Uneven Subgrade: Concrete Volume from a Depth Grid

Why nominal thickness under-orders on a wavy base

Concrete fills the space between the finished surface and whatever is underneath. The finished surface is controlled by the form tops and the screed. The bottom is controlled by the base. When the base sits lower than planned anywhere inside the forms, that extra depth is filled with concrete, and the nominal thickness quietly stops describing the pour.

On many jobs the error tends to run in one direction. A base that is high in places should be corrected before placement, because a thin spot means the slab does not meet its specified thickness. A base that is low in places is often left as is, because extra thickness is less likely to be treated as a problem. So the low spots stay and the high spots get fixed, and the real average depth ends up at or above the drawing value. An estimate that uses the drawing value is biased toward running short.

Running short is the expensive direction. A partial second delivery, an extra trip for bags while the first batch is already setting, or a cold joint in an area that was meant to be placed in one go all cost more than a modest, measured allowance. The goal here is not to pad the order with an unexplained percentage. It is to replace the assumed depth with a measured one, and to state how precise that measurement is.

Setting up the grid and taking readings

Mark a square grid across the slab area, including points along the forms and at the corners. Stretch a tight line between form tops, or use a straightedge that bears on both forms, so the reference represents the finished surface. At each grid point, measure straight down from the line to the prepared base and record the reading in inches. If the finished surface is designed to slope for drainage, the line should follow the form tops, so the slope is already built into each reading.

Write readings in a table that matches the layout on the ground, row by row and column by column. Label rows by their distance from one form and columns by their distance from the other, so another person can find the same point later. Record the reading resolution as well. A tape read to the nearest eighth of an inch carries an uncertainty of about plus or minus one-eighth inch per reading, and that number becomes the width of the final bracket.

Choose spacing so the grid can see the features that matter. A 4-foot grid on a small patio catches a broad dip, but it can miss a narrow trench left by a removed root or a utility line. Where you can see or feel a local low spot between grid points, add a reading there and handle that area as its own small rectangle rather than letting it disappear between nodes.

Check every reading against the specified thickness while you are there. Any reading below the specified value is a base problem, not an estimating input. Fix the base, then measure that point again. Do not average a thin spot into the estimate and then pour over it.

Worked example: a 12 × 16 ft slab on a 4 ft grid

The example below is illustrative arithmetic using explicitly stated, hypothetical readings. It does not describe a real site, product, or recommended thickness.

A slab measures 12 ft by 16 ft, so the plan area is 12 × 16 = 192 ft². A 4-foot grid gives 4 points across the 12-foot direction and 5 points along the 16-foot direction: 20 readings and 12 square cells, each 16 ft². The drawing thickness is 4 in. Readings from the string line down to the base, in inches, row by row:

Row at 0 ft: 4.00, 4.25, 4.50, 4.25. Row at 4 ft: 4.25, 4.75, 5.00, 4.50. Row at 8 ft: 4.50, 5.00, 5.50, 4.75. Row at 12 ft: 4.25, 4.75, 5.00, 4.50. Row at 16 ft: 4.00, 4.25, 4.50, 4.25. No reading is below 4.00 in, so the base meets the drawing thickness everywhere it was checked, and the center of the slab sits about an inch and a half low.

Each cell's average depth is the mean of its four corner readings. The top-left cell, for example, has corners 4.00, 4.25, 4.25, and 4.75, so its average is 17.25 ÷ 4 = 4.3125 in. Working through all 12 cells and averaging the results gives a slab average of 4.6875 in. Volume is area times average depth: 192 × 4.6875 ÷ 12 = 75.0 ft³. Dividing by 27 gives 75 ÷ 27 = 2.777778 yd³.

The nominal estimate uses 4 in everywhere: 192 × 4 ÷ 12 = 64.0 ft³, or 2.370370 yd³. The measured base needs 11 ft³ more, about 0.41 yd³, roughly 17 percent above the drawing quantity for this hypothetical slab. That gap belongs to these readings only; it is not a general rule for how much a base deviates.

The weighting shortcut, and why a plain average is wrong

Averaging twelve cells by hand is tedious, and there is a faster route that gives the same answer. Each reading is shared by every cell it touches. A corner point touches one cell, a point along an edge touches two, and an interior point touches four. Give each reading that many votes, add them up, and divide by four times the number of cells.

