Excavation Volume Formulas
Our calculator applies standardized geometric and civil engineering formulas to ensure high accuracy for earthworks:
A/B. Vertical Sides (Rectangular/Trench):
Volume = Length × Width × Depth
C. Trench with Sloped Sides (Trapezoidal Cross-Section):
Area = ((Top Width + Bottom Width) / 2) × Depth
Volume = Area × Length
D. Rectangular Pit with Sloped Sides (Prismoidal Formula):
Mid Area = ((Top L + Bottom L) / 2) × ((Top W + Bottom W) / 2)
Volume = (Depth / 6) × (Top Area + 4 × Mid Area + Bottom Area)
E. Circular Excavation:
Volume = π × (Diameter / 2)² × Depth
Understanding Earthwork Volumes
Bank Volume: The volume of soil in its natural, undisturbed state in the ground. This is equivalent to the geometric volume of the excavation.
Loose Volume: When soil is excavated, it expands because air voids are introduced. Loose volume is calculated by applying a Swell Factor. E.g., a 25% swell factor means 1 m³ of bank soil becomes 1.25 m³ of loose soil.
Estimated Truckloads: Calculated by dividing the Loose Volume by the capacity of a single haul truck, always rounding up to the nearest whole trip.
Frequently Asked Questions
How do you calculate excavation volume?
For basic vertical-sided holes, you multiply the length, width, and depth. For more complex shapes with sloped sides to prevent cave-ins, specific mathematical formulas like the prismoidal formula must be used to find the true volume.
What is the formula for trench excavation?
If the trench has straight vertical walls, the formula is simple: Volume = Length × Width × Depth. If the walls are sloped outwards for safety, calculate the average width first: Volume = Length × ((Top Width + Bottom Width) / 2) × Depth.
How do you calculate excavation with sloped sides?
For a pit with four sloped sides, averaging the top and bottom areas is inaccurate. Civil engineers use the Prismoidal formula which incorporates a "mid-section area" to yield mathematically accurate earthwork quantities.
What is the difference between bank volume and loose volume?
Bank volume (or in-situ volume) measures the dirt packed naturally in the ground. Loose volume measures that same dirt after it has been dug up, disturbed, and aerated, taking up significantly more physical space in a truck.
How does soil swell factor affect excavation volume?
It dictates transportation requirements. While the hole in the ground (bank volume) might be 100 cubic meters, a clay soil with a 30% swell factor will result in 130 cubic meters of loose dirt that must be hauled away.
How do I estimate the number of truckloads?
First, calculate your loose volume (Bank Volume + Swell Percentage). Then, divide that loose volume by the rated volumetric capacity of your dump trucks. Since you can't hire a fraction of a truck trip, round the final number up.
This calculator provides preliminary geometric estimates for planning purposes. Actual excavation quantities may vary due to site conditions, irregular ground profiles, soil characteristics, working space, groundwater, construction methods, and project specifications. Verify critical calculations with qualified project personnel before using them for engineering, safety, or contractual decisions.