Cut and fill calculator

Work out earthwork volumes from cross sections. Enter each station along the line with its cut area and fill area in square feet. The calculator applies the average end area method between each pair of stations and totals the cut, the fill and the net in cubic yards.

Stations and end areas

Station 1Cut area (sq ft)Fill area (sq ft)
Station 2Cut area (sq ft)Fill area (sq ft)
Station 3Cut area (sq ft)Fill area (sq ft)
Station 4Cut area (sq ft)Fill area (sq ft)

Each segment: (end area 1 + end area 2) ÷ 2 × length, in cubic feet, then ÷ 27 for cubic yards.
Segment	Length (ft)	Cut (ft³)	Fill (ft³)	Cut (yd³)	Fill (yd³)
0+00 to 0+50	50	5,000	250	185.19	9.26
0+50 to 1+00	50	2,500	1,750	92.59	64.81
1+00 to 1+50	50	500	3,750	18.52	138.89

Total cut: 8,000 ft³ ÷ 27 = 296.3 yd³
Total fill: 5,750 ft³ ÷ 27 = 212.96 yd³
Net (cut − fill): 83.33 yd³, excess cut (haul off or waste)
Length of line: 150 ft

Enter stations in order, as feet (150) or station notation (1+50). Areas are the cut and fill cross-section areas in square feet at each station; enter 0 where a section has none. Volumes are in place (bank and compacted measure) with no swell or shrinkage applied.

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This is covered in Site construction, excavation and stormwater of the Bid Bond course.

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The formula: average end area

A cross section shows the ground and the design grade at one station. Where the ground is above grade the area is cut; where it is below, the area is fill. The average end area method treats the earth between two sections as a prism whose area is the average of the two ends.

Volume (cubic feet) = (end area 1 + end area 2) ÷ 2 × distance between the stations.
Cubic yards = cubic feet ÷ 27, because a cubic yard is 3 × 3 × 3 ft.
Net = total cut − total fill. A positive net is spare cut to haul off; a negative net is fill to bring in.

Stations are distances along the line in feet. In station notation 1+50 means 150 ft, so two stations 0+50 and 1+00 are 50 ft apart. The calculator takes either form.

Worked example 1: two sections

Cut areas of 40 sq ft and 60 sq ft at stations 50 ft apart. These are invented study numbers.

Average area = (40 + 60) ÷ 2 = 50 sq ft.
Volume = 50 × 50 = 2,500 cubic feet.
Cubic yards = 2,500 ÷ 27 = 92.59 cubic yards.

Check: 92.59 × 27 = 2,499.93, which rounds back to 2,500.

Worked example 2: four stations with cut and fill

Stations 0+00, 0+50, 1+00 and 1+50. Cut areas are 120, 80, 20 and 0 sq ft; fill areas are 0, 10, 60 and 90 sq ft. This is the calculator's starting example.

Cut: (120 + 80) ÷ 2 × 50 = 5,000; (80 + 20) ÷ 2 × 50 = 2,500; (20 + 0) ÷ 2 × 50 = 500. Total 8,000 cubic feet = 296.30 cubic yards.
Fill: (0 + 10) ÷ 2 × 50 = 250; (10 + 60) ÷ 2 × 50 = 1,750; (60 + 90) ÷ 2 × 50 = 3,750. Total 5,750 cubic feet = 212.96 cubic yards.
Net = 8,000 − 5,750 = 2,250 cubic feet = 83.33 cubic yards of excess cut.

Check with equal spacing: each inner section counts twice, so cut = 50 ÷ 2 × (120 + 2 × 80 + 2 × 20 + 0) = 25 × 320 = 8,000, and fill = 25 × (0 + 2 × 10 + 2 × 60 + 90) = 25 × 230 = 5,750. These are original arithmetic examples, not exam questions.

These volumes are in place. Dug soil swells and compacted fill shrinks, so a haul or borrow figure needs the swell and shrinkage your question or soil report gives. The NASCLA site construction guide covers bank, loose and compacted volume.

Cut and fill questions

What is the average end area method?

It finds the earth volume between two cross sections by averaging their areas and multiplying by the distance between them. Sections of 40 and 60 sq ft that are 50 ft apart hold (40 + 60) ÷ 2 × 50 = 2,500 cubic feet, which is 2,500 ÷ 27 = 92.59 cubic yards.

How are cut and fill kept apart?

Each station has its own cut area and fill area, and the calculator averages each one separately. In the four-station example the cut totals 8,000 cubic feet (296.30 cubic yards) and the fill 5,750 cubic feet (212.96 cubic yards), so the net is 83.33 cubic yards of excess cut.

Does the calculator allow for swell or shrinkage?

No. The volumes are in place, as measured from the sections. Dug soil swells when loose and compacted fill shrinks, so apply the swell and shrinkage figures your question, soil report or estimate gives.

Where is this on the NASCLA exam?

Site Construction is one of the twelve subject areas on the NASCLA outline, with 15 of the 115 scored questions. The Bid Bond course works earthwork volumes, including average end area, in its Site Construction lesson.

See the NASCLA exam outline for all twelve subject areas and their question counts.