Earthwork
Cut and Fill Volume Calculator (Average End Area)
Highway and site grading quantities are commonly computed by averaging the cut or fill area of two adjacent cross-sections and multiplying by the distance between them. Run it for each pair of stations and add the results.
Formula
Average end area: V (ft³) = L × (A1 + A2) ÷ 2, where A1 and A2 are cut (or fill) areas at the two stations in ft² and L is the distance in ft. Divide by 27 for cubic yards. Cut and fill are computed separately.
Worked example
Cut areas of 120 ft² and 180 ft² at stations 100 ft apart: V = 100 × (120 + 180) ÷ 2 = 15,000 ft³ = 555.56 yd³.
Assumptions and limits
- Accurate when areas are similar; overestimates volume when one end area is much smaller (the prismoidal formula is more exact).
- Areas are bank (in-place) measurements. Apply swell and shrink factors separately.
Frequently asked questions
What is the difference between average end area and prismoidal volume?
The prismoidal formula adds a middle section area and is more exact for shapes that taper. Average end area is simpler and is the standard method on many highway projects.
How far apart should cross-sections be?
Highway work often uses 50 ft or 100 ft stations, with extra sections at breaks in grade or where the ground changes sharply.
How do I account for compaction?
Fill volumes are compacted; cut is bank volume. Use the swell and shrink calculator to convert between bank, loose and compacted yards.