Pit Volume from Dimensions Calculator
Estimate the excavation volume of a rectangular pit with sloped (battered) walls. The pit is treated as a truncated pyramid (prismatoid) using its top and bottom dimensions and depth, giving a fast earthworks volume for planning digging, spoil handling and haulage.
Enter Values
How to use this calculator
- Enter the top length and top width measured at ground level around the rim of the pit.
- Enter the bottom length and bottom width measured on the floor of the pit, then the vertical depth.
- Read the pit volume in cubic metres, with the top and bottom areas shown for a quick sanity check.
How it works
The calculator multiplies length by width to get the top area (A_top) and bottom area (A_bot). It then applies the prismatoid (truncated pyramid) formula V = (depth / 3) × (A_top + A_bot + √(A_top × A_bot)). This averages the two end areas together with their geometric mean, which correctly accounts for the walls sloping inward from the rim to the floor rather than being vertical.
Worked example
Worked example. A pit measures 100 m × 80 m at the top and 60 m × 40 m on the floor, 20 m deep. A_top = 8,000 m², A_bot = 2,400 m². V = (20 / 3) × (8,000 + 2,400 + √(8,000 × 2,400)) = (20 / 3) × (10,400 + 4,381.78) = 98,545.2 m³.
Common mistakes
- Swapping top and bottom dimensions — the top opening should be equal to or larger than the floor for an inward battered pit.
- Using the slope distance instead of the true vertical depth, which overstates the volume.
- Assuming flat, uniform walls and floor; real ground is irregular, so a survey surface gives a more accurate figure.
Frequently asked questions
Why use the prismatoid formula instead of averaging the two areas?
Simply averaging the top and bottom areas overestimates the volume of a tapering shape. The prismatoid formula adds the geometric mean √(A_top × A_bot), which gives the exact volume for a shape whose sides slope in straight lines.
What if the pit has vertical walls?
Enter identical top and bottom dimensions. The formula then reduces to area × depth, the volume of a simple rectangular prism.
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Tip: Enter any known values to calculate the remaining results.
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