How to use the Earthwork Volume Calculator
- 1. Choose the inputCentre-line depths of level sections, or cross-section areas.
- 2. Enter valuesList them in order with the distance between sections, width and side slope.
- 3. Compare volumesPrismoidal and trapezoidal volumes, the difference and each area.
Formulas
For a level section with formation width b, side slope s : 1 and depth h, the area is A = (b + s·h)·h.
- Trapezoidal (average end area): V = d [(A1 + An)/2 + A2 + A3 + … + A(n−1)]
- Prismoidal (Simpson's): V = d/3 [A1 + An + 4(A2 + A4 + …) + 2(A3 + A5 + …)]
The prismoidal formula needs an odd number of sections. With an even number, the tool applies it to all but the last strip and adds that strip by the trapezoidal rule.
Worked example and exam tips
Depths of 2.0, 2.5, 3.0, 2.8 and 2.2 m at 30 m intervals, b = 10 m, s = 1.5. Areas: 26, 34.38, 43.5, 39.76 and 29.26 m². Trapezoidal V = 30 × (27.63 + 117.64) = 4358 m³. Prismoidal V = 10 × (55.26 + 4 × 74.14 + 2 × 43.5) = 4388 m³.
- Keep cutting and filling separate.
- The difference between the two methods is the prismoidal correction.
- Check the number of sections before using Simpson's rule.
Frequently asked questions
Which formula is more accurate?
The prismoidal formula is exact for sections that vary as a quadratic along the length, and is usually closer to the true volume.
What if the ground has a cross slope?
Work out the area of each section separately (for example with the two-level section formula) and enter the areas.
Can I mix cutting and filling?
Enter them as two separate runs. Negative values are not accepted.
Is this calculator free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form. Everything is calculated in your browser.