Rough Approximation of Power Transformer Required

Just a general and roughly close approximation would do for my purpose. Thanks in advance!

You can go to Digi-Key (not an endorsement) or other transformer websites and get dimensions directly from their listing of transformers, if you know the requirements.

Don't know about form factor guessing.

The Henway Technique would provide "a general and roughly close approximation".

What's a henway?

Which dimensions are you talking about? There's the three spatial dimensions, total energy, transfered energy, mass, core losses, bandwidth, saturation, step up ratio, input and output induction, isolation, eddy current loss, etc. There are formulas for all of these and they all interrelate. The first equation you should know to help in grasping the rest is Maxwell's equations.

Not really, there are too many variables to consider. Transformer design (especially utility sized ones) is a combination of art, science and engineering. For starters we need to know the MVA and Voltage ratings, type of construction (shell, core), type of cooling (air, oil, forced, natural, combo), winding materials (copper, aluminum), insulation material (oil, paper, cast resin), short circuit and transient voltage withstand capability due to location in system (generator stepup, distribution, transmission, etc.), and don't forget cost and logistics.

If you're only interested in low voltage, open frame industrial transformers you could easily go into Google, get some manufacturers' catalogs, prepare a spreadsheet with the critical values, and create an empirical formula from the results....and when you're done please post the results in this forum for all of us to see.

Transformers come in standard sizes. See catalogues. Then there are minor details, like open, closed, shielded, Exposed power strip, weather proof, explosion proof. Open catalogue, pore thru hundreds of choices, pick one, buy. Mystery solved.

You forgot cryogenic cooled super-conducting, vacuum compatible, armored, dry nitrogen filled, submersible and at least a half dozen other choices.

For a start,

area of core varies as (power output) ** 0.5

area of winding space varies as (Power Output) ** 0.5

the volume varies as (power output) **0.75.

So grab a few transformers of known power output preferably from same maker, and using same steel), and a manufacturer's table of laminations, do some measurements, and scale from there, using microsoft excel or other spreadsheet.