This cut and fill calculator turns the sections you already measured into earthwork volumes. Enter cross sections station by station and it applies the average end area method; or enter a grid of depths over a pad, a lot or a borrow pit and it applies the corner-average grid method. Both modes report cut and fill separately, net the two, and apply a swell or shrinkage factor so the numbers match what the trucks and the compactor will actually do. Free, in your browser, no login.
Enter swell as a positive percentage (soil loosens on excavation, so 1 m³ in the ground becomes more in the truck) or shrinkage as a negative percentage (fill compacts to less than its bank volume). Leave at 0 for raw bank volumes.
Areas are in m² for metric units and ft² for imperial. Stations are distances along the
alignment in the same length unit — station numbers such as 12+50 are accepted and
read as 1250.
Check the input — every line needs the same shape, and numbers must be readable.
Each pair of adjacent sections forms a prism. Its volume is the distance between the sections
multiplied by the mean of the two areas:
V = L × (A₁ + A₂) ÷ 2. Cut and fill are computed on the same pairs but kept apart, so
a section that changes from cut to fill produces both a cut prism and a fill prism. A section with
cut on one side of the centre line and fill on the other is normally split at the centre line
before the areas are entered.
Over an area that is broad in both directions, depths are taken at grid nodes. Each cell of the
grid contributes V = cell area × (d₁ + d₂ + d₃ + d₄) ÷ 4, where the four depths are
the corners of that cell. Summing the cells gives the total, and because cut cells and fill cells
are signed differently they can be summed separately. This is sometimes called the borrow pit
method, and it is the natural companion to a survey of a pad or a stockpile.
The volumes above are bank volumes — the volume as measured in the ground. What leaves the site is a larger loose volume, because excavation breaks the soil apart and adds voids. What arrives in the fill is a smaller compacted volume, because compaction removes voids. The calculator applies your percentage to both cut and fill totals and reports the adjusted figures alongside the bank figures, so you can see the difference the factor makes.
| Method | Best for | Field data needed | Typical accuracy |
|---|---|---|---|
| Average end area | Roads, railways, canals, pipelines, anything linear | Cross-section areas at regular stations | Within a few percent when sections are spaced at 15–30 m in changing ground |
| Grid (corner average) | Building pads, parking lots, borrow pits, stockpiles, subdivisions | Spot depths at the nodes of a regular grid | Governed by the grid spacing; halving the spacing roughly quarters the error |
| Prismoidal | High-value earthwork where a few percent is money | Cross sections plus a mid-section area | Closer than average end area, at the cost of extra survey work |
The two methods are not competing answers to the same question, they are answers to different questions. A road is a long thin solid, so it is cut into prisms. A pad is a wide flat solid, so it is cut into cells. Where an alignment widens into a pad — an interchange, a lay-by, a treatment works — the earthwork is often split, with the linear part done by sections and the wide part by grid, and the two results added.
Almost every disagreement between a contractor and a designer about earthwork quantities is a disagreement about which volume is being counted. There are three, and they are different numbers.
| Volume | Where it exists | Used for | Typical relation to bank volume |
|---|---|---|---|
| Bank (in situ) | In the ground | Payment quantities, project totals | 1.00 by definition |
| Loose | In the truck or the stockpile | Truck counts, haulage, stockpile space | 1.05–1.45 depending on soil |
| Compacted | Placed and rolled in the fill | Borrow quantity, fill capacity | 0.85–0.95 depending on soil and specification |
The practical consequence is that cut and fill totals rarely balance even when the design intends them to. Suppose a site needs 10,000 m³ of compacted fill and offers 10,000 m³ of bank cut of the same material with a shrinkage of 10 percent. The usable fill from the cut is 9,000 m³ compacted, so roughly 1,100 m³ of bank borrow has to be imported — an outcome nobody would predict from comparing the two headline numbers. Run the conversion before the quantities are priced.
Take the default sections in the calculator. Between station 0, with 12.4 m² of cut, and station
50, with 18.9 m² of cut, the average end area method gives
50 × (12.4 + 18.9) ÷ 2 = 782.5 m³ of cut. Between station 100 (7.2 m² cut, 3.1 m² fill)
and station 150 (0 m² cut, 14.6 m² fill), the cut prism is
50 × (7.2 + 0) ÷ 2 = 180.0 m³ and the fill prism is
50 × (3.1 + 14.6) ÷ 2 = 442.5 m³. The cut prism ends where the cut area reaches zero,
which is what makes the mid-section the natural transition point.
In grid mode, a 10 m grid with corner depths of 0.4, 0.6, 0.5 and 0.2 m gives an average depth of 0.425 m over a 100 m² cell, or 42.5 m³ of cut in that one cell. Four rows and four columns of depths create a 3 × 3 grid of cells, so the default grid above is nine cells and about 400 m² of ground — small enough to check by hand, which is exactly what a calculator of this kind should let you do.
| Conversion | Value | Notes |
|---|---|---|
| 1 cubic yard | 27 ft³ = 0.764554858 m³ | The default US earthwork unit |
| 1 cubic metre | 1.30795062 yd³ = 35.3146667 ft³ | Metric earthwork unit |
| 1 acre-foot | 43,560 ft³ = 1,233.4818375 m³ | One acre covered one foot deep |
| 1 m³ of water | 1,000 kg = 1 tonne | Useful for soil moisture sanity checks |
| Truck load, tandem axle | Roughly 10–14 bank m³ | Varies with machine, soil and permits |
| Fills placed in 200 mm layers | About 20 m² per m³ of compacted fill | Layer thickness governs compaction cost |
Swell and shrinkage factors vary widely with soil type, moisture content and the compaction specification. Always use the factors stated in the project specification or measured on site rather than a general figure from a web page.
For each pair of adjacent cross sections, multiply the distance between them by the mean of the two areas: V = L × (A₁ + A₂) ÷ 2. Compute cut and fill separately, then sum along the whole alignment. For wide areas, use the grid method instead and average the four corner depths of each cell.
The standard earthwork method. It treats the ground between two sections as a prism whose volume is length times the mean end area. It suits anything linear — roads, rail, pipelines, canals — and is accurate to a few percent when sections are spaced at 15–30 m in ground that is changing.
When the area is wide in both directions rather than linear: a pad, a lot, a borrow pit or a stockpile. Depth is measured at grid nodes, each cell volume is its area times the average of its four corner depths, and the cells are summed.
A refinement of average end area. The prism assumption slightly overstates volume when two sections differ in shape as well as size. The prismoidal formula uses a mid-section area — V = L ÷ 6 × (A₁ + 4Am + A₂) — and worth applying on high-value earthwork.
Yes, if the volumes are going to be used for truck counts, haulage, borrow or fill capacity. Bank volumes are what is in the ground; loose volumes are what you haul, and compacted volumes are what you place. Swell typically runs 5–45 percent and shrinkage about 5–15 percent, depending on soil.
Multiply cubic yards by 0.764554858 to get cubic metres, or multiply cubic metres by 1.30795062 to get cubic yards. Cubic yards come from cubic feet divided by 27.
On a balanced site, the compacted fill requirement should be compared with the usable compacted volume yielded by the cut, not with the bank volume of the cut. A cut of 10,000 m³ of bank soil at 10 percent shrinkage yields only about 9,000 m³ of compacted fill, so an apparently balanced site can still need imported borrow.
Yes — free, no login, no account, no usage limit. Every calculation runs locally in your browser, so no project data is uploaded.
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