Cut and Fill Calculator to compute your site’s net earthwork balance. Input grading dimensions and soil type to output compacted fill needs, bank cut volume, and haul-off export capacity.
The Cut and Fill Calculator computes the net earthwork balance between excavated bank soil and compacted fill requirements for site grading projects, outputting exact surplus export or deficit import volumes alongside swell and shrinkage adjustments.
Site Grading Geometric Parameters
The algorithm processes planar dimensions and soil classification to output true volumetric requirements.
- Cut Area & Depth: The two-dimensional footprint and vertical excavation depth of the soil removal zone. Supported inputs include square feet ($sqft$), square meters ($sqm$), feet ($ft$), inches ($in$), and centimeters ($cm$).
- Fill Area & Depth: The footprint and vertical buildup required to reach the target grade elevation.
- Soil Classification: Dictates the specific swell and shrink mechanics applied to the geometric volume. Options include Sand, Clay, Rock, or a generalized Default earth profile.
- Target Output Unit: Normalizes all internal cubic foot calculations into cubic yards ($yd^3$), cubic meters ($m^3$), or cubic feet ($ft^3$).
Earthwork Volume and Soil Dynamics Equations
The calculator normalizes all area and depth inputs into base cubic feet ($ft^3$) before applying conversion factors and soil mechanic modifiers.
Bank cut volume is derived strictly from the geometric dimensions prior to excavation: $$V_{bank}=A_{cut}\times D_{cut}$$
Compacted fill represents the final required geometric volume at target density: $$V_{fill}=A_{fill}\times D_{fill}$$
The net geometric balance determines if a site requires structural import or generates export: $$V_{net}=V_{bank}-V_{fill}$$
To calculate the loose cut volume required for truck hauling logistics, the bank volume is multiplied by the soil’s natural swell factor ($F_{swell}$): $$V_{loose}=V_{bank}\times(1+F_{swell})$$
Because soil compresses beyond its natural bank state when mechanically compacted, the actual source material required to achieve the fill target is calculated by dividing by the inverse of the shrink factor ($F_{shrink}$): $$V_{source}=\frac{V_{fill}}{1-F_{shrink}}$$
The cut-to-fill ratio establishes the site’s self-sufficiency threshold: $$R=\frac{V_{bank}}{V_{fill}}$$
Standardized Volumetric Conversions
Internal base volumes ($ft^3$) are multiplied by fixed conversion constants to yield the final selected output metric.
- Cubic Yards: $$V_{yd^3}=V_{ft^3}\times(\frac{1}{27})$$
- Cubic Meters: $$V_{m^3}=V_{ft^3}\times(\frac{1}{35.3146667})$$
Excavation and Import/Export Yields
Based on the geometric inputs and soil dynamics, the calculator yields six distinct volumetric profiles.
- Bank Cut Volume: The raw, undisturbed geometric earth to be excavated.
- Compacted Fill Target: The absolute geometric volume of the filled space.
- Net Geometric Balance: The raw differential indicating Surplus Cut (Export), Fill Deficit (Import), or a Perfectly Balanced site ($V_{net}=0$).
- Loose Cut Volume: The expanded volume of excavated soil once disturbed, driving haul-off capacity.
- Required Fill Source: The inflated volume of loose dirt that must be imported to successfully hit the compacted target after shrinkage.
- Cut-to-Fill Ratio: Expressed as $R:1$, identifying the proportional relationship between excavated material and fill demands.
Calculating Balanced Excavation Yields: A Step-by-Step Evaluation
The following scenario demonstrates a site calculation utilizing the tool’s default parameters: a $1500\text{ sq ft}$ cut area at $2.5\text{ ft}$ depth, and a $1000\text{ sq ft}$ fill area at $1.0\text{ ft}$ depth, using Default soil (25% swell, 10% shrink) outputting to cubic yards.
