How this calculation works
Use each pair of supplied cross-section areas as the end areas of an interval. Average cut areas and multiply by spacing, then do the same independently for fill. Sum all intervals without replacing simultaneous cut and fill with a signed net section.
Interval volume = (A₁ + A₂) × station spacing / 2; sum cut and fill separatelyA worked example
At stations 0, 10 and 30 m, cut areas 4, 8 and 2 m² give 60 + 100 = 160 m³. Fill areas 0, 2 and 4 m² give 10 + 60 = 70 m³. Geometric cut minus fill is 90 m³ before any material-state or suitability model.
Good to know
Average-end-area estimate from supplied sections, not a surveyed terrain grid. Assumes linear area change between sections. No prismoidal or curved-alignment correction, topsoil, shrink/swell, material suitability, haul, loads, payment certification or design recommendation. Additional measured sections can change the estimate.
Reference: FHWA: average-end-area method and geometric limitations (opens in a new tab) ↗
Check the land-unit definitions and sources
The standard factors use the international foot and an acre of 43,560 sq ft. Cent means 1/100 acre; gunta means 1/40 acre; the selected Chennai ground means 2,400 sq ft.
The Assam report defines bigha as 14,400 sq ft, katha as 2,880 sq ft and lecha as 144 sq ft. The cited West Bengal court order mentions a 720-sq-ft katha convention. These are explicit presets, not an automatic definition for every record or every place using the same name. Match your record to the stated convention, or use its verified custom factor.
- NIST: exact international-foot and acre factors (opens in a new tab) ↗
- API Setu MDDS: acre/cent and acre/gunta relationships (opens in a new tab) ↗
- Greater Chennai Corporation: one ground is 2,400 sq ft (opens in a new tab) ↗
- Government of Assam AIRBMP framework: section 7.2, page 28 (bigha, katha and lecha) (opens in a new tab) ↗
- Supreme Court order, 7 May 2025: paragraph 2, page 2 (West Bengal katha) (opens in a new tab) ↗
The acre relationships are converted using exact base factors. Rounded or unrelated regional values in a reference table are not substituted for these definitions.
Section areas and terrain nodes are different inputs
This page starts with a cut area and a fill area already determined at each increasing station. It estimates volume between adjacent sections by multiplying their spacing by the average of their two end areas. The grid cut and fill calculator instead starts with elevation nodes on a rectangular grid and an explicit interpolation diagonal.
Cut areas of 4, 8 and 2 m² at stations 0, 10 and 30 m give 10 × (4 + 8) / 2 = 60 m³ and 20 × (8 + 2) / 2 = 100 m³. The sum is 160 m³. The two intervals have different lengths and must not share an assumed station spacing.
Fill areas of 0, 2 and 4 m² at those stations give 10 m³ and 60 m³, totaling 70 m³. Cut and fill can both be present at one section, so enter them separately. Replacing them with a signed net area can conceal both gross quantities.
The grid cut and fill calculator starts from elevation nodes, whereas cross-section earthwork starts from supplied section areas. A geometric balance does not by itself determine soil delivery loads.
A geometric balance does not determine usable material
The example’s cut-minus-fill balance is 90 m³. That subtraction does not establish that 90 m³ of suitable loose material is available for disposal. Excavated material can change volume, and some cut may be unsuitable for the intended fill.
Average-end-area interpolation assumes each entered area changes linearly between the two sections. It can differ from a prismoidal calculation or a more detailed model. Additional surveyed sections can change the estimate by revealing variations between the earlier endpoints; no hidden intermediate cross-section is reconstructed here.
Use cubic units consistently: feet for station distances require square feet for section areas and produce cubic feet for the interval quantities. The output separately converts those volumes to cubic metres using the cube of the international-foot factor. A soil fill volume scenario can model separately supplied material-state and load assumptions, but this page does not infer them.
A few questions, answered
Can one section contain both cut and fill?
Yes. Supply its two nonnegative areas separately. Each series is averaged and accumulated independently.
Does the result include a prismoidal or curved-alignment correction?
No. It is the stated average-end-area estimate. Appropriate survey and design methods may require additional information and corrections.
Can a negative station be used?
Yes. Stations are local coordinates with magnitude at most 1,000,000. They must increase strictly; shifting every station by the same amount does not change the interval volumes.