Cut and fill is one subtraction with two names
Every number on this page is existing ground minus design grade at the same point. Positive means the ground is above where it needs to be and material comes off, which is cut. Negative means the ground is below and material goes on, which is fill. That is the whole calculation, and the reason it still causes trouble on site is that the answer is written on a stake as a bare number with a letter in front of it, and letters get smudged.
Pick the convention before the first stake goes in, write it on the plan set, and say out loud what the reference is. A mark measured down from the top of the stake and a mark measured from the ground line at the stake differ by however far the stake is sticking out, which on a hub is nothing and on a lath is a foot and a half.
The grade line
The design surface here is a straight line from a starting elevation at a stated grade. Percent grade, fall per foot in inches, and "it has to come out at this elevation at the far end" are three ways of writing the same line, and the page will take any of them. Two of them can disagree with each other by more than people expect: minus 1.5 percent over 150 feet is a fall of 2.25 feet, and an eighth of an inch per foot over the same run is 1.5625 feet. If somebody hands you a fall per foot and somebody else hands you a percentage, check they describe the same line before staking anything.
Offset stakes sit clear of where the machine works, so the design elevation at the stake is not the design elevation on the line. With a cross slope on the finished surface, the stake is lower or higher than the centreline by the offset times the cross slope. Ten feet off at 2 percent is 0.2 feet, which is a lot to be wrong by on a slab subgrade.
Reading a grade rod
| Situation | Rod reads | Meaning |
|---|---|---|
| Rod foot exactly on grade | Equal to the grade rod | Nothing to do |
| Rod reads more than the grade rod | Larger number | Foot is low — fill by the difference |
| Rod reads less than the grade rod | Smaller number | Foot is high — cut by the difference |
| Rod will not read at all | Off the top or below zero | Line of sight is wrong for this station — move the instrument or use a turning point |
The grade rod is height of instrument minus design elevation. Once you have it, nobody at the stake has to do elevation arithmetic — they read the rod, subtract, and the difference is the cut or fill. That is the whole reason the number is worth calculating in advance for every station.
What this does not do
It compares a straight grade line to ground elevations you supply, at the stations you supply them for. It knows nothing about vertical curves, about what happens between your stations, or about whether the design grade is the right grade. The elevations themselves come from somewhere else — the differential levelling calculator is how a loop of shots turns into them. For volume rather than depth, the grid cut and fill calculator works over an area and the average end area calculator works along a corridor. For the slope stakes that catch the side slopes rather than the finished surface, see the slope stake calculator.
Questions people ask
Does positive mean cut or fill?
On this page positive is cut: the existing ground is above the design grade, so material comes off. Negative is fill. That is stated in the output as well as here because the opposite convention exists in the wild and mixing the two on one job is expensive. The safest habit is to never rely on the sign alone — write the letter, C or F, on the stake and say which reference point it is measured from.
What is a grade point?
The station where the design grade line crosses the existing ground, so the cut or fill is zero and the stakes on either side of it carry opposite letters. It is a useful stake to set on its own because it is the boundary between the part of the job the machine is digging and the part it is filling. The location here is interpolated straight between the two shots either side, which is only as good as the assumption that the ground runs straight between them.
How do offset stakes change the numbers?
The design elevation at an offset stake is the centreline design elevation adjusted for the cross slope over the offset distance. Ten feet off the line at a 2 percent cross slope puts the stake 0.2 feet below the centreline grade, and a stake marked with the centreline number would send the machine 0.2 feet deep across the whole surface. Enter the offset and the cross slope and the table gives the design elevation at the stake, not at the line.
Why does my fall per foot disagree with my percent grade?
Because they are different units and an eighth of an inch is not one percent. One inch per foot is 8.333 percent. An eighth of an inch per foot is 1.042 percent. A quarter is 2.083 percent. Over a 150 foot run those differences turn into feet: 1.5 percent gives 2.25 feet of fall, an eighth per foot gives 1.5625 feet. Convert once and check both numbers against the same total drop before anything gets staked.
How far apart should the stations be?
Close enough that the ground between two stakes actually runs straight, which is a site question rather than a rule. Twenty-five or fifty feet is common on open ground with steady fall. Where the ground rolls, where the cut or fill passes through zero, and anywhere the surface changes direction, the spacing has to tighten or the interpolation between stakes is fiction. If two adjacent stakes disagree by a lot, that gap is where an extra shot pays for itself.