How big an area do you need to calculate?
The engineering method to calculate cut and fill involves drawing cross sections. For a barn sized area, you may be able to do this by estimation, by eyballing and pacing a few points or using a five dollar hand level from Home Despot.
The hand level is a viewing device with a bubble, you look through the level and the bubble or a cross hair shows when you're looking at something at the same elevation as your eyeball. An old f(r)iend used to do one man survey for septic tanks by pacing and using and his pickup truck for a rod. E.g. If you sight on the bumper, your feet are 4 feet below the truck wheels, if you sight on the hood ... etc. It's probably good enough for what you want. You can calibrate your truck in about ten minutes.
Then draw up each cross section on graph paper. We usually exaggerate the vertical dimension 5:1 or 10:1 so we can actually draw something visible. Get the 10 squares to the inch paper. It makes the calculations and counting go easier. Figure your scale so you can more or less use up an 8-1/2 x 11 inch sheet of paper for each cross section.
Draw the existing grade and add your proposed grade to each cross section.
We generally do cross sections every 50 or 100 feet. For a little tiddly job 10 or 25 feet is not out of line. You won't need a million X-Sects like they do for a highway job. I guess you'll have 5 or 7 X-Sects; one on each end of the barn, one on each end of the fill, where it meets existing, and maybe one in the middle of the barn.
Calculate the area of one graph square. If it's 1 foot wide by 1/10 foot high, it's 0.1 sq ft.
Count the squares, between the existing and the proposed lines. If a square is more than half in, by eye, it's in. If it's less than half in, it's out. Use a colored pencil to put a dot in each square as you count it. Counting squares is mind grinding work, so it's easy to forget where you were. Don't ask me how I know this. /forums/images/graemlins/wink.gif
The volume between each pair of cross sections is the average of the two areas times the distance. L*(A1 + A2)/2 Add up the areas between the pairs of cross sections. Remember that the ends of the fill, where it tapers away to nothing, have a cross section with zero area on each end. You don't need to draw it, but you need to add it in. Those end pieces have a volume of L*A/2.
Convert to cubic yards. 1 CY = 27 CF.
Account for compaction. Fill on the truck will shrink something around 15%, when you place it and compact it.
Account for waste, losses, and errors. 5 - 15% depending on how confident you are in your numbers. It's not as bad as concrete; it's easier to lose two yards of dirt on site than two yards of concrete. But you hate to buy another truckload, and pay a minimum charge, because you were two yards short.
I've always bought fill by the yard; many operations don't have a scale. But it's easier to cheat you by the yard. How much dirt can you carry in a ten yard truck, anyway? We deal with that by surveying to get the numbers. You probably don't want to do that. Talk to your supplier. They'll know how many yards they can get out of a ton of dirt. In the end, you should plan on buying a truckload more than you thought you needed, and you'll never figure out where it went.
Be sure you compact the fill as it goes in. A heavy tractor or a bulldozer is nice for that, but you may want to rent a plate compactor or a walk-behind sheeps foot roller. Place the dirt in six inch lifts and compact each lift.
Plan your fill so the drainage goes somewhere. If you don't, it will go where you don't want it - guaranteed. I try to slope dirt to 2% (1/4 inch per ft) minimum. Flatter than that, you'll get frog habitat. Of course, your slab wants to be flatter, but you can set forms for that, and screed your gravel base and concrete pretty accurately.
