Ditches, swales, retaining walls, troughs and many concrete foundations have trapezoidal cross-sections. Their volume tells you how much soil to dig or concrete to order.
How to use the Trapezoidal Prism Volume Calculator
- Long base B
- Short base b
- Trapezoid height h
- Length ℓ
Results update as you type, and everything is calculated in your browser.
How it works
Enter the long base B, the short base b, the height h of the trapezoid and the length ℓ.
Inputs explained
| Field | What to enter |
|---|---|
| Long base B | Units: cm, m, mm, in, ft, yd … |
| Short base b | Units: cm, m, mm, in, ft, yd … |
| Trapezoid height h | Units: cm, m, mm, in, ft, yd … |
| Length ℓ | Units: cm, m, mm, in, ft, yd … |
What each result means
- Volume = ([Long base B] + [Short base b])÷2×[Trapezoid height h]×[Length ℓ]
- Cross-section area = ([Long base B] + [Short base b])÷2×[Trapezoid height h]
Example values
How the main result changes when Long base B changes and everything else stays at the example values above:
| Long base B (cm) | Volume (cm³) |
|---|---|
| 5 | 440 |
| 7.5 | 540 |
| 10 | 640 |
| 12.5 | 740 |
| 15 | 840 |
| 20 | 1,040 |
Formula
V = (B + b)/2 · h · ℓ
Worked example
Inputs — Long base B: 10 cm; Short base b: 6 cm; Trapezoid height h: 4 cm; Length ℓ: 20 cm.
Results — Volume = 640 cm³; Cross-section area = 32 cm².
Key terms
- Cross-section
- The shape you get by slicing the solid.
Frequently asked questions
How much soil is in a trench 1 m deep, 2 m wide at the top, 1 m at the bottom and 10 m long?
(2 + 1)/2 × 1 × 10 = 15 m³.
Does it matter which base is on top?
No.
How do I convert m³ to litres?
Multiply by 1,000 – or change the unit menu.
Is a trapezoidal prism a frustum?
No – a frustum tapers in both directions.