You won't need any info on the octagon portion that is left after you shorten and make half-round. That weight remains the same.
Takes three calculations. 
1.) Measure across the flats at the mid-point of the length of the round portion you plan to have when the barrel is 28" long. This will be the "average" diameter of the round area (unless you plan to take off more metal). Use that as the A in this online calculator:
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Once you have the B from the above, you can use this formula:
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The B from the first calculation is the small 'a' in the second calculation. You now have the cross-sectional area of the octagonal section prior to being turned half-round. 
Multiply this number by the length of the new round portion of the barrel.
2.) Again, use the across the flat measurement from 1.), above and calculate the area of a circle with that diameter:
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This is how much the round portion of the barrel will weigh. Multiply this number by the length of the round section.
3.) Subtract the number you end up with from part 1.) and part 2.) and that is the volume of metal that you will be removing. To get the weight, multiply this number by the volumetric weight of 4130 metal.

For the 4" section, make calculation 1.) for the 4" length you want to cut off. Then calculate 2.) for the diameter of the bore (0.409", or so, for 40cal, etc.) and 4" length and subtract from the 1.) calculation you made for the 4" section. This will be the weight you've cut off. Add this number to the number you get from 3.) above and that will be the total weight removed. Should be accurate within a couple ounces, as you've neglected the grooves, etc., (which are beyond the scope of this discussion  ). Have fun.