Calculate the expansion or shrink of steel at various temperatures

In the forging industry and probably any industry that heats and cools steel there is a change in volume when the material is heated or cooled. General rule (not exact) is that plain carbon steel will expand and contract at a rate of 3/16" per foot diameter between ambient temperature(100F) to forging temperature (2300F).A 10.000" diameter bar of plain carbon steel at ambient temperature will expand to about 10.156" diameter when heated to 2300F, and then contract back to 10.000" when cooled to ambient temperature. It is almost certain that the expansion and contraction is not linear between those temperature ranges, and the expansion/contraction rate is different for the significantly different material grades (Carbon steel, Chrome alloy steel, Stainless steel, Nickel grade, Copper grade, aluminum grade, etc.) .
With that preface, the industries that heat and cool metals could use a calculator that takes (5) inputs: Material family (carbon, stainless, etc), Starting material shape (round, cylindrical or square/rectangular), Starting material size (diameter if round; inside and outside diameters if cylindrical, width/height if square or rectangular),Starting temperature (default is "Ambient" but could be any temperature), Final temperature (the temperature at which the material is being heated or cooled). The result would be the dimensions of the material at the final temperature and the expansion/contraction density factor (Final cross-sectional volume divided by Starting cross-sectional volume). Example: Family = Carbon Steel, Shape = Square/Rectangular, Size = 10.000" X 14.000" rectangular, Starting temp = 100F, Final temp = 1500F. Results: Size = 10.072" X 14.914", Factor = 1:1.07295.
Final note: Arguably there are infinite factors that will affect this calculation such as exact element composition of the material, the length or mass, the surface conditions, the heating method, and so on. This needs to be simple enough to use as a reference and let the user determine if the level of accuracy is useful. It will be highly useful in my business of heavy forging and heat treating.
Please let me know your thoughts!
Thank you.
Ed Murphy
Forge Shop Manager
Forged Components Inc.
Navasota, TX
emurphy@forgedcomponents.com