Cut and Fill Volume Calculator
The cut and fill volume calculator estimates the volume of earthwork between two surveyed cross sections using the average end area method, the standard technique in road and site grading. The method is simple and well established: average the two cross-section areas and multiply by the distance between them. The result is a volume in cubic feet, which is divided by 27 to convert to cubic yards, the unit earthwork is usually priced and hauled in. Cut is the material you excavate where the ground sits above the design grade, and fill is the material you place where it sits below; the same calculation finds each from its own pair of end areas. The method is most accurate when the ground changes gradually and the sections are close together, and engineers apply a prismoidal correction where the shape changes sharply. Enter your own two end areas and the length between them to estimate a haul quantity, balance cut against fill, or check a contractor's earthwork takeoff. Every figure here is computed deterministically from the formula shown in full below, with a worked example that reconciles exactly to the calculator so you can follow each step and trust the result.
The average end area volume is the mean of the two end areas times the length, then divided by 27: V = ((A1 + A2) / 2) x L / 27. End areas of 20 and 30 sq ft over 100 ft give 92.59 cubic yards.
Average end area formula
V (cubic yards) = ((A1 + A2) / 2) x L / 27
A1, A2 = the two cross-section areas in square feet
L = distance between the sections in feet
27 = cubic feet in one cubic yard
The mean of the two end areas approximates the average cross section over the length. Multiplying by the length gives the volume in cubic feet, and dividing by 27 converts it to cubic yards.
Worked example
Two cross sections measure 20 and 30 square feet, spaced 100 feet apart.
- Average area = (20 + 30) / 2 = 25 square feet
- Volume in cubic feet = 25 x 100 = 2,500
- Volume in cubic yards = 2,500 / 27 = 92.59
The earthwork volume is 92.59 cubic yards. These are the calculator's default inputs, so the result above matches the widget exactly.
Volume at different lengths
Cubic yards for end areas of 20 and 30 square feet at a range of station lengths.
| A1 (sq ft) | A2 (sq ft) | Length (ft) | Cubic yards |
|---|---|---|---|
| 20 | 30 | 50 | 46.30 |
| 20 | 30 | 100 | 92.59 |
| 20 | 30 | 150 | 138.89 |
Survey and geodetic standards: US National Geodetic Survey (NOAA).
Cut and fill volume calculator: frequently asked questions
What is the average end area method?
The average end area method estimates the volume of earthwork between two cross sections by averaging their areas and multiplying by the distance between them. It is the standard approach in road and site grading. The volume equals the mean of the two end areas times the length, giving cubic feet, which is then converted to cubic yards by dividing by 27.
How do I calculate cut and fill volume?
Add the two cross-section areas, divide by two to get the average area, then multiply by the distance between the sections. With end areas of 20 and 30 square feet over 100 feet, the average is 25 square feet, the volume is 2,500 cubic feet, and dividing by 27 gives about 92.59 cubic yards.
Why divide by 27?
Earthwork is usually priced and hauled in cubic yards, but cross-section areas in feet give a volume in cubic feet. One cubic yard is 3 feet by 3 feet by 3 feet, which is 27 cubic feet. Dividing the cubic-foot volume by 27 converts it to cubic yards for estimating and ordering.
What is the difference between cut and fill?
Cut is material excavated and removed where the existing ground is higher than the design grade. Fill is material added where the ground is lower than the design grade. The same average end area method finds each volume from its own cross sections. Balancing cut against fill on site reduces the need to haul material on or off.
How accurate is the average end area method?
It is accurate when the ground changes gradually between sections and the cross sections are close together. Where the shape changes sharply, the method can over- or under-estimate, and engineers may apply a prismoidal correction or take sections at shorter intervals. For preliminary estimating it is the accepted standard.
Official sources
- Survey, cross-section and geodetic standards: US National Geodetic Survey (NOAA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.