 102 for C in uF with exponents 10 00 uf
M = 20 % tolerance on C
xxx voltage rating
A letter code for Case Dia &amp; radial lead space
xxx height xx.x mm 


The height and Voltage reduce ESR while the diameter affects everything.

The parameters for selection of these low ESR caps are;   


C, Vdc, Size, max temp range, xxxx Hrs Endurance of accelerated MTBF at extreme temp &amp; RMS ripple current 
the electrical variables for these choices are % DF at 120Hz, Ripple current @ 100kHz,  @ 10kHz, ESR 


I don't know the formula, but the diameter is determined by foil area, thickness, turns, ESR,and temp rise due to ripple current rating at max temp for xxxx hours due to thermal conductance and  temp rise above max ambient rating and Arrhenius effects on Endurance.