Earthwork volume by the average-end-area method
Two cross-sections bound a length of earthwork. This method estimates the volume by using the average of the two end areas across the distance between them.
What the formula is saying
Average A₁ and A₂, then multiply by length L. The method is exact when area varies linearly along the length; otherwise it is an approximation.
Read the symbols in plain language
- L
- Section spacingm
- A₁
- Area 1m²
- A₂
- Area 2m²
Sort out the units first
Use m² for each cross-sectional area and m for the spacing, giving m³. These are cross-sectional areas, not ground-plan areas.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- L · Section spacing
- 20 m
- A₁ · Area 1
- 10 m²
- A₂ · Area 2
- 14 m²
Average the end areas
Add both areas and divide by two, because there are two sections.
((10) + (14)) ÷ 2 = 12 m²Extend the average area along the spacing
Area times length becomes a volume.
(12) × (20) = 240 m³
Does this worked answer make sense?
Equal end areas A should reduce to V = AL. Here the mean 12 m² over 20 m gives 240 m³.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- L · Section spacing
- 15 m
- A₁ · Area 1
- 8 m²
- A₂ · Area 2
- 12 m²
Find: Earthwork volume by the average-end-area method
A hint, not the answer
Average A₁ and A₂, then multiply by length L. The method is exact when area varies linearly along the length; otherwise it is an approximation.
Use m² for each cross-sectional area and m for the spacing, giving m³. These are cross-sectional areas, not ground-plan areas.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Average the end areas
Add both areas and divide by two, because there are two sections.
((8) + (12)) ÷ 2 = 10 m²Extend the average area along the spacing
Area times length becomes a volume.
(10) × (15) = 150 m³
Avoid the common trap
Do not average a cut area and a fill area as if they were the same material quantity. Split at transitions and calculate cut and fill separately.
When this method applies — and when it does not
Geometric in-place volume estimate. No shrinkage, swell, compaction allowance or contractual measurement rule is included.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.