Free calculator

Earthwork Volume — Average End Area & Prismoidal

Enter the end cross-section areas, the distance between stations, and (for the prismoidal method) the mid-section area. The calculator returns the volume in cubic feet and cubic yards, and converts loose yards to bank yards if you give a swell percentage.

V = L (A₁ + A₂) / 2 V = L (A₁ + 4A_m + A₂) / 6

V	volume, ft³ (1 CY = 27 ft³)
L	distance between the end sections, ft
A₁, A₂, A_m	end and mid-section areas, ft²

Method Area A₁ (ft²) Area A₂ (ft²) Mid-section area Aₚ (ft²) Distance L (ft) Swell (%) — optional

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.

Worked example: average end area vs prismoidal

Two sections 100 ft apart: A₁ = 120 ft², A₂ = 180 ft², mid-section A_m = 145 ft².

Average end area: V = 100 × (120 + 180)/2 = 15,000 ft³ = 15,000/27 = 555.6 CY
Prismoidal: V = 100 × (120 + 4 × 145 + 180)/6 = 100 × 880/6 = 14,666.7 ft³ = 543.2 CY
The mid-section is leaner than the average of the ends, so prismoidal correctly trims the volume by about 12 CY

Exam tip: divide ft³ by 27 to get CY — a volume answer in the thousands is almost certainly still in cubic feet.

Go deeper

Preparing for exam day? The 110-question FE Civil practice exam is a full 5-hour-20-minute rehearsal with detailed solutions.