What This Page Covers
This page summarizes the formulas used by the excavation calculator, trench volume calculator, swell and shrink calculator, and spoil pile calculator.
The goal is to show the estimating math in plain language so you can check the arithmetic by hand. Where a tool uses a simplified planning assumption, that limitation is stated directly.
Methodology and Limitations
Rectangular and trench examples on this page are straightforward geometry checks. The slope-sided example is different: it is a planning estimate based on a rectangular bottom and one uniform horizontal-to-vertical slope on all four sides.
That slope-sided method does not model irregular ground, benches, shoring, or different slopes by side. If the excavation geometry changes by location or depth, this page is no longer the right quantity method without a more specific takeoff.
Last reviewed: July 13, 2026
Core Formula Set
Rectangular Excavation Volume
For rectangular pits and straight-sided open cuts, the bank-volume formula is:
Bank volume = length × width × depth
In the excavation calculator, those dimensions are entered in millimeters and converted to cubic meters internally. If the result is needed for hauling, the calculator then applies swell to convert bank volume to loose volume.
Trapezoidal Trench Cross-Section
For a trench that is narrower at the bottom than at the top, the trench calculator first calculates cross-sectional area, then multiplies by trench length:
Cross-section area = ((top width + bottom width) / 2) × depth
Bank volume = cross-section area × length
This is the formula used in trench volume for trapezoidal sections.
Slope-Sided Prismoidal Estimate
The general excavation calculator includes a slope-sided mode that widens the bottom dimensions upward using the entered slope ratio. It assumes a rectangular bottom and the same horizontal-to-vertical slope on all four sides, then checks the bottom, mid-depth, and top rectangular areas with the prismoidal formula.
Top length = bottom length + 2 × (depth × slope ratio)
Top width = bottom width + 2 × (depth × slope ratio)
Mid-depth length = bottom length + depth × slope ratio
Mid-depth width = bottom width + depth × slope ratio
Prismoidal volume = (depth / 6) × (bottom area + 4 × mid-area + top area)
This is a planning estimate for that one simplified excavation geometry. It is not a universal method for irregular side slopes, benched sections, or support systems.
Bank-To-Loose Conversion Using Swell
Both excavation calculators convert in-ground volume to excavated loose volume with the same rule:
Loose volume = bank volume × (1 + swell percentage / 100)
The correct swell assumption depends on the material. The soil swell and shrink factors guide is the reference point for understanding why the hauled or stockpiled quantity is larger than the hole measured in place.
Simple Loose-Volume-To-Truck-Capacity Workflow
Once loose volume is known, a basic haul planning check is just division by truck capacity:
Truckloads = loose volume / truck capacity
If the result is not a whole number, round up to the next full load for a simple planning count. That same loose volume can also be carried into spoil pile planning if material will be staged on site instead of hauled away immediately.
Worked Examples
Example 1: Rectangular Excavation With Swell
Inputs: length 12 m, width 4 m, depth 2.5 m, swell 25%.
Formula substitution: bank volume = 12 × 4 × 2.5 = 120 m³.
Intermediate result: bank volume = 120 m³.
Loose-volume substitution: 120 × (1 + 25 / 100) = 120 × 1.25 = 150 m³.
Final result: 120 m³ bank volume and 150 m³ loose volume.
This matches the output from the excavation calculator for a rectangular excavation using the compact-soil 25% swell factor.
Example 2: Trapezoidal Trench Section
Inputs: trench length 18 m, bottom width 0.8 m, top width 1.6 m, depth 1.5 m, swell 15%.
Formula substitution: cross-section area = ((1.6 + 0.8) / 2) × 1.5 = (2.4 / 2) × 1.5 = 1.2 × 1.5 = 1.8 m².
Intermediate result: bank volume = 1.8 × 18 = 32.4 m³.
Loose-volume substitution: 32.4 × (1 + 15 / 100) = 32.4 × 1.15 = 37.26 m³.
Final result: 32.4 m³ bank volume and 37.26 m³ loose volume.
This aligns with the trench volume calculator for a trapezoidal trench using the dry-sand swell factor.
Example 3: Slope-Sided Prismoidal Estimate
Inputs: bottom length 10 m, bottom width 3 m, depth 2 m, slope ratio 1:1, swell 35%.
Formula substitution: top length = 10 + 2 × (2 × 1) = 14 m, and top width = 3 + 2 × (2 × 1) = 7 m.
Intermediate result: bottom area = 10 × 3 = 30 m², mid-depth area = (10 + 2) × (3 + 2) = 12 × 5 = 60 m², and top area = 14 × 7 = 98 m².
Bank-volume substitution: (2 / 6) × (30 + 4 × 60 + 98) = (1 / 3) × 368 = 122.67 m³.
Loose-volume substitution: 122.67 × (1 + 35 / 100) = 122.67 × 1.35 = 165.6 m³.
Final result: 122.67 m³ bank volume and 165.6 m³ loose volume.
This matches the slope-sided output in the excavationcalculator for that rectangular-bottom, uniform-slope setup.
Example 4: Loose Volume to Truck Capacity
Inputs: bank volume 30.24 m³, swell 25%, truck capacity 10 m³ per load.
Formula substitution: loose volume = 30.24 × (1 + 25 / 100) = 30.24 × 1.25 = 37.8 m³.
Intermediate result: truckloads = 37.8 / 10 = 3.78 loads.
Final result: plan on 4 truckloads when rounding up to a whole-trip estimate.
The loose-volume step matches the calculation logic used in both excavation and trench volume. If the material is not leaving the site right away, compare the same 37.8 m³ against the spoil pile calculator instead.
How To Use These Formulas In Practice
Start with the geometry that matches the excavation shape as closely as the current calculators allow. Use the rectangular formula for simple pits, the trench cross-section method for repeated linear work, and the slope-sided prismoidal method only when the excavation really is a rectangular bottom with one uniform slope on all four sides.
Then move from bank volume to loose volume before planning haul-off or staging. That is where the swell and shrink calculator and the soil swell and shrink factors guide become useful follow-ons.