Not a scientific way to calculate but as close as you will ever get for just the rail.
I can imagine that the Union Pacific's requirement was about the same so — for the total mileage of the transcontinental railroad of 1776 miles required 177,600 tons (metric tons) of rail for the track alone. more that a standard 2000 lb ton andthat if you reported the railtonnageat a 2,000 lb./ton the total rail weight alone would weigh198,912 tons of iron rail. Just remember that in the 1860's that rail was measured by the metric ton but bolts, spikes and rail fastenings were measured by the standard 2,000 lb. Then you would have to add the weight of spikes bolts, rail chairs, fish plates (rail fastenings).
The CP's engines ranged in weight from 56,000 to 77,450 at the heaviest and they would average out at about 62-65,000 lbs.
The UPRR's engines were a little heavier, ranging from 54,500 to 93,300 lbs for an approximate average of about 75,000 lbs.
Some other major uses for lumber: There were many, many wooden trestles, most of them were huge and they required an enormous amount of lumber.can you imagine the labor of weighting 3 million, three hundred fifty five thousand, one hundred an seventy pounds of rail? Strobridge comments: I can't speak to the Union Pacific rail but can add to the information on the Central Pacific's 690 miles of "Iron." Here is some information on the Central Pacific track.The first approximately 112 miles of railvaried in weight from60 to 66 lb pattern, that is 60 to 66 lbsper lineal yard.If the rail is 56 lb/yard, then the total rail weight is about 175 thousand tons (about a hundred tons of rail per mile).To this you would need to add the weight of about 5,500 spikes and 1,408 bolts per mile, 900 tons of iron used in the construction of the Sierra snow sheds, plates, switches and sidings, iron hardware used in constructing wooden trestle bridges, 20-40 ton locomotives, cars, etc.See the discussion of "dollars per mile of track" including the question of exactly where do the Sierra Nevada mountains begin and end. Graves states that the 1887 Pacific RR Commission said the cost of construction from Sacramento City to Promontory, as of July, 1869 was ,249,916.11; cash or cash equivalent was ,397,135.58.