Cut and fill volumes along an alignment by the prismoidal (Simpson's rule) or average end-area method.
Stations
One row per surveyed cross-section. Rows are sorted by chainage to compute.
- Segments
- 2
- Prismoidal correction (AEA − prism.) cut / fill
- 10 / 15 m³
- Intervals not paired (odd / unequal) — end-area used
- 1
| Segment (m) | L | Cut m³ | Fill m³ |
|---|---|---|---|
| 0–60 | 60 | 380 | 180 |
| 60–90 | 30 | 22.5 | 330 |
Reference only. The average end-area method over-estimates volume where sections change sharply; the prismoidal (Simpson) method is exact for prismoids and needs pairs of equal intervals. Bulking and shrinkage are soil-specific — use values from the soil report. Need to cost the haul? Take your net volume into the Cost Estimator for a quick BOQ.
How the Earthwork Volume Calculator (Cut & Fill) works
Along a road, canal or embankment you survey cross-sections at a series of chainages and measure the area of cut and the area of fill at each one. This calculator turns those areas into cut and fill volumes. Enter one row per station: the chainage in metres, the cut area and the fill area in m². Rows are sorted by chainage before the calculation.
Two methods are available. The average end-area method takes the mean of the two end areas times the distance between them, for every interval. The prismoidal method applies Simpson's rule over each pair of equal intervals, d/3 × (A1 + 4A2 + A3), which is exact for prismoids. An interval that cannot be paired, because the number of intervals is odd or the spacing is unequal, falls back to the end-area value and is flagged. The difference between the two methods is reported as the prismoidal correction.
Cut is measured in place (bank measure). To compare it with fill, the fill volume is divided by (1 − shrinkage) to give the bank material it needs. Net = cut − fill bank volume: a positive result is surplus to dispose of, a negative one is borrow required. The haul volume is the net volume times (1 + bulking), because excavated soil swells when loose. The defaults are 25% bulking and 10% shrinkage.
- Average end-area, per interval
- V = L × (A1 + A2) / 2
- Prismoidal (Simpson), per pair of equal intervals d
- V = (d / 3) × (A1 + 4A2 + A3)
- Prismoidal correction
- C = V(end-area) − V(prismoidal)
- Bank material needed for fill
- Fill(bank) = Fill / (1 − shrinkage)
- Net volume (bank)
- Net = Cut − Fill(bank) (+ surplus, − borrow)
- Loose haul volume
- Haul = |Net| × (1 + bulking)
Worked example: cut and fill over 40 m of road
Given
- Ch 0 m: cut 12 m², fill 0 m²
- Ch 20 m: cut 5 m², fill 2 m²
- Ch 40 m: cut 2 m², fill 8 m²
- Method: prismoidal; bulking 25%, shrinkage 10%
Steps
- Two equal 20 m intervals, so Simpson's rule applies to the whole 40 m: d = 20 m.
- Cut: (20 / 3) × (12 + 4 × 5 + 2) = (20 / 3) × 34 = 226.67 m³.
- Fill: (20 / 3) × (0 + 4 × 2 + 8) = (20 / 3) × 16 = 106.67 m³.
- For comparison, average end-area gives cut 20 × (12 + 5)/2 + 20 × (5 + 2)/2 = 170 + 70 = 240 m³ and fill 20 + 100 = 120 m³, so the prismoidal correction is 13.33 m³ for both.
- Bank material needed for the fill: 106.67 / (1 − 0.10) = 118.52 m³.
- Net: 226.67 − 118.52 = 108.15 m³ bank, positive, so it is surplus.
- Loose volume to haul away: 108.15 × 1.25 = 135.19 m³.
Result: Cut 226.67 m³, fill 106.67 m³; surplus of 108.15 m³ bank, or 135.19 m³ loose to haul.
Enter the same values in the calculator above to check each step.
Frequently asked questions
How do you calculate earthwork volume for excavation?
Measure the cut area at cross-sections along the alignment, then find the volume between each pair of sections. By the average end-area method it is the distance times the mean of the two areas: sections of 12 m² and 5 m² that are 20 m apart give 20 × (12 + 5)/2 = 170 m³. Add up all the intervals for the total.
Which is more accurate, the average end-area method or the prismoidal formula?
The prismoidal formula is exact for prismoids, and the average end-area method usually overestimates where the sections change sharply. In the worked example the end-area method gives 240 m³ of cut against 226.67 m³ by the prismoidal formula, a correction of 13.33 m³. When the area changes linearly between sections the two methods give the same answer.
Can the prismoidal formula be used with an odd number of sections?
Simpson's rule needs pairs of equal intervals, which means an odd number of equally spaced sections. If you have an even number of sections, or the spacing changes, the calculator pairs what it can and uses the end-area method for the leftover interval, and shows how many intervals were not paired. For example, four sections at 30 m spacing give one Simpson pair over 0–60 m and one end-area interval over 60–90 m.
What bulking and shrinkage factors should be used for earthwork?
They depend on the soil type and should come from the soil report. The calculator starts at 25% bulking (swell when excavated) and 10% shrinkage (loss when compacted in fill), and you can change both. Shrinkage increases the bank volume needed for fill; bulking increases the loose volume to be hauled.
Does the calculator work out cross-section areas or a mass-haul diagram?
No. You enter the cut and fill area at each station yourself, from your levels or a drawing; it does not compute areas from ground levels, formation levels or side slopes. It gives volumes, the net balance and the loose haul volume, but not a mass-haul diagram, haul distances or costs.
Step-by-step guides
- Earthwork Calculation: Prismoidal vs Average End Area (Worked Example)Work out cutting and filling volumes from cross-sections by the average end area and prismoidal methods, with bulking, shrinkage and a 100 m road example.
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