Excavation Volume Calculator
About Excavation Volume Calculation
The earthworks calculator calculates the excavation volume for rectangular pits and trenches with vertical walls or slopes. From the base dimensions, depth and slope ratio, it determines the geometric excavation volume and top dimensions. It also calculates the loose soil volume and soil mass for planning excavation, stockpiling and removal.
Guidelines and recommendations
Excavation geometry
Calculation model represents a rectangular excavation with a level base, constant depth and straight walls. The ground surface is assumed to be level. Where slopes are present, the same slope ratio applies to all four sides of the excavation.
Initial dimensions are the base length L1, base width B1 and depth H, all in metres. With vertical walls, the top dimensions are equal to the base dimensions. With slopes, the top dimensions increase according to the depth and slope ratio.
Slope ratio and top dimensions
Slope ratio is the horizontal displacement of a wall divided by the vertical height difference. The coefficient m indicates how many metres the wall moves horizontally for each 1 m of height. For example, a ratio of 0.5:1 means a horizontal displacement of 0.5 m for each 1 m of depth.
Relationship between slope ratio and wall angle measured from the horizontal:
- 0 - vertical wall, angle 90°.
- 0.25:1 - angle approximately 76°.
- 0.5:1 - angle approximately 63.4°.
- 1:1 - angle 45°.
Horizontal displacement of one wall is calculated by multiplying the depth by the slope coefficient. Since the slopes lie on opposite sides, the overall top length and width increase by twice this displacement.
L2 = L1 + 2 * H * m
B2 = B1 + 2 * H * m
Here L2 and B2 are the top length and width in metres. When m = 0, the walls are vertical. The greater m is at the same depth, the flatter the slopes become and the greater the excavation volume.
Geometric excavation volume
Excavation volume is calculated using the prismoidal formula and the areas of three horizontal cross-sections: bottom, middle and top. This method accounts for the simultaneous increase in length and width from the base to ground level.
First, the base and top areas are calculated in m2:
S1 = L1 * B1
S2 = L2 * B2
Mid-section area is taken halfway down the excavation. Its length and width are the arithmetic means of the corresponding base and top dimensions.
Sm = ((L1 + L2) / 2) * ((B1 + B2) / 2)
The geometric excavation volume V is then calculated in m3:
V = H / 6 * (S1 + 4 * Sm + S2)
The factor 4 accounts for how the mid-section area varies relative to the bottom and top areas. For the assumed geometry, the formula gives the exact volume without approximating the sloping sides as rectangular sections.
Vertical walls correspond to a zero slope ratio. In that case, all three cross-sectional areas are equal and the calculation reduces to base length multiplied by base width and depth.
V = L1 * B1 * H
Example. With a base length of 6 m, width of 4 m, depth of 2 m and slope ratio of 0.25:1, the top length is 7 m and top width is 5 m. The geometric excavation volume is 58.67 m3. With the same base dimensions and depth but vertical walls, the volume is 48 m3.
Soil bulking after excavation
Bulking factor accounts for the increase in soil volume after excavation. Digging disturbs the natural soil structure and increases the spaces between particles. As a result, excavated soil usually occupies more space than the excavation itself.
The loose soil volume is calculated by multiplying the geometric volume by factor k:
Vr = V * k
Here Vr is the loose excavated soil volume in m3, and V is the geometric excavation volume in m3. For example, a factor of 1.30 means a 30% increase in volume. When k = 1, bulking is not taken into account.
Typical factors used for preliminary calculations depend on soil composition and condition. The calculator uses the following initial values:
- Dry sand - 1.10.
- Wet sand - 1.20.
- Sandy loam - 1.20.
- Loam - 1.30.
- Clay - 1.40.
These are indicative values. The actual factor depends on soil composition, moisture and excavation method. If more accurate data are available, the factor can be changed manually.