In the example, the four corners add to 16.50, weighted by 1, giving 16.50. The ten edge points that are not corners add to 44.25, weighted by 2, giving 88.50. The six interior points add to 30.00, weighted by 4, giving 120.00. The total is 16.50 + 88.50 + 120.00 = 225.00. Four votes for each of 12 cells is 48, and 225 ÷ 48 = 4.6875 in, the same value the cell-by-cell method produced.

A plain average of all 20 readings gives a different answer: 90.75 ÷ 20 = 4.5375 in, which works out to 72.6 ft³ or 2.688889 yd³. That is 2.4 ft³ short of the weighted result. The plain average over-represents the perimeter, because there are many more edge and corner points than interior points on a small grid, and in this example the perimeter readings are the shallowest. The deeper interior readings, where the dip sits, are under-counted by a plain average.

The weights only work for a regular grid of equal square or rectangular cells. If you add an extra reading at a local low spot, treat the area around it as a separate rectangle with its own corner readings, compute that piece on its own, and add it to the rest. Do not drop an extra point into the weighted sum without a cell to belong to.

Bracketing the result for reading resolution

Every reading carries the resolution you recorded. If each reading could be off by up to one-eighth inch in either direction, the average depth could be off by the same amount in the worst case, when all errors line up. That gives a depth bracket of 4.5625 to 4.8125 in for the example.

Applied to the 192 ft² area, the bracket is 192 × 4.5625 ÷ 12 = 73.0 ft³ to 192 × 4.8125 ÷ 12 = 77.0 ft³, or 2.703704 to 2.851852 yd³. Even the low end of the bracket is well above the nominal 64 ft³, so in this example the reading resolution is not what decides the order. The base shape is.

The bracket only covers reading resolution. It does not cover form movement during placement, base that is disturbed after you measure, spillage, material left in a mixer or chute, or concrete that is wasted at the end of the pour. Keep those as separate, labeled lines if you choose to include them, so the measured quantity stays visible on its own.

From cubic feet to bags or a ready-mix order

The conversion from cubic feet to cubic yards uses the exact relation in the NIST table of units: one cubic yard is 27 cubic feet (NIST Handbook 133, Appendix E). Divide the bracketed cubic feet by 27 only after you have settled which bound you are ordering against, and keep the unrounded values until the final step.

For bags, divide cubic feet by the yield printed for the specific product. The QUIKRETE Concrete Mix 1101 data sheet lists an 80 lb bag as yielding approximately 0.60 ft³ and a 60 lb bag as approximately 0.45 ft³ (QUIKRETE 1101 data sheet). With 80 lb bags, the example bracket is 73.0 ÷ 0.60 = 121.7 to 77.0 ÷ 0.60 = 128.3 bags, which rounds up to 122 to 129 bags. With 60 lb bags it is 162.2 to 171.1, or 163 to 172 bags. The nominal 4 in estimate would have called for 107 bags of the 80 lb size, about 15 bags fewer than even the low end of the measured bracket.

Bag yield is an approximate manufacturer figure for one product and depends on mixing water and consolidation. Use the yield printed on the bags you are actually buying, and do not swap in bag weight for bag volume. For a quantity this size, compare bags against a ready-mix delivery; concrete bags vs. ready-mix walks through that choice. Ask the supplier about order increments, short-load charges, and how they round, because those rules belong to the seller, not to this arithmetic.

Limits, assumptions, and what this does not decide

This worksheet estimates the volume between a reference line and a measured base at the points you chose. Its accuracy depends on the line representing the finished surface, the base not moving after measurement, and the grid being fine enough to catch the low spots. It cannot detect a dip that falls between readings, and it cannot tell you whether the base was compacted or prepared correctly.

It also does not authorize any change to the slab. A reading above the drawing thickness is extra concrete to order, not permission to thin the slab somewhere else. A reading below it means the base needs work before placement. Thickened edges, footings, and steps are separate volumes; calculate them on their own, as in how to estimate concrete for a slab with thickened edges, and make sure the grid area and the thickened area do not count the same volume twice.

Keep the reading table, the grid spacing, the reading resolution, and the date with the order. That record lets someone else recompute the same average and the same bracket, and it shows which part of the order came from measurement and which part from any allowance you added on top.

Sources and method

• NIST Handbook 133 (2026), Appendix E: General Tables of Units of Measurement — retrieved 2026-10-20
• QUIKRETE Concrete Mix Product No. 1101 Data Sheet — retrieved 2026-10-20

AI-assisted writing with automated source, calculation and editorial checks. No hands-on testing or professional certification is claimed. Check the stated assumptions before applying this guide.