Step 1: Calculate Geometric Bank Cut $$V_{bank}=1500\times2.5=3750\text{ ft}^3$$$$V_{bank(yd^3)}=3750\times(\frac{1}{27})=138.88\text{ yd}^3$$
Step 2: Calculate Geometric Compacted Fill $$V_{fill}=1000\times1.0=1000\text{ ft}^3$$$$V_{fill(yd^3)}=1000\times(\frac{1}{27})=37.03\text{ yd}^3$$
Step 3: Determine Net Geometric Balance $$V_{net}=138.88-37.03=+101.85\text{ yd}^3\text{ (Surplus)}$$
Step 4: Calculate Loose Volume for Haul-Off $$V_{loose}=138.88\times(1+0.25)=173.61\text{ yd}^3$$
Step 5: Calculate Required Import Source $$V_{source}=\frac{37.03}{1-0.10}=41.14\text{ yd}^3$$
Step 6: Establish Cut-to-Fill Ratio $$R=\frac{138.88}{37.03}=3.75:1$$
Geotechnical Limitations and Algorithmic Assumptions
- The calculator assumes flat, uniform planar depths and does not integrate topographic contour data, grid methods, or average end area methods required for complex sloped terrain.
- Shrinkage mathematics assume the fill soil is mechanically compacted to its optimal moisture content and maximum dry density.
- Soil dynamics are based on rigid algorithmic constants rather than lab-tested Proctor values. Default applies $25\%$ swell/$10\%$ shrink; Sand applies $12\%$ swell/$12\%$ shrink; Clay applies $30\%$ swell/$20\%$ shrink; Rock applies $50\%$ swell/$0\%$ shrink.
- The algorithm disables the cut-to-fill ratio entirely if the base compacted fill volume equals exactly zero.
Advanced Soil Mechanics and Haul-Off Inquiries
Why is the Required Fill Source larger than the final Compacted Fill target?
Mechanically compacting soil removes air voids present in both loose and natural bank states. To achieve $100\text{ yd}^3$ of compacted fill in a soil with a $10\%$ shrink factor, you must transport $111.11\text{ yd}^3$
of source dirt to the location because $11.11\text{ yd}^3$ of volume will be lost to compression. The calculator uses division by the inverse shrink percentage ($\frac{V}{1-F}$) rather than standard multiplication to prevent under-calculating the required import.
How does the script handle Rock dynamics compared to standard soil?
Rock excavation triggers a unique logic branch where the shrink factor is forced to $0.00$ ($0\%$) while the swell factor is elevated to $0.50$ ($50\%$). Because blasted or crushed rock does not shrink below its original solid bank state when used as fill, the Required Fill Source will exactly match the Compacted Fill Target. Conversely, its massive void ratio when excavated means haul-off volume expands by exactly half of the bank yardage.
Geotechnical Reference Literature
This tool’s algorithms, conversion constants, and baseline soil mechanics are validated against the following authoritative civil engineering standards:
- Burch, D. (1997). Estimating Excavation. Craftsman Book Company.
- Algorithm Validated: Establishes the core volumetric equations transitioning between Bank Cubic Yards (BCY), Loose Cubic Yards (LCY), and Compacted Cubic Yards (CCY).
- Source Link: ISBN-13: 978-0934041966
- Federal Highway Administration (FHWA). Standard Specifications for Construction of Roads and Bridges (FP-14).
- Algorithm Validated: Provides the regulatory baseline for embankment compaction mechanics, confirming the inverse-shrink division calculation required for structural import sizing.
- Source Link: FHWA Spec Library
- McCarthy, D. F. (2007). Essentials of Soil Mechanics and Foundations. Pearson.
- Algorithm Validated: Corroborates the tool’s specific algorithmic constants for soil dynamics, validating the default $25\%$ swell / $10\%$ shrink parameters and the $50\%$ void ratio expansion applied to rock.
- Source Link: ISBN-13: 978-0131145603