Example. If the geometric excavation volume is 58.67 m3 and the bulking factor is 1.30, the calculated loose soil volume is 76.27 m3. This value is used to estimate the space needed for stockpiling and transporting excavated soil.
Calculating soil mass
Soil density is the mass of one cubic metre of soil in its natural in-situ state, before excavation. It is expressed in t/m3 and depends on mineral composition, moisture and compaction.
Soil mass is calculated by multiplying the geometric excavation volume by density:
M = V * ρ
Here M is the soil mass in tonnes, V is the excavation volume in m3, and ρ is the in-situ soil density in t/m3.
Indicative density values used for automatic selection:
- Dry sand - 1.60 t/m3.
- Wet sand - 1.90 t/m3.
- Sandy loam - 1.70 t/m3.
- Loam - 1.80 t/m3.
- Clay - 1.90 t/m3.
If the actual soil density is known, it can be entered manually. At the same excavation volume, denser soil has a greater mass.
Example. At a geometric volume of 58.67 m3 and density of 1.80 t/m3, the mass is 105.60 t. The original excavation volume is used without multiplying it by the bulking factor, because bulking increases occupied volume, not soil mass.
Calculation accuracy and assumptions
Geometric assumptions include a level ground surface, rectangular base, constant depth and identical straight slopes on all four sides. If the actual excavation differs from these conditions, the actual earthworks volume will also differ from the calculation.
Input validation requires positive length, width and depth. The slope coefficient cannot be negative, the bulking factor must be at least 1, and soil density must be positive. When a value is invalid, the corresponding results are not calculated.
Rounding is applied only when displaying results. Geometric volumes and mass are shown to 0.01 m3 and 0.01 t, respectively. Intermediate calculations are performed without prior rounding.
European standards and guidance
Earthworks are covered by the European EN 16907 series. EN 16907-1:2018 "Earthworks - Part 1: Principles and general rules" sets out general provisions for planning and executing earthworks. EN 16907-2:2018 "Earthworks - Part 2: Classification of materials" addresses the description and classification of soils and other materials.
Geotechnical design is covered by Eurocode 7, including EN 1997-1:2024 "Geotechnical design - Part 1: General rules", EN 1997-2:2024 "Geotechnical design - Part 2: Ground properties" and EN 1997-3:2025 "Geotechnical design - Part 3: Geotechnical structures".
When determining slope ratios, soil properties, excavation depth, groundwater and site conditions must be considered. The bulking factors and densities shown are reference values for preliminary calculations, not mandatory values set by European standards. The applicability of specific editions of the standards is governed by the national rules of each country.
FAQs
Why is the excavated soil volume larger than the excavation volume?
After excavation, soil becomes looser and occupies more space because the voids between particles increase. The geometric excavation volume stays the same, while the loose soil volume grows in proportion to the bulking factor. For example, with a factor of 1.30, soil volume increases by 30%.
How does the slope ratio affect earthworks volume?
As the slope coefficient increases, the walls become flatter and the top dimensions of the pit or trench increase. With the same base dimensions and depth, this increases the excavation volume. For example, a 1:1 slope produces a greater volume than 0.25:1 because the horizontal wall displacement per metre of depth is larger.
Why is the volume before bulking used to calculate mass?
Bulking changes soil volume but does not change the amount of material it contains. Mass is therefore determined from the in-situ excavation volume and the original soil density. For removal planning, two different results matter: loose soil volume in m3 and mass in tonnes.
How accurate is soil mass calculated from soil type?
Accuracy depends primarily on the density value used. Even soils of the same type can have different densities due to moisture, composition and compaction. Automatically selected values are suitable for preliminary estimates, whereas a measured density should be used when available.
Why can the actual earthworks volume differ from the calculated volume?
The calculation assumes a regular shape with a level base, constant depth and identical slopes on all four sides. In practice, the ground may be uneven and wall dimensions or slopes may vary between sections. Accuracy therefore depends on how closely the actual excavation geometry matches the assumed